From 886c19540adf8590b22ddad07413dd5d91aa79c1 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Wed, 17 Apr 2019 19:38:46 +0200 Subject: [PATCH 01/36] planar_arrangement_1 documented --- src/arrangement/planar_arrangement.jl | 164 ++++++++++++++++++++++++-- 1 file changed, 152 insertions(+), 12 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index ddcf7790..a3dd0d7a 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -1,6 +1,10 @@ using LinearAlgebraicRepresentation Lar = LinearAlgebraicRepresentation + +""" + frag_edge_channel(in_chan, out_chan, V, EV, bigPI) +""" function frag_edge_channel(in_chan, out_chan, V, EV, bigPI) run_loop = true while run_loop @@ -13,6 +17,38 @@ function frag_edge_channel(in_chan, out_chan, V, EV, bigPI) end end + +""" + frag_edge(V, EV, edge_idx, bigPI) + +This... + +# Examples +``` +julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0; 1.0 1.0]; # By Rows! + +julia> EV = [[1, 2], [2, 5], [3, 4], [4, 5]]; + +julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); + +julia> bigPI = Lar.spaceindex((convert(Lar.Points, V'), EV)); + +julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[1] +5×2 Array{Float64,2}: + 1.0 0.0 + 0.0 1.0 + 1.0 0.0 + 0.25 0.75 + 0.0 1.0 + +julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[2] +2×5 SparseMatrixCSC{Int8,Int64} with 4 stored entries: + [1, 1] = 1 + [2, 2] = 1 + [1, 4] = 1 + [2, 4] = 1 +``` +""" function frag_edge(V::Lar.Points, EV::Lar.ChainOp, edge_idx::Int, bigPI) alphas = Dict{Float64, Int}() edge = EV[edge_idx, :] @@ -39,6 +75,10 @@ function frag_edge(V::Lar.Points, EV::Lar.ChainOp, edge_idx::Int, bigPI) return verts, ev end + +""" + intersect_edges(V, edge1, edge2) +""" function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell) err = 10e-8 @@ -83,6 +123,10 @@ function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell) return ret end + +""" + merge_vertices!(V, EV, edge_map, err=1e-4) +""" function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map, err=1e-4) vertsnum = size(V, 1) edgenum = size(EV, 1) @@ -144,6 +188,10 @@ function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map, err=1e-4) return Lar.Points(nV), nEV end + +""" + biconnected_components(EV) +""" function biconnected_components(EV::Lar.ChainOp) ps = Array{Tuple{Int, Int, Int}, 1}() es = Array{Tuple{Int, Int}, 1}() @@ -240,6 +288,10 @@ function biconnected_components(EV::Lar.ChainOp) return bicon_comps end + +""" + get_external_cycle(V, EV, FE) +""" function get_external_cycle(V::Lar.Points, EV::Lar.ChainOp, FE::Lar.ChainOp) FV = abs.(FE)*EV vs = sparsevec(mapslices(sum, abs.(EV), dims=1)').nzind @@ -272,6 +324,11 @@ function get_external_cycle(V::Lar.Points, EV::Lar.ChainOp, FE::Lar.ChainOp) end end end + + +""" + pre_containment_test(bboxes) +""" function pre_containment_test(bboxes) n = length(bboxes) containment_graph = spzeros(Int8, n, n) @@ -286,6 +343,11 @@ function pre_containment_test(bboxes) return containment_graph end + + +""" + prune_containment_graph(n, V, EVs, shells, graph) +""" function prune_containment_graph(n, V, EVs, shells, graph) for i in 1:n @@ -309,6 +371,11 @@ function prune_containment_graph(n, V, EVs, shells, graph) end return graph end + + +""" + transitive_reduction!(graph) +""" function transitive_reduction!(graph) n = size(graph, 1) for j in 1:n @@ -324,6 +391,10 @@ function transitive_reduction!(graph) end end + +""" + cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) +""" function cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) function bboxes(V::Lar.Points, indexes::Lar.ChainOp) boxes = Array{Tuple{Any, Any}}(undef, indexes.n) @@ -380,6 +451,9 @@ function cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bb end +""" + componentgraph(V, copEV, bicon_comps) +""" function componentgraph(V, copEV, bicon_comps) # arrangement of isolated components @@ -426,6 +500,9 @@ function componentgraph(V, copEV, bicon_comps) end +""" + cleandecomposition(V, copEV, sigma) +""" function cleandecomposition(V, copEV, sigma) # Deletes edges outside sigma area todel = [] @@ -489,18 +566,81 @@ function cleandecomposition(V, copEV, sigma) end - +#-------------------------------------------------------------------------------------------------------------------------------- +# MAIN PIPELINE +#-------------------------------------------------------------------------------------------------------------------------------- + """ - function planar_arrangement_1( V::Lar.Points, copEV::Lar.ChainOp, - sigma::Lar.Chain=spzeros(Int8, 0), - return_edge_map::Bool=false, - multiproc::Bool=false) + function planar_arrangement_1(V, copEV[, sigma[, return_edge_map[, multiproc]]]) -Compute the arrangement on the given cellular complex 1-skeleton in 2D. -First part of arrangement's algorithmic pipeline. +First part of arrangement's algorithmic pipeline. + +This function computes the pairwise intersection between each edge of a given 2D cellular complex 1-skeleton. +The computation is speeded up via the evaluation of the Spatial Index. See [`Lar.spaceindex`](@ref). + +See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. + +--- + +# WARNING +This structure expects the vector points organised by rows! + +--- + +# Arguments + - `V::Lar.Points`: Vertices of the complex. + - `copEV::Lar.ChainOp`: Chain Coboundary of the edge vector. + +## Additional Arguments + - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. (*by defaults* = empty cell, no boundary) ### TO BE IMPLEMENTED + - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to the corresponding output ones (*by default* = false) ### TO BE IMPLEMENTED + - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential) + +## Return + - `V::Lar.Poins`: Vertices of the new complex. + - `copEV::Lar.ChainOp`: Chain Coboundary of the new edge vector. +--- + +# Examples +```jldoctest +julia> using Plasm + +julia> using LinearAlgebraicRepresentation + +julia> Lar = LinearAlgebraicRepresentation; + +julia> EV = [[1, 2], [3, 4], [1, 3], [2, 4], [5, 6], [7, 8], [5, 7], [6, 8]]; + +julia> V = [ + 0.0 0.5 0.0 0.5 0.3 1.0 0.3 1.0; + 0.0 0.0 1.0 1.0 0.5 0.5 1.0 1.0 + ]; + +julia> W = convert(Lar.Points, V'); # Infering type for W = V' + +julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); + +julia> W1, copEV1 = Lar.planar_arrangement_1(W::Lar.Points, cop_EV::Lar.ChainOp) +([0.0 0.0; 0.5 0.0; … ; 1.0 0.5; 1.0 1.0], + [1 , 1] = 1 + [4 , 1] = 1 + [1 , 2] = 1 + ⋮ + [11, 8] = 1 + [9 , 9] = 1 + [11, 9] = 1) + +julia> EV1 = Lar.cop2lar(copEV1); + +julia> V1 = convert(Lar.Points, W1'); + +julia> Plasm.view(Plasm.numbering(0.1)((V,[[[k] for k=1:size(V,2)], EV]))); + +julia> Plasm.view(Plasm.numbering(0.1)((V1,[[[k] for k=1:size(V1,2)], EV1]))); +``` """ -function planar_arrangement_1( V, copEV, +function planar_arrangement_1(V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain=spzeros(Int8, 0), return_edge_map::Bool=false, multiproc::Bool=false) @@ -558,8 +698,9 @@ function planar_arrangement_1( V, copEV, V, copEV = rV, rEV V, copEV = Lar.Arrangement.merge_vertices!(V, copEV, edge_map) return V, copEV -end - +end + + """ function planar_arrangement_2(V, copEV, bicon_comps, sigma::Lar.Chain=spzeros(Int8, 0), @@ -597,7 +738,6 @@ function planar_arrangement_2(V, copEV, bicon_comps, end - """ planar_arrangement(V::Points, copEV::ChainOp, [sigma::Chain], [return_edge_map::Bool], [multiproc::Bool]) @@ -627,4 +767,4 @@ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, # 2-complex and containment graph V, copEV, copFE = Lar.planar_arrangement_2(V, copEV, bicon_comps) return V, copEV, copFE -end +end \ No newline at end of file From c7a10a12a190211be05fb7104aafa4de2e6a67ec Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Thu, 18 Apr 2019 16:26:00 +0200 Subject: [PATCH 02/36] frag_edge documented --- src/arrangement/planar_arrangement.jl | 72 +++++++++++++++++++++------ 1 file changed, 56 insertions(+), 16 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index a3dd0d7a..618bfda7 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -2,6 +2,10 @@ using LinearAlgebraicRepresentation Lar = LinearAlgebraicRepresentation +#-------------------------------------------------------------------------------------------------------------------------------- +# PIPELINE PART 1 +#-------------------------------------------------------------------------------------------------------------------------------- + """ frag_edge_channel(in_chan, out_chan, V, EV, bigPI) """ @@ -21,7 +25,30 @@ end """ frag_edge(V, EV, edge_idx, bigPI) -This... +Splits the `edge_idx`-th edge in `EV`. + +This method splits the `edge_idx`-th edge in `EV` into several parts by confronting it +with the others that intersect its bounding box (see also [`Lar.Arrangement.intersect_edges`](@ref)). + +The method returns a set of the new vertices that the segment is made of (with redundancies) and +the associated cochain (with no redundancies). + +See also: [`Lar.Arrangement.planar_arrangement_1`](@ref) + +--- + +# WARNING +This structure expects the vector points organised by rows! + +--- + +# Arguments + - `V::Lar.Points`: Vertices of the whole complex. + - `copEV::Lar.ChainOp`: Chain Coboundary of the whole edge vector. + - `edge_idx::Int`: Intersecting edge index. + - `bigPI::Array{Array{Int64,1},1}`: Bounding box of the complex (see also [`Lar.spaceindex`](@ref)). + +--- # Examples ``` @@ -33,7 +60,7 @@ julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); julia> bigPI = Lar.spaceindex((convert(Lar.Points, V'), EV)); -julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[1] +julia> Lar.Arrangement.frag_edge(V, cop_EV, 1, bigPI)[1] 5×2 Array{Float64,2}: 1.0 0.0 0.0 1.0 @@ -41,7 +68,7 @@ julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[1] 0.25 0.75 0.0 1.0 -julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[2] +julia> Lar.Arrangement.frag_edge(V, cop_EV, 1, bigPI)[2] 2×5 SparseMatrixCSC{Int8,Int64} with 4 stored entries: [1, 1] = 1 [2, 2] = 1 @@ -49,14 +76,13 @@ julia> Lar.Arrangement.frag_edge(V, copEV, 1, bigPI)[2] [2, 4] = 1 ``` """ -function frag_edge(V::Lar.Points, EV::Lar.ChainOp, edge_idx::Int, bigPI) +function frag_edge(V::Lar.Points, EV::Lar.ChainOp, edge_idx::Int, bigPI::Array{Array{Int64,1},1})::Tuple{Lar.Points, Lar.ChainOp} alphas = Dict{Float64, Int}() edge = EV[edge_idx, :] verts = V[edge.nzind, :] for i in bigPI[edge_idx] - if i != edge_idx - intersection = Lar.Arrangement.intersect_edges( - V, edge, EV[i, :]) + if i != edge_idx && edge_idx in bigPI[i] #<------------------------- Could be usefull? + intersection = Lar.Arrangement.intersect_edges(V, edge, EV[i, :]) for (point, alpha) in intersection verts = [verts; point] alphas[alpha] = size(verts, 1) @@ -189,6 +215,11 @@ function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map, err=1e-4) end + +#-------------------------------------------------------------------------------------------------------------------------------- +# PIPELINE BICONNECTED COMPONENTS +#-------------------------------------------------------------------------------------------------------------------------------- + """ biconnected_components(EV) """ @@ -289,6 +320,11 @@ function biconnected_components(EV::Lar.ChainOp) end + +#-------------------------------------------------------------------------------------------------------------------------------- +# PIPELINE PART 2 +#-------------------------------------------------------------------------------------------------------------------------------- + """ get_external_cycle(V, EV, FE) """ @@ -404,7 +440,7 @@ function cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bb end boxes end - # initiolization + # initialization sums = Array{Tuple{Int, Int, Int}}(undef, 0); # assembling child components with father components for father in 1:n @@ -592,8 +628,10 @@ This structure expects the vector points organised by rows! - `copEV::Lar.ChainOp`: Chain Coboundary of the edge vector. ## Additional Arguments - - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. (*by defaults* = empty cell, no boundary) ### TO BE IMPLEMENTED - - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to the corresponding output ones (*by default* = false) ### TO BE IMPLEMENTED + - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. + (*by defaults* = empty cell, no boundary) ### TO BE IMPLEMENTED + - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to + the corresponding output ones (*by default* = false) ### TO BE IMPLEMENTED - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential) ## Return @@ -723,7 +761,7 @@ function planar_arrangement_2(V, copEV, bicon_comps, @show containment_graph # only in the context of 3D arrangement if sigma.n > 0 - todel, V, copEV = cleandecomposition(V, copEV, sigma) + todel, V, copEV = Lar.Arrangement.cleandecomposition(V, copEV, sigma) V, copEV = Lar.delete_edges(todel, V, copEV) end # final shell poset aggregation and FE output @@ -751,8 +789,10 @@ The basic method of the function without the `sigma`, `return_edge_map` and `mul returns the full arranged complex `V`, `EV` and `FE`. ## Additional arguments: -- `sigma::Chain`: if specified, `planar_arrangement` will delete from the output every edge and face outside this cell. Defaults to an empty cell. -- `return_edge_map::Bool`: makes the function return also an `edge_map` which maps the edges of the imput to the one of the output. Defaults to `false`. +- `sigma::Chain`: if specified, `planar_arrangement` will delete from the output every edge and face outside this cell. + Defaults to an empty cell. +- `return_edge_map::Bool`: makes the function return also an `edge_map` which maps the edges of the imput to the one of the output. + Defaults to `false`. - `multiproc::Bool`: Runs the computation in parallel mode. Defaults to `false`. """ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, @@ -761,10 +801,10 @@ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, multiproc::Bool=false) # edge subdivision - V, copEV = Lar.planar_arrangement_1(V::Lar.Points, copEV::Lar.ChainOp) + V, copEV = Lar.Arrangement.planar_arrangement_1(V::Lar.Points, copEV::Lar.ChainOp) # biconnected components - bicon_comps = Lar.Arrangement.biconnected_components(copEV) + bicon_comps = Lar.Arrangement.biconnected_components(copEV::Lar.ChainOp) # 2-complex and containment graph - V, copEV, copFE = Lar.planar_arrangement_2(V, copEV, bicon_comps) + V, copEV, copFE = Lar.Arrangement.planar_arrangement_2(V::Lar.Points, copEV::Lar.ChainOp, bicon_comps) return V, copEV, copFE end \ No newline at end of file From 80bc694d97af7d6aceb6494de045c1b232d8d8d5 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 11:37:47 +0200 Subject: [PATCH 03/36] frag_edge_channel and intersect_edges Documented --- src/arrangement/planar_arrangement.jl | 95 ++++++++++++++++++++++++--- 1 file changed, 87 insertions(+), 8 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 618bfda7..0e8a0615 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -8,8 +8,36 @@ Lar = LinearAlgebraicRepresentation """ frag_edge_channel(in_chan, out_chan, V, EV, bigPI) + +Utility function for parallel edge fragmentation. + +This function handles the edge fragmentation in the first part of arrangement's algorithmic pipeline +(see also [`Lar.Arrangement.planar_arrangement_1`](@ref)) during multiprocessing computation. +In order to do so it needs two `Distributed.RemoteChannel`s, one with the inputs and one for outputs. + +See also: [`Lar.Arrangement.frag_edge`](@ref) + +--- + +# WARNING +This structure expects the vector points organised by rows! + +--- + +# Arguments + - `in_chan::Distributed.RemoteChannel{Channel{Int64}}`: an input channel made of the edges indices to be intersected; + the channel must also hold at the end an EoW (`-1`) indicator for each worker thread in use. + - `out_chan::Distributed.RemoteChannel{Channel{Int64}}`: a ready-to-use output channel. + - `V::Lar.Points`: Vertices of the whole complex. + - `copEV::Lar.ChainOp`: Chain Coboundary of the whole edge vector. + - `bigPI::Array{Array{Int64,1},1}`: Bounding box of the complex (see also [`Lar.spaceindex`](@ref)). + """ -function frag_edge_channel(in_chan, out_chan, V, EV, bigPI) +function frag_edge_channel( in_chan::Distributed.RemoteChannel{Channel{Int64}}, + out_chan::Distributed.RemoteChannel{Channel{Tuple}}, + V::Lar.Points, + EV::Lar.ChainOp, + bigPI::Array{Array{Int64,1},1}) run_loop = true while run_loop edgenum = take!(in_chan) @@ -33,7 +61,9 @@ with the others that intersect its bounding box (see also [`Lar.Arrangement.inte The method returns a set of the new vertices that the segment is made of (with redundancies) and the associated cochain (with no redundancies). -See also: [`Lar.Arrangement.planar_arrangement_1`](@ref) +See also: + - [`Lar.Arrangement.planar_arrangement_1`](@ref) + - [`Lar.Arrangement.frag_edge_channel`](@ref) --- @@ -51,7 +81,7 @@ This structure expects the vector points organised by rows! --- # Examples -``` +```jldoctest julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0; 1.0 1.0]; # By Rows! julia> EV = [[1, 2], [2, 5], [3, 4], [4, 5]]; @@ -104,6 +134,55 @@ end """ intersect_edges(V, edge1, edge2) + +Finds the intersection point (if there exists) between the two given edges. + +This method compute the points where `edge2` intersect `edge1`. +If they are collinear only the vertices of `edge2` are considered (see the second example). + +See also: [`Lar.Arrangement.frag_edge`](@ref) + +--- + +# WARNING +This structure expects the vector points organised by rows! +The Error tollerance is set to 10e-8. + +--- + +# Arguments + - `V::Lar.Points`: Vertices of the whole complex. + - `edge1::Lar.Cell`: The edge to be intersected. + - `edge2::Lar.Cell`: The intersecting edge. + +# Examples +```jldoctest +julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0]; + +julia> EV = [[1, 2], [3, 4]]; + +julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); + +julia> Lar.Arrangement.intersect_edges(V, cop_EV[1, :], cop_EV[2, :]) +1-element Array{Tuple{Array{T,2} where T,Float64},1}: + ([0.25 0.75], 0.75) +``` + +```jldoctest +julia> V = [1.0 0.0; 0.0 1.0; 0.75 0.25; 0.5 0.5]; + +julia> EV = [[1, 2], [3, 4]]; + +julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); + +julia> Lar.Arrangement.intersect_edges(V, cop_EV[1, :], cop_EV[2, :]) +2-element Array{Tuple{Array{T,2} where T,Float64},1}: + ([0.75 0.25], 0.25) + ([0.5 0.5], 0.5) + +julia> Lar.Arrangement.intersect_edges(V, cop_EV[2, :], cop_EV[1, :]) +0-element Array{Tuple{Array{T,2} where T,Float64},1} +``` """ function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell) err = 10e-8 @@ -116,20 +195,20 @@ function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell) v2 = [x4-x3, y4-y3]; v3 = [x3-x1, y3-y1]; - ang1 = dot(normalize(v1), normalize(v2)) - ang2 = dot(normalize(v1), normalize(v3)) + ang1 = Lar.dot(Lar.normalize(v1), Lar.normalize(v2)) + ang2 = Lar.dot(Lar.normalize(v1), Lar.normalize(v3)) parallel = 1-err < abs(ang1) < 1+err - colinear = parallel && (1-err < abs(ang2) < 1+err || -err < norm(v3) < err) + colinear = parallel && (1-err < abs(ang2) < 1+err || -err < Lar.norm(v3) < err) if colinear o = [x1 y1] v = [x2 y2] - o - alpha = 1/dot(v,v') + alpha = 1/Lar.dot(v,v') ps = [x3 y3; x4 y4] for i in 1:2 - a = alpha*dot(v',(reshape(ps[i, :], 1, 2)-o)) + a = alpha*Lar.dot(v',(reshape(ps[i, :], 1, 2)-o)) if 0 < a < 1 push!(ret, (ps[i:i, :], a)) end From 3b2606d6c720620ecc49543a724137cfb2ed6c09 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 12:36:17 +0200 Subject: [PATCH 04/36] PIPELINE PART 1 Documented --- src/arrangement/planar_arrangement.jl | 79 +++++++++++++++++++++++---- 1 file changed, 68 insertions(+), 11 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 0e8a0615..f2b3db45 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -42,7 +42,7 @@ function frag_edge_channel( in_chan::Distributed.RemoteChannel{Channel{Int64}}, while run_loop edgenum = take!(in_chan) if edgenum != -1 - put!(out_chan, (edgenum, frag_edge(V, EV, edgenum, bigPI))) + put!(out_chan, (edgenum, Lar.Arrangement.frag_edge(V, EV, edgenum, bigPI))) else run_loop = false end @@ -157,7 +157,7 @@ The Error tollerance is set to 10e-8. # Examples ```jldoctest -julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0]; +julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0]; # By Rows! julia> EV = [[1, 2], [3, 4]]; @@ -169,7 +169,7 @@ julia> Lar.Arrangement.intersect_edges(V, cop_EV[1, :], cop_EV[2, :]) ``` ```jldoctest -julia> V = [1.0 0.0; 0.0 1.0; 0.75 0.25; 0.5 0.5]; +julia> V = [1.0 0.0; 0.0 1.0; 0.75 0.25; 0.5 0.5]; # By Rows! julia> EV = [[1, 2], [3, 4]]; @@ -230,9 +230,63 @@ end """ - merge_vertices!(V, EV, edge_map, err=1e-4) + merge_vertices!(V, EV[, edge_map[, err]]) + +Compact the vertices closer than `err` in a single one. + +This method check one at time each vertex `v` in `V` and identifies each other vertex within `err` with `v` itself. +The cochain `EV` is coherently modified (multiple edges between two vertices are not allowed). +If an `edge_map` is given in input (this could be usefull during the planar arrangements), then also +the map is coherently modified and given back in output. + +See also: [`Lar.Arrangement.planar_arrangement_1`](@ref) + +--- + +# WARNING +This structure expects the vector points organised by rows! + +--- + +# Arguments + - `V::Lar.Points`: Vertices of the complex. + - `EV::Lar.ChainOp`: Chain Coboundary of the edge vector. + +## Additional Arguments + - `edge_map::Array{Array{Int64,1},1}`: Mapping from a set of edges to the edges of the given cochain. + If it is given than it will also be rearranged coherently with the vertices merging (*by default* = [[-1]]). + - `err::Float64`: Range of the vertex identification (*by default* = 1e-4). + +## Return + - `V::Lar.Points`: Merged Vertices. + - `EV::Lar.ChainOp`: Merged Cochain of the merged vertices. + - `edge_map::Array{Array{Int64,1},1}`: the merged cochain `edge_map` (if given in input). + +--- + +# Examples +```jldoctest +julia> V = [0.5 0.5; 0.0 0.0; 0.5 0.5; 1.0 1.0; 0.5 0.5; 1.0 1.0]; # By Rows! + +julia> EV = [[1, 4], [3, 2], [5, 6], [1, 6], [5, 3]]; + +julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); + +julia> Lar.Arrangement.merge_vertices!(V, cop_EV)[1] +3×2 Array{Float64,2}: + 0.5 0.5 + 0.0 0.0 + 1.0 1.0 + +julia> Lar.Arrangement.merge_vertices!(V, cop_EV)[2] +2×3 SparseArrays.SparseMatrixCSC{Int8,Int64} with 4 stored entries: + [1, 1] = 1 + [2, 1] = 1 + [2, 2] = 1 + [1, 3] = 1 +``` """ -function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map, err=1e-4) +function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map::Array{Array{Int64,1},1}=[[-1]], err=1e-4) vertsnum = size(V, 1) edgenum = size(EV, 1) newverts = zeros(Int, vertsnum) @@ -281,12 +335,15 @@ function merge_vertices!(V::Lar.Points, EV::Lar.ChainOp, edge_map, err=1e-4) etuple2idx[nedges[ei]] = ei end - for i in 1:length(edge_map) - row = edge_map[i] - row = map(x->edges[x], row) - row = filter(t->t[1]!=t[2], row) - row = map(x->etuple2idx[x], row) - edge_map[i] = row + if edge_map != [[-1]] + for i in 1:length(edge_map) + row = edge_map[i] + row = map(x->edges[x], row) + row = filter(t->t[1]!=t[2], row) + row = map(x->etuple2idx[x], row) + edge_map[i] = row + end + return Lar.Points(nV), nEV, edge_map end From 76941af480aa9684e2c184b0327bd92cb22960ae Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Fri, 19 Apr 2019 15:22:02 +0200 Subject: [PATCH 05/36] [CISkip] Update readme --- README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index b19e81aa..b7ce53ee 100644 --- a/README.md +++ b/README.md @@ -24,9 +24,13 @@ add("LinearAlgebraicRepresentation") ## Documentation -Go to [the documentation page](https://cvdlab.github.io/LinearAlgebraicRepresentation.jl/) +BUilding EOnofri julia-1.0 [![Build Status](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl.svg?branch=master)](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl) +Go to [the documentation page](https://eonofri04.github.io/LinearAlgebraicRepresentation.jl/) + + ## Authors * [Giulio Martella](https://github.com/giuliom95) * [Alberto Paoluzzi](https://github.com/apaoluzzi) * [Francesco Furiani](https://github.com/furio) + From 126a2c297746389b91d11cf6e691d9e57fccc4c5 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 16:29:39 +0200 Subject: [PATCH 06/36] adding Tests for Planar_arrangement_1 Pipeline --- src/arrangement/planar_arrangement.jl | 6 ++- test/refactor_planar_arrangement.jl | 64 +++++++++++++++++++++++++++ test/runtests.jl | 3 +- 3 files changed, 71 insertions(+), 2 deletions(-) create mode 100644 test/refactor_planar_arrangement.jl diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index f2b3db45..c56df3aa 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -767,7 +767,7 @@ This structure expects the vector points organised by rows! - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. (*by defaults* = empty cell, no boundary) ### TO BE IMPLEMENTED - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to - the corresponding output ones (*by default* = false) ### TO BE IMPLEMENTED + the corresponding output ones (*by default* = false) - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential) ## Return @@ -870,6 +870,10 @@ function planar_arrangement_1(V::Lar.Points, copEV::Lar.ChainOp, end # merging of close vertices and edges (2D congruence) V, copEV = rV, rEV + if return_edge_map + V, copEV, edge_map = Lar.Arrangement.merge_vertices!(V, copEV, edge_map) + return V, copEV, edge_map + end V, copEV = Lar.Arrangement.merge_vertices!(V, copEV, edge_map) return V, copEV end diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl new file mode 100644 index 00000000..26acc425 --- /dev/null +++ b/test/refactor_planar_arrangement.jl @@ -0,0 +1,64 @@ +using Test +using SparseArrays +using LinearAlgebra +using LinearAlgebraicRepresentation +using LinearAlgebraicRepresentation.Arrangement +Lar = LinearAlgebraicRepresentation +Lara = LinearAlgebraicRepresentation.Arrangement + +@testset "Pipeline Arrangement 1" begin + V = [0.0 1.0; 1.0 1.0; 3.0 1.0; 4.0 1.0; 2.0 2.0; 2.0 0.0]; + EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 0 1 0 0] #1->1,4 + [0 1 1 0 0 0] #2->2,3 + [0 0 0 0 1 1] #3->5,6 + [0 1 0 0 1 0] #4->2,5 + [0 0 1 0 0 1] #5->3,6 + ])) + bigPI = Lar.spaceindex((convert(Lar.Points, V'), Lar.cop2lar(copEV))); + + @testset "intersect_edges" begin + @test Lara.intersect_edges(V, EV[1, :], EV[3, :]) == [([2.0 1.0], 0.5)]; + @test Lara.intersect_edges(V, EV[1, :], EV[3, :]) == Lara.intersect_edges(V, EV[2, :], EV[3, :]) + @test Lara.intersect_edges(V, EV[1, :], EV[2, :]) == [([1.0 1.0], 0.25); ([3.0 1.0], 0.75)]; + @test Lara.intersect_edges(V, EV[2, :], EV[1, :]) == Lara.intersect_edges(V, EV[4, :], EV[5, :]); + @test Lara.intersect_edges(V, EV[1, :], EV[4, :]) == [([1.0 1.0], 0.25)]; + @test Lara.intersect_edges(V, EV[2, :], EV[4, :]) == [([1.0 1.0], 0.0)]; + + end + + @testset "merge_vertices" begin + V1, EV1 = Lara.frag_edge(V, EV, 1, bigPI); + ans1 = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 1 0 0] #1->1,3 + [0 0 1 0 1] #2->3,5 + [0 0 0 1 1] #3->4,5 + [0 1 0 1 0] #4->2,4 + ])); + ans2 = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 1] #1->1,3 + [0 1 1] #2->2,3 + ])); + @test Lara.merge_vertices!(V1, EV1)[1] == [0.0 1.0; 4.0 1.0; 1.0 1.0; 3.0 1.0; 2.0 1.0]; + @test Lara.merge_vertices!(V1, EV1)[2] == ans1; + + @test Lara.merge_vertices!(V1, EV1, [[-1]], 1)[1] == [0.0 1.0; 4.0 1.0; 2.0 1.0]; + @test Lara.merge_vertices!(V1, EV1, [[-1]], 1)[2] == ans2; + end + + @testset "Complete Pipeline 1" begin + Vans = [0.0 1.0; 4.0 1.0; 1.0 1.0; 3.0 1.0; 2.0 1.0; 2.0 2.0; 2.0 0.0]; + EVans = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 1 0 0 0 0] # 1->3 + [0 0 1 0 1 0 0] # 3->4 + [0 0 0 1 1 0 0] # 4->5 + [0 1 0 1 0 0 0] # 2->4 + [0 0 0 0 1 1 0] # 5->6 + [0 0 0 0 1 0 1] # 5->7 + [0 0 1 0 0 1 0] # 3->6 + [0 0 0 1 0 0 1] # 4->7 + ])); + @test Lara.planar_arrangement_1(V, EV)[1] == Vans + @test Lara.planar_arrangement_1(V, EV)[2] == EVans + end +end \ No newline at end of file diff --git a/test/runtests.jl b/test/runtests.jl index 4cb0243a..d18732d4 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -2,7 +2,8 @@ #Lar = LinearAlgebraicRepresentation include("./utilities.jl") -include("./planar_arrangement.jl") +#include("./planar_arrangement.jl") +include("./refactor_planar_arrangement.jl") include("./dimension_travel.jl") include("./largrid.jl") From aba60fdf3cad4692fe13d26e0129b394ae95c7ab Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 16:36:01 +0200 Subject: [PATCH 07/36] Fixing notational error in test --- test/refactor_planar_arrangement.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index 26acc425..48caa1ff 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -15,7 +15,7 @@ Lara = LinearAlgebraicRepresentation.Arrangement [0 1 0 0 1 0] #4->2,5 [0 0 1 0 0 1] #5->3,6 ])) - bigPI = Lar.spaceindex((convert(Lar.Points, V'), Lar.cop2lar(copEV))); + bigPI = Lar.spaceindex((convert(Lar.Points, V'), Lar.cop2lar(EV))); @testset "intersect_edges" begin @test Lara.intersect_edges(V, EV[1, :], EV[3, :]) == [([2.0 1.0], 0.5)]; From 2b9d968a82e6c082028fea90f54ea0382771cf94 Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Fri, 19 Apr 2019 16:50:29 +0200 Subject: [PATCH 08/36] Update .travis.yml --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index b23ad684..98fd0b72 100644 --- a/.travis.yml +++ b/.travis.yml @@ -32,4 +32,4 @@ deploy: keep-history: true local-dir: docs/build on: - branch: master + branch: julia-1.0 From 26f90d0deb7562560c5ac4cbb1c18bce30f81b41 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 20:42:09 +0200 Subject: [PATCH 09/36] moving documentation from function to Docs --- .travis.yml | 1 + docs/make.jl | 5 +- docs/src/arrangement.md | 13 +- docs/src/images/2d-arrangement-pipeline.jpg | Bin 0 -> 2870920 bytes docs/src/planar_arrangement.md | 151 ++++++++++++++++++++ src/arrangement/planar_arrangement.jl | 83 ----------- 6 files changed, 161 insertions(+), 92 deletions(-) create mode 100644 docs/src/images/2d-arrangement-pipeline.jpg create mode 100644 docs/src/planar_arrangement.md diff --git a/.travis.yml b/.travis.yml index 98fd0b72..7d6b2338 100644 --- a/.travis.yml +++ b/.travis.yml @@ -16,6 +16,7 @@ julia: matrix: allow_failures: - julia: nightly + - julia: 0.7 notifications: email: false diff --git a/docs/make.jl b/docs/make.jl index 2c0ea8ca..8d8a8830 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -12,7 +12,10 @@ makedocs( "Home" => "index.md", "L.A.R. Intro" => "lar.md", "Interface" => "interface.md", - "Arrangement" => "arrangement.md", + "Arrangement" => [ + "Arrangement module" => "arrangement.md", + "Planar arrangement" => "planar_arrangement.md" + ], "Parametric primitives" => [ "Mapper" => "mapper.md", "Assemblies" => "struct.md" diff --git a/docs/src/arrangement.md b/docs/src/arrangement.md index 528460ef..a21f415a 100644 --- a/docs/src/arrangement.md +++ b/docs/src/arrangement.md @@ -4,22 +4,19 @@ The **arrangement** is an algorithm which gets two general ``d``-dimensional cel * ``\sigma_1 \cap \sigma_2 = \emptyset,\quad \forall`` couple of cells ``(\sigma_1, \sigma_2)`` * ``\bigcup_i\sigma_i = \mathbb{E}^d`` -This operation can be seen as a boolean union of two cellular complexes. Here an exploded visualization of the final result of the arrangement algorithm ran on 2 cubes made by ``10\times10\times10`` smaller cubes. +This operation can be seen as a boolean union of two cellular complexes. Here an exploded visualization of the final result of the arrangement algorithm run on 2 cubes made by ``10\times10\times10`` smaller cubes. ![10 x 10 Cube](./images/cube10x10.jpg) > **Figure 1:** Arrangement of ``2000=2\times10\times10\times10`` cubes -## API +## Organisation -Every function strictly relative to the arrangement has been collected in the `Lar.Arrangement` sub-module but the two main functions are accessible directly from the `LinearAlgebraicRepresentation` namespace. +Every function strictly relative to the arrangement has been collected in the `Lar.Arrangement` sub-module but the two main functions are accessible directly from the `LinearAlgebraicRepresentation` namespace. They are: + - [`Lar.planar_arrangement`]() that evaluates the arrangements in 2D spaces. + - [`Lar.spatial_arrangement`]() that evaluates the arrangements in 3D spaces. !!! warning `Lar.Arrangement` is the only place in `LinearAlgebraicRepresentation` where `Point` matrices store points per row and not per column as described in the documentation of `Lar.Points` -```@docs -Lar.spatial_arrangement -Lar.planar_arrangement -``` - !!! note Even if the arrangement algorithm is theoretically dimension independent, we implemented "only" the ``d=2`` and ``d=3`` version of it. diff --git a/docs/src/images/2d-arrangement-pipeline.jpg b/docs/src/images/2d-arrangement-pipeline.jpg new file mode 100644 index 0000000000000000000000000000000000000000..8aae7cb985e15e71e27c7549486b93f4b5e5b38d GIT binary patch literal 2870920 zcmeF42UrwKy09Ao0Ywl66(tEMg5)S!M8b&VsE9}yg1`(gWQ0*r5tN(+L{u`8BnpUQ z1SRL3BnQbEhMB(ymE+lScK6)9ckkWjx0{EauBxvqbyf9SUxmhZ;J;9RQE;=i00320 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organised by rows! -The Error tollerance is set to 10e-8. - ---- - -# Arguments - - `V::Lar.Points`: Vertices of the whole complex. - - `edge1::Lar.Cell`: The edge to be intersected. - - `edge2::Lar.Cell`: The intersecting edge. - # Examples ```jldoctest julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0]; # By Rows! @@ -243,27 +203,6 @@ See also: [`Lar.Arrangement.planar_arrangement_1`](@ref) --- -# WARNING -This structure expects the vector points organised by rows! - ---- - -# Arguments - - `V::Lar.Points`: Vertices of the complex. - - `EV::Lar.ChainOp`: Chain Coboundary of the edge vector. - -## Additional Arguments - - `edge_map::Array{Array{Int64,1},1}`: Mapping from a set of edges to the edges of the given cochain. - If it is given than it will also be rearranged coherently with the vertices merging (*by default* = [[-1]]). - - `err::Float64`: Range of the vertex identification (*by default* = 1e-4). - -## Return - - `V::Lar.Points`: Merged Vertices. - - `EV::Lar.ChainOp`: Merged Cochain of the merged vertices. - - `edge_map::Array{Array{Int64,1},1}`: the merged cochain `edge_map` (if given in input). - ---- - # Examples ```jldoctest julia> V = [0.5 0.5; 0.0 0.0; 0.5 0.5; 1.0 1.0; 0.5 0.5; 1.0 1.0]; # By Rows! @@ -754,28 +693,6 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. --- -# WARNING -This structure expects the vector points organised by rows! - ---- - -# Arguments - - `V::Lar.Points`: Vertices of the complex. - - `copEV::Lar.ChainOp`: Chain Coboundary of the edge vector. - -## Additional Arguments - - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. - (*by defaults* = empty cell, no boundary) ### TO BE IMPLEMENTED - - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to - the corresponding output ones (*by default* = false) - - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential) - -## Return - - `V::Lar.Poins`: Vertices of the new complex. - - `copEV::Lar.ChainOp`: Chain Coboundary of the new edge vector. - ---- - # Examples ```jldoctest julia> using Plasm From c8a6de85ff3454fe4e0b2c77f8e52e33b6711f6c Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 21:39:44 +0200 Subject: [PATCH 10/36] Fixing Docs Errors --- docs/src/arrangement.md | 8 +++---- docs/src/planar_arrangement.md | 34 +++++++++++++++++---------- src/arrangement/planar_arrangement.jl | 2 +- src/refactoring.jl | 2 +- 4 files changed, 27 insertions(+), 19 deletions(-) diff --git a/docs/src/arrangement.md b/docs/src/arrangement.md index a21f415a..73b2205c 100644 --- a/docs/src/arrangement.md +++ b/docs/src/arrangement.md @@ -44,14 +44,14 @@ the spatial index: it is a mapping ``\mathcal{I}(\sigma)`` from a cell where the ``box`` function provides the axis aligned bounding box (AABB) of a cell [fig. 2, c, ``\sigma`` in red and ``\mathcal{I}(\sigma)`` in blue]. The spatial arrangement calculation is speeded up by storing the AABBs as dimensional wise intervals -into an interval tree \cite{interval_trees}. +into an interval tree ``\cite{interval_trees}``. Now for each cell ``\sigma`` we transform ``\sigma \cup \mathcal{I}(\sigma)`` in a way that ``\sigma`` lays on the ``x_3=0`` plane [fig. 2, d] and we find the intersections of the ``\mathcal{I}(\sigma)`` cells with ``x_3=0`` plane. So we have a "soup" of 1-cells in ``\mathbb{E}^2`` [fig. 2, e], and we fragment each 1-cell with every other cell obtaining a valid 1-skeleton [fig. 2, f]. From this data it is possible to build the 2-cells using the ALGORITHM 1 -presented and explored by Paoluzzi et al. \cite{Paoluzzi} +presented and explored by Paoluzzi et al. ``\cite{Paoluzzi}`` [fig. 2, g, exploded]. The procedure to fragment 1-cells on a plane and return a 2-complex is called *planar arrangement*. When the planar arrangement is complete, fragmented ``\sigma`` can be transformed back to its original position @@ -80,14 +80,14 @@ are to discard: the ones outside the area of ``\sigma`` and the ones which are not part of a maximal biconnected component (We can talk about biconnected components because we can consider the 1-skeleton as a graph: 0-cells are nodes, 1-cells are edges and the boundary operator is -a incidence matrix.). +a incidence matrix). The result of this edge pruning outputs a 1-skeleton [fig. 3, c, exploded]. After this, 2-cells must be computed: For each connected component we build a containment tree, which indicates which component is spatially inside an other component. -Computing these relations lets us launch the ALGORITHM 1 \cite{Paoluzzi} +Computing these relations lets us launch the ALGORITHM 1 ``\cite{Paoluzzi}`` on each component and then combine the results to create 2-cells with non-intersecting shells [fig. 3, d, 2-cells numbered in green; please note that cell 2 has cell 1 as an hole]. diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 796d4881..ea8fe312 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -8,7 +8,6 @@ Lar.planar_arrangement In general we recall the notation we have used in source code: - `V::Lar.Poins` is the 1-cells (Vertices) complex. - **NOTE** that the points are organized by rows (instead of Columns like described in `Lar.Points`). - `EV::Lar.Cells` is the 2-cells (Edges) complex. - `FV::Lar.` is the 3-cells (Faces) complex. - `copEV::Lar.ChainOp`: is the Chain Coboundary of the 2-cells. @@ -16,6 +15,9 @@ In general we recall the notation we have used in source code: - `bigPI::Array{Array{Int64,1},1}`: is the bounding box intersection array: each row is associated to a 2-cell and contains the indices of the other 2-cells intersecting its bounding box. +!!! warning + Do remember that in `planar_arrangement` (`Lar.Arrangement` module) matrices store points per row and not per column as described in the documentation of `Lar.Points`. + ## The algorithm In this section we will provide a general overview of how the `planar_arrangement` is meant to work. @@ -35,11 +37,11 @@ This part of the pipeline is covered by: Lar.Arrangement.planar_arrangement_1 ``` A small set of optional parameters could be choosen in order to personalize the computation: - - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge and face outside this cell. - (*by defaults* = empty cell, no boundary) + - `sigma::Lar.Chain`: if specified, the arrangement will delete from the output every edge outside this cell + (*by defaults* = empty cell, no boundary). - `return_edge_map::Bool`: If set to true, the function will also return an `edge_map` that maps the input edges to - the corresponding output ones - - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential) + the corresponding output ones. + - `multiproc::Bool`: If set to true, execute the arrangement in parallel (*by default* = false, sequential). @@ -63,7 +65,7 @@ if the parallel way is choosen (namely `frag_edge_channel` is used) then a few m -In order to do so, at a lower level, each pair of possible intersecting 2-cells are compared via: +In order to split the edge, at a lower level, each pair of possible intersecting 2-cells are compared via: ```@docs Lar.Arrangement.intersect_edges ``` @@ -75,15 +77,20 @@ Lar.Arrangement.merge_vertices! ``` Here also two optional parameters could be specified: - `edge_map::Array{Array{Int64,1},1}`: Mapping from a set of edges to the edges of the given cochain. - If it is given in input than a copy of it would be returned in output, with its values coherently rearranged with the vertices merging (*by default* = [[-1]]). - - `err::Float64`: Range of the vertex identification (*by default* = 1e-4). + If it is given in input than a copy of it would be returned in output, with its values coherently rearranged with the vertices merging (*by default* = ``[[-1]]``). + - `err::Float64`: Range of the vertex identification (*by default* = ``1e-4``). !!! note - Choosing a good value for `err` is a very important issue. Note that the identification is sequentially made; therefore the following situation could happend: - if three vertices are collinear and evenly spaciated, then - - if the second is identified in the third, the first and the third won't be identified; - - if the thiird is identified with the second, then the first and the second will be identified; - This situation could be seen in the secon example given by the function documentation. + Choosing a good value for `err` is a very important issue. + Note that the identification is sequentially made; + therefore the following situation could happend: + if three vertices are collinear and evenly spaciated, then + - if the second is identified in the third, + then the first and the third won't be identified; + - if the thiird is identified with the second, + then the first and the second will be identified; + + This situation could be seen in the secon example given by the function documentation. ### Biconnected Components Detection. @@ -147,5 +154,6 @@ Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) ``` ![Pipeline visualization](./images/2d-arrangement-pipeline.jpg) +> **Figure 1:** Pipeline visualization over a sample structure. diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 943300ac..d94674f8 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -194,7 +194,7 @@ end Compact the vertices closer than `err` in a single one. -This method check one at time each vertex `v` in `V` and identifies each other vertex within `err` with `v` itself. +This method check one at time each vertex ``v`` in `V` and identifies each other vertex within `err` with ``v`` itself. The cochain `EV` is coherently modified (multiple edges between two vertices are not allowed). If an `edge_map` is given in input (this could be usefull during the planar arrangements), then also the map is coherently modified and given back in output. diff --git a/src/refactoring.jl b/src/refactoring.jl index 0ed47a7b..5eda071a 100644 --- a/src/refactoring.jl +++ b/src/refactoring.jl @@ -238,7 +238,7 @@ end Generation of *space indexes* for all ``(d-1)``-dim cell members of `model`. *Spatial index* made by ``d`` *interval-trees* on -bounding boxes of ``sigma in S_{d−1}``. Spatial queries solved by +bounding boxes of ``\sigma \in S_{d−1}``. Spatial queries solved by intersection of ``d`` queries on IntervalTrees generated by bounding-boxes of geometric objects (LAR cells). From d7dd1327a7e03384deb89ff4afe227036a5fe2b1 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 19 Apr 2019 21:54:41 +0200 Subject: [PATCH 11/36] Fixing typo error --- src/refactoring.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/refactoring.jl b/src/refactoring.jl index 5eda071a..6af7e85e 100644 --- a/src/refactoring.jl +++ b/src/refactoring.jl @@ -238,7 +238,7 @@ end Generation of *space indexes* for all ``(d-1)``-dim cell members of `model`. *Spatial index* made by ``d`` *interval-trees* on -bounding boxes of ``\sigma \in S_{d−1}``. Spatial queries solved by +bounding boxes of ``σ ∈ S_{d−1}``. Spatial queries solved by intersection of ``d`` queries on IntervalTrees generated by bounding-boxes of geometric objects (LAR cells). From d1e84ac1ff04ca9335ce86b78bdf48758cfaeaeb Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Sat, 20 Apr 2019 12:26:32 +0200 Subject: [PATCH 12/36] Minor style change in Docs --- docs/src/planar_arrangement.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index ea8fe312..92eb7015 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -16,7 +16,7 @@ In general we recall the notation we have used in source code: each row is associated to a 2-cell and contains the indices of the other 2-cells intersecting its bounding box. !!! warning - Do remember that in `planar_arrangement` (`Lar.Arrangement` module) matrices store points per row and not per column as described in the documentation of `Lar.Points`. + Do remember that in `planar_arrangement` (`Lar.Arrangement` module) matrices store points per row and not per column as described in the documentation of `Lar.Points`. ## The algorithm @@ -110,7 +110,7 @@ V = [ ]; EV = [[1, 4], [2, 3], [5, 6], [2, 5], [3, 6], [7, 10], [8, 10], [9, 10]]; -## Display Data +## 1 - Input Reading Plasm.view(Plasm.numbering(0.5)((V,[[[k] for k=1:size(V,2)], EV]))); # Planar Arrangement 1 @@ -118,7 +118,7 @@ W = convert(Lar.Points, V'); # Infering type for W = V' copEV = Lar.coboundary_0(EV::Lar.Cells); W1, copEV1 = Lar.planar_arrangement_1(W::Lar.Points, copEV::Lar.ChainOp); -## Planar Arrangement 1 Displaying +## 2 - 2-cells fragmentation EV1 = Lar.cop2lar(copEV1); V1 = convert(Lar.Points, W1'); Plasm.view(Plasm.numbering(0.5)((V1,[[[k] for k=1:size(V1,2)], EV1]))); @@ -126,18 +126,18 @@ Plasm.view(Plasm.numbering(0.5)((V1,[[[k] for k=1:size(V1,2)], EV1]))); # Biconnected COmponent Evaluation bicon_comps = Lar.Arrangement.biconnected_components(copEV1); -## Displaying Biconnected Components +## 3 - Biconnected Components hpcs = [ Plasm.lar2hpc(V1,[EV1[e] for e in comp]) for comp in bicon_comps ] Plasm.view([ Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) for k = 1 : (length(hpcs)) ]) # computation of 2-cells and 2-boundary W2, copEV2, copFE2 = Lar.planar_arrangement_2(W1, copEV1, bicon_comps) -## visualization of numbered arrangement +## 4 - 3-cells identification & dangling 1-cells elimination Plasm.view( Plasm.numbering1(0.5)((W2, copEV2, copFE2)) ) -# final solid visualization +# 5 - Colorfull Representation triangulated_faces = Lar.triangulate2D(W2, [copEV2, copFE2]) V2 = convert(Lar.Points, W2') FVs2 = convert(Array{Lar.Cells}, triangulated_faces) @@ -148,7 +148,7 @@ EVs2 = Lar.FV2EVs(copEV2, copFE2) EVs2 = convert(Array{Array{Array{Int64,1},1},1}, EVs2) Plasm.viewcolor(V2::Lar.Points, EVs2::Array{Lar.Cells}) -# exploded polygons +# 6 - Exploded Representation model = V2,EVs2 Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) ``` From 609191859e73a7056c4c07f0c8ff0438be0275e9 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Sat, 20 Apr 2019 20:00:55 +0200 Subject: [PATCH 13/36] biconnected_components Docs and Tests --- docs/src/planar_arrangement.md | 16 ++++++++++ src/arrangement/planar_arrangement.jl | 45 +++++++++++++++++++++++---- test/refactor_planar_arrangement.jl | 45 +++++++++++++++++++++++++++ 3 files changed, 100 insertions(+), 6 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 92eb7015..f7d9da0a 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -70,6 +70,8 @@ In order to split the edge, at a lower level, each pair of possible intersecting Lar.Arrangement.intersect_edges ``` + + In the end, the 1-cells are identified if they are located spatially very close one to the other (_i.e_ ``\epsilon = 10^{-4}``). Of course if two 2-cells share the same endpoints then they are also identified in a unique 2-cell. ```@docs @@ -80,6 +82,8 @@ Here also two optional parameters could be specified: If it is given in input than a copy of it would be returned in output, with its values coherently rearranged with the vertices merging (*by default* = ``[[-1]]``). - `err::Float64`: Range of the vertex identification (*by default* = ``1e-4``). + + !!! note Choosing a good value for `err` is a very important issue. Note that the identification is sequentially made; @@ -92,8 +96,20 @@ Here also two optional parameters could be specified: This situation could be seen in the secon example given by the function documentation. + + ### Biconnected Components Detection. +This part of the pipeline is covered by +```@docs +Lar.Arrangement.biconnected_components +``` +As a reader can see the components are evaluated regardless the model geometrical structure; +in fact the 1-cells are not considered during the computation. This means that the abstract +graph made by the edges is the only input needed by the function. + + + ### 3-Cells Evaluation and Dangling 2-Cells Elimination. ## Examples diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index d94674f8..99c3291a 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -144,7 +144,7 @@ julia> Lar.Arrangement.intersect_edges(V, cop_EV[2, :], cop_EV[1, :]) 0-element Array{Tuple{Array{T,2} where T,Float64},1} ``` """ -function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell) +function intersect_edges(V::Lar.Points, edge1::Lar.Cell, edge2::Lar.Cell)::Array{Tuple{Lar.Points, Float64}, 1} err = 10e-8 x1, y1, x2, y2 = vcat(map(c->V[c, :], edge1.nzind)...) @@ -297,8 +297,45 @@ end """ biconnected_components(EV) + +Compute sets of 2-cells on the same 3-cells biconnected components. + +The method evaluate the 2-cells ``σ_i`` wich lies on the same 3-cells biconnected +component ``χ_j`` and gives back an array that contains an array of ``σ_i`` for each ``j``. +Do note that if the cochain EV contains more copies of the same 2-cell then +it will be considered like a 3-cell. + +Intermediate part of the Planar Arrangement Pipeline (see also [`Lar.Arrangement.planar_arrangement`](@ref)). + +# Examples +```jldoctest +julia> EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0 0] #1 -> 1,2 | + [1 0 1 0 0 0] #2 -> 1,3 | + [1 0 0 1 0 0] #3 -> 1,4 | + [1 0 0 0 1 0] #4 -> 1,5 | + [1 0 0 0 0 1] #5 -> 1,6 + [0 1 1 0 0 0] #6 -> 2,3 | + [0 0 0 1 1 0] #7 -> 4,5 | + ])); +julia> Lar.Arrangement.biconnected_components(EV) +2-element Array{Array{Int64,1},1}: + [2, 6, 1] + [4, 7, 3] +``` + +```jldoctest +julia> EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0] #1 -> 1,2 | + [1 1 0] #2 -> 1,2 | + [1 0 1] #3 -> 1,2 + ])); +julia> Lar.Arrangement.biconnected_components(EV) +1-element Array{Array{Int64,1},1}: + [2, 1] +``` """ -function biconnected_components(EV::Lar.ChainOp) +function biconnected_components(EV::Lar.ChainOp)::Array{Array{Int, 1}, 1} ps = Array{Tuple{Int, Int, Int}, 1}() es = Array{Tuple{Int, Int}, 1}() todel = Array{Int, 1}() @@ -697,10 +734,6 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. ```jldoctest julia> using Plasm -julia> using LinearAlgebraicRepresentation - -julia> Lar = LinearAlgebraicRepresentation; - julia> EV = [[1, 2], [3, 4], [1, 3], [2, 4], [5, 6], [7, 8], [5, 7], [6, 8]]; julia> V = [ diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index 48caa1ff..6faae1de 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -61,4 +61,49 @@ Lara = LinearAlgebraicRepresentation.Arrangement @test Lara.planar_arrangement_1(V, EV)[1] == Vans @test Lara.planar_arrangement_1(V, EV)[2] == EVans end +end + +@testset "Biconnected Components" begin + @testset "Normal Execution" begin + EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0 0 0 0 0 0] #1 -> 1,2 | + [0 1 1 0 0 0 0 0 0 0] #2 -> 2,3 | + [1 0 1 0 0 0 0 0 0 0] #3 -> 3,1 | + [0 0 1 1 0 0 0 0 0 0] #4 -> 3,4 | + [0 0 1 0 0 1 0 0 0 0] #5 -> 3,6 | + [0 0 1 0 0 0 1 0 0 0] #6 -> 3,7 - + [0 0 0 1 1 0 0 0 0 0] #7 -> 4,5 | + [0 0 0 0 1 1 0 0 0 0] #8 -> 5,6 | + [0 0 0 0 0 0 0 1 1 0] #9 -> 8,9 | + [0 0 0 0 0 0 0 0 1 1] #10-> 9,10 | + [0 0 0 0 0 0 0 1 0 1] #11-> 8,10 | + ])); + bicomp = sort(Lara.biconnected_components(EV)); + + @test length(Lara.biconnected_components(EV)) == 3; + @test sort(bicomp[1]) == [1, 2, 3]; + @test sort(bicomp[2]) == [4, 5, 7, 8]; + @test sort(bicomp[3]) == [9, 10, 11]; + end + + @testset "Void Components" begin + EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0] #1 -> 1,2 + [1 0 1 0] #2 -> 1,3 + [1 0 0 1] #3 -> 1,4 + ])); + + @test length(Lara.biconnected_components(EV)) == 0; + end + + @testset "Couple of Components" begin + EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0] #1 -> 1,2 | + [1 1 0] #2 -> 1,2 | + [1 0 1] #3 -> 1,2 + ])); + + @test length(Lara.biconnected_components(EV)) == 1; + @test sort(Lara.biconnected_components(EV)[1]) == [1, 2]; + end end \ No newline at end of file From d9179d2e24c586b0856c82ca3687fcfdacd92153 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Sat, 20 Apr 2019 20:21:59 +0200 Subject: [PATCH 14/36] Minor Docs fixing --- docs/src/planar_arrangement.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index f7d9da0a..665c9600 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -91,7 +91,7 @@ Here also two optional parameters could be specified: if three vertices are collinear and evenly spaciated, then - if the second is identified in the third, then the first and the third won't be identified; - - if the thiird is identified with the second, + - if the third is identified with the second, then the first and the second will be identified; This situation could be seen in the secon example given by the function documentation. From 101bd7ceed8007e25556873e4138c575d6c33634 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Sat, 20 Apr 2019 20:22:32 +0200 Subject: [PATCH 15/36] Minor Docs fixing2 --- docs/src/planar_arrangement.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 665c9600..69169e11 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -144,7 +144,10 @@ bicon_comps = Lar.Arrangement.biconnected_components(copEV1); ## 3 - Biconnected Components hpcs = [ Plasm.lar2hpc(V1,[EV1[e] for e in comp]) for comp in bicon_comps ] -Plasm.view([ Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) for k = 1 : (length(hpcs)) ]) +Plasm.view([ + Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) + for k = 1 : (length(hpcs)) +]) # computation of 2-cells and 2-boundary W2, copEV2, copFE2 = Lar.planar_arrangement_2(W1, copEV1, bicon_comps) From da6f876e1a8f4731af29b0960a58d48021020a67 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Sat, 20 Apr 2019 20:29:43 +0200 Subject: [PATCH 16/36] Prepearing Documentation for part 2 --- src/arrangement/planar_arrangement.jl | 114 ++++++++++++++++++++++---- 1 file changed, 100 insertions(+), 14 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 99c3291a..ae39a88e 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -305,7 +305,11 @@ component ``χ_j`` and gives back an array that contains an array of ``σ_i`` fo Do note that if the cochain EV contains more copies of the same 2-cell then it will be considered like a 3-cell. -Intermediate part of the Planar Arrangement Pipeline (see also [`Lar.Arrangement.planar_arrangement`](@ref)). +Intermediate part of Planar Arrangement's algorithmic pipeline. + +See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. + +--- # Examples ```jldoctest @@ -439,6 +443,17 @@ end """ get_external_cycle(V, EV, FE) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function get_external_cycle(V::Lar.Points, EV::Lar.ChainOp, FE::Lar.ChainOp) FV = abs.(FE)*EV @@ -476,6 +491,17 @@ end """ pre_containment_test(bboxes) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function pre_containment_test(bboxes) n = length(bboxes) @@ -495,6 +521,17 @@ end """ prune_containment_graph(n, V, EVs, shells, graph) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function prune_containment_graph(n, V, EVs, shells, graph) @@ -523,6 +560,17 @@ end """ transitive_reduction!(graph) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function transitive_reduction!(graph) n = size(graph, 1) @@ -542,6 +590,17 @@ end """ cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) function bboxes(V::Lar.Points, indexes::Lar.ChainOp) @@ -601,6 +660,17 @@ end """ componentgraph(V, copEV, bicon_comps) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function componentgraph(V, copEV, bicon_comps) @@ -650,6 +720,17 @@ end """ cleandecomposition(V, copEV, sigma) + +More goes HERE... + +See also: [`Lar.Arrangement.planar_arrangement`](@ref). + +--- + +# Examples +```jldoctest + +``` """ function cleandecomposition(V, copEV, sigma) # Deletes edges outside sigma area @@ -830,15 +911,20 @@ end """ - function planar_arrangement_2(V, copEV, bicon_comps, - sigma::Lar.Chain=spzeros(Int8, 0), - return_edge_map::Bool=false, - multiproc::Bool=false) + function planar_arrangement_2(V, copEV, bicon_comps[, sigma[, return_edge_map[, multiproc]]]) +Second part of arrangement's algorithmic pipeline. -Compute the arrangement on the given cellular complex 1-skeleton in 2D. -Second part of arrangement's algorithmic pipeline. +More goes HERE... + +See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. + +--- +# Examples +```jldoctest + +``` """ function planar_arrangement_2(V, copEV, bicon_comps, sigma::Lar.Chain=spzeros(Int8, 0), @@ -875,15 +961,15 @@ Whole arrangement's algorithmic pipeline. A cellular complex is arranged when the intersection of every possible pair of cell of the complex is empty and the union of all the cells is the whole Euclidean space. -The basic method of the function without the `sigma`, `return_edge_map` and `multiproc` arguments -returns the full arranged complex `V`, `EV` and `FE`. +The method with no additional arguments specified gives back the full arranged complex +`V`, `EV` and `FE`. ## Additional arguments: -- `sigma::Chain`: if specified, `planar_arrangement` will delete from the output every edge and face outside this cell. - Defaults to an empty cell. -- `return_edge_map::Bool`: makes the function return also an `edge_map` which maps the edges of the imput to the one of the output. - Defaults to `false`. -- `multiproc::Bool`: Runs the computation in parallel mode. Defaults to `false`. + - `sigma::Chain`: if specified, `planar_arrangement` will delete from + the output every edge and face outside this cell. Defaults to an empty cell. + - `return_edge_map::Bool`: makes the function return also an `edge_map` which + maps the edges of the imput to the one of the output. Defaults to `false`. + - `multiproc::Bool`: Runs the computation in parallel mode. Defaults to `false`. """ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain=spzeros(Int8, 0), From 9f24b42c1453260d3d7769c38f319b94df8b5cc3 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Mon, 22 Apr 2019 13:34:01 +0200 Subject: [PATCH 17/36] Docs for TGW ongoing --- docs/src/planar_arrangement.md | 13 ++-- src/arrangement/planar_arrangement.jl | 94 ++++++++++++++++++++++----- 2 files changed, 84 insertions(+), 23 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 69169e11..579f336b 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -23,12 +23,15 @@ In general we recall the notation we have used in source code: In this section we will provide a general overview of how the `planar_arrangement` is meant to work. The algorithm is divided into the following pipeline: - - Fragmentation of the 2-Cells - - Spatial Indexing - - Pairwise 2-Cells Fragmentation - - Vertices Identification + - Fragmentation of the 2-Cells. + - Spatial Indexing. + - Pairwise 2-Cells Fragmentation. + - Vertices Identification. - Biconnected Components Detection. - - 3-Cells Evaluation and Dangling 2-Cells Elimination. + - 3-Cells Evaluation and Dangling 2-Cells Elimination + - Topological Gift Wrapping (TGW) algorithm. + - Dcomposition Cleaning. + - Shell poset aggregation. ### Fragmentation of the 2-Cells diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index ae39a88e..8d46acce 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -446,7 +446,7 @@ end More goes HERE... -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.componentgraph`](@ref). --- @@ -494,7 +494,7 @@ end More goes HERE... -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.componentgraph`](@ref). --- @@ -524,7 +524,7 @@ end More goes HERE... -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.componentgraph`](@ref). --- @@ -563,7 +563,7 @@ end More goes HERE... -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.componentgraph`](@ref). --- @@ -591,9 +591,11 @@ end """ cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) -More goes HERE... +Cells composing for the Topological Gift Wrapping algorithm. + +This is the online part of the TGW algorithm. -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.planar_arrangement_2`](@ref). --- @@ -661,9 +663,20 @@ end """ componentgraph(V, copEV, bicon_comps) -More goes HERE... +Topological Gift Wrapping algorithm on 2D skeletons. + +This is the offline part of the TGW algorithm. It takes in input a model and its +biconnected components mapping and evaluates usefull informations: + - number of biconnected components + - ? + - The 1-cells structure (UNMODIFIED). <----------------------------- Could be removed? + - Association between non-dangling 2-cells and their orientation. + - Association between 3-cells and 2-cells (with orientation). + - Association between 3-cells and their orientation. + - Shell bounding boxes + -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +See also: [`Lar.Arrangement.planar_arrangement_2`](@ref) for the TGW. --- @@ -721,18 +734,39 @@ end """ cleandecomposition(V, copEV, sigma) -More goes HERE... +!!! NOT WORKING + +This function clears the model `(V, copEV)` from all edges outside ``σ``. -See also: [`Lar.Arrangement.planar_arrangement`](@ref). +This function takes a model `(V, copEV)` and a `Lar.Chain` ``σ`` and +gives back the dropped model and and a vector `todel` of the 2-cells to drop. --- # Examples ```jldoctest +julia> V = [0.0 0.0; 2.0 0.0; 4.0 0.0; 1.0 1.5; 3.0 1.5; 2.0 3.0; 2.0 -3.; -2. 3.0; 6.0 3.0]; + +julia> EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 1 0 0 0 0 0 0] #1 -> 1,3 + [1 0 0 0 0 1 0 0 0] #2 -> 1,6 + [0 0 1 0 0 1 0 0 0] #3 -> 3,6 + [0 1 0 1 0 0 0 0 0] #4 -> 2,4 + [0 1 0 0 1 0 0 0 0] #5 -> 2,5 + [0 0 0 1 1 0 0 0 0] #6 -> 4,5 + [0 0 0 0 0 0 1 1 0] #7 -> 7,8 + [0 0 0 0 0 0 1 0 1] #8 -> 7,9 + [0 0 0 0 0 0 0 1 1] #9 -> 8,9 + ])); +julia> σ = SparseArrays.sparse([0; 0; 0; 1; 1; 1; 0; 0; 0]); + +todel, V, EV = Lar.Arrangement.cleandecomposition(V, EV, convert(Lar.Chain, σ)) + +Plasm.view(convert(Lar.Points, V'), Lar.cop2lar(EV)); ``` """ -function cleandecomposition(V, copEV, sigma) +function cleandecomposition(V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain) # Deletes edges outside sigma area todel = [] new_edges = [] @@ -915,7 +949,12 @@ end Second part of arrangement's algorithmic pipeline. -More goes HERE... +This function is the complete Topological Gift Wrapping (TGW) algorithm that is firstly +locally used in order to decompose the 2-cells and then globally to generate the 3-cells +of the arrangement of the ambient space ``E^3``. + +During this process each dangling 2-cell is removed. +Do note that the isolated 1-cells are not removed by this procedure. See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. @@ -923,30 +962,49 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. # Examples ```jldoctest +julia> V = [0.0 0.0; 2.0 0.0; 4.0 0.0; 1.0 1.5; 3.0 1.5; 2.0 3.0; 3.0 3.0]; +julia> W = convert(Lar.Points, V'); +julia> EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0 0 0] #1 -> 1,2 + [0 1 1 0 0 0 0] #2 -> 2,3 + [1 0 0 1 0 0 0] #3 -> 1,4 + [0 0 0 1 0 1 0] #4 -> 4,6 + [0 0 1 0 1 0 0] #5 -> 3,5 + [0 0 0 0 1 1 0] #6 -> 5,6 + [0 1 0 1 0 0 0] #7 -> 2,4 + [0 1 0 0 1 0 0] #8 -> 2,5 + [0 0 0 1 1 0 0] #9 -> 4,5 + [0 0 0 0 0 1 1] + ])); + +julia> Plasm.view(Plasm.numbering(0.5)((W,[[[k] for k=1:size(W,2)], Lar.cop2lar(EV)]))); + +julia> bicon_comps = Lar.Arrangement.biconnected_components(EV); + +julia> V, EV, FE = Lar.Arrangement.planar_arrangement_2(V, EV, bicon_comps); +julia> Plasm.view( Plasm.numbering1(0.5)((V, EV, FE)) ); ``` """ -function planar_arrangement_2(V, copEV, bicon_comps, +function planar_arrangement_2(V::Lar.Points, copEV::Lar.ChainOp, bicon_comps::Array{Array{Int, 1}, 1}, sigma::Lar.Chain=spzeros(Int8, 0), return_edge_map::Bool=false, multiproc::Bool=false) # Topological Gift Wrapping n, containment_graph, V, EVs, boundaries, shells, shell_bboxes = - componentgraph(V, copEV, bicon_comps) + Lar.Arrangement.componentgraph(V, copEV, bicon_comps) @show containment_graph # only in the context of 3D arrangement - if sigma.n > 0 + if sigma.n > 0 ## number of columns of sigma > 0 todel, V, copEV = Lar.Arrangement.cleandecomposition(V, copEV, sigma) - V, copEV = Lar.delete_edges(todel, V, copEV) + V, copEV = Lar.delete_edges(todel, V, copEV) # <----------------------non mi è chiaro perchè non è dentro la fun end # final shell poset aggregation and FE output copEV, FE = Lar.Arrangement.cell_merging( n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) if (return_edge_map) return V, copEV, FE, edge_map - else - return V, copEV, FE end return V, copEV, FE end From f88f92ab689408a0dd6918271238cab6452557f7 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Mon, 22 Apr 2019 14:54:20 +0200 Subject: [PATCH 18/36] Proceding with TGW docs --- docs/src/planar_arrangement.md | 53 +++++++++++++++++++++++++++++++--- 1 file changed, 49 insertions(+), 4 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 579f336b..6c34c574 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -28,10 +28,14 @@ The algorithm is divided into the following pipeline: - Pairwise 2-Cells Fragmentation. - Vertices Identification. - Biconnected Components Detection. - - 3-Cells Evaluation and Dangling 2-Cells Elimination - - Topological Gift Wrapping (TGW) algorithm. - - Dcomposition Cleaning. - - Shell poset aggregation. + - 3-Cells Evaluation and Dangling 2-Cells Elimination via Topological Gift Wrapping (TGW) algorithm. + - Component graph evaluation (TGW offline part). + - Evalution of the external cicle. + - Containment graph evaluation. + - Pruning of the containment graph. + - Transitive ``R`` reduction of ``S`` and generation of forest of flat trees + - Decomposition Cleaning (if a boundary has been specified). + - Shell poset aggregation (TGW onloine part). ### Fragmentation of the 2-Cells @@ -115,6 +119,47 @@ graph made by the edges is the only input needed by the function. ### 3-Cells Evaluation and Dangling 2-Cells Elimination. +This part of the pipeline is covered by +```@docs +Lar.Arrangement.planar_arrangement_2 +``` + + +First of all the components of the graph are evaluated via +```@docs +Lar.Arrangement.componentgraph +``` + + +Then, if a special chain ``\sigma`` has been specified, the given decomposition is cleaned +from all the 2-cells (and consequently from alle the 1-cells) that are located ouside its boundary via +```@docs +Lar.Arrangement.cleandecomposition +``` + + +Lastly the 2-cells are merged in order to retrieve the 3-cell of the complex. +By doing so, all the 2-cells that are not linked to any 3-cell (_i.e._ dangling edges) +are lost. +!!! note + Do note that the 1-cells are not pruned during this computation. + Therefore the vertices associated with dangling edges will still be there. + +This last part of the computation is done via: +```@docs +Lar.Arrangement.cell_merging +``` + + +#### Component graph evaluation + +```@docs +Lar.Arrangement.get_external_cycle +Lar.Arrangement.pre_containment_test +Lar.Arrangement.prune_containment_graph +Lar.Arrangement.transitive_reduction +``` + ## Examples ```julia From 7e9f5c82d0f41030db197aaf826840faaf22efcc Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Mon, 22 Apr 2019 18:12:47 +0200 Subject: [PATCH 19/36] Udating Refernces and Docs --- README.md | 11 +++++++++-- docs/src/planar_arrangement.md | 12 +++++++++--- src/arrangement/planar_arrangement.jl | 11 +++++++++-- 3 files changed, 27 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index b7ce53ee..45cae86c 100644 --- a/README.md +++ b/README.md @@ -24,9 +24,12 @@ add("LinearAlgebraicRepresentation") ## Documentation -BUilding EOnofri julia-1.0 [![Build Status](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl.svg?branch=master)](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl) -Go to [the documentation page](https://eonofri04.github.io/LinearAlgebraicRepresentation.jl/) +Building EOnofri julia-1.0 [![Build Status](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl.svg?branch=master)](https://travis-ci.org/eOnofri04/LinearAlgebraicRepresentation.jl) +Go to [eonofri documentation page](https://eonofri04.github.io/LinearAlgebraicRepresentation.jl/) + + +Go to [cvdlab documentation page](https://cvdlab.github.io/LinearAlgebraicRepresentation.jl/) ## Authors @@ -34,3 +37,7 @@ Go to [the documentation page](https://eonofri04.github.io/LinearAlgebraicRepres * [Alberto Paoluzzi](https://github.com/apaoluzzi) * [Francesco Furiani](https://github.com/furio) +## Additional Documenters +* [Elia Onofri](https://github.com/eonofri04) +* [Maria Teresa Graziano](https://github.com/marteresagh) +* [Luca Angelini]() diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 6c34c574..2febc745 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -18,7 +18,7 @@ In general we recall the notation we have used in source code: !!! warning Do remember that in `planar_arrangement` (`Lar.Arrangement` module) matrices store points per row and not per column as described in the documentation of `Lar.Points`. -## The algorithm +## The Arrangement Algorithm In this section we will provide a general overview of how the `planar_arrangement` is meant to work. @@ -152,16 +152,21 @@ Lar.Arrangement.cell_merging #### Component graph evaluation +Component Graph evaluation relies on different functions that could be use separatelly in order to obtain different results. ```@docs Lar.Arrangement.get_external_cycle Lar.Arrangement.pre_containment_test Lar.Arrangement.prune_containment_graph -Lar.Arrangement.transitive_reduction +Lar.Arrangement.transitive_reduction! ``` ## Examples +Lastly we close this section by giving a small example of how Planar Arrangement Works. +Using `Plasm` we are able to visualize the step of the computation grafically. + + ```julia using Plasm using LinearAlgebraicRepresentation @@ -220,7 +225,8 @@ model = V2,EVs2 Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) ``` +The described commands gives the following representation via Plasm. Here we have reunited all the images in order to clarify the example. It could be seen in (4) that the 1-cells are not removed via the Pipeline. ![Pipeline visualization](./images/2d-arrangement-pipeline.jpg) > **Figure 1:** Pipeline visualization over a sample structure. - +More examples could be find in the `test` and `examples` directory. diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 8d46acce..b7771860 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -1011,8 +1011,8 @@ end """ - planar_arrangement(V::Points, copEV::ChainOp, - [sigma::Chain], [return_edge_map::Bool], [multiproc::Bool]) + planar_arrangement(V::Points, copEV::ChainOp + [, sigma::Chain[, return_edge_map::Bool[, multiproc::Bool]]]) Compute the arrangement on the given cellular complex 1-skeleton in 2D. Whole arrangement's algorithmic pipeline. @@ -1022,12 +1022,19 @@ of the complex is empty and the union of all the cells is the whole Euclidean sp The method with no additional arguments specified gives back the full arranged complex `V`, `EV` and `FE`. +See also: + - [`Lar.Arrangement.planar_arrangement_1`](@ref) + - [`Lar.Arrangement.biconnected_components`](@ref) + - [`Lar.Arrangement.planar_arrangement_2`](@ref) + ## Additional arguments: - `sigma::Chain`: if specified, `planar_arrangement` will delete from the output every edge and face outside this cell. Defaults to an empty cell. - `return_edge_map::Bool`: makes the function return also an `edge_map` which maps the edges of the imput to the one of the output. Defaults to `false`. - `multiproc::Bool`: Runs the computation in parallel mode. Defaults to `false`. + +Many examples could be found in Lar Documentation. """ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain=spzeros(Int8, 0), From f03fc418ae757859bf26e6cc41a99b4750ad3479 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Mon, 22 Apr 2019 18:45:57 +0200 Subject: [PATCH 20/36] get_external_cycle Documentation --- src/arrangement/planar_arrangement.jl | 28 +++++++++++++++++++++++++-- 1 file changed, 26 insertions(+), 2 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index b7771860..eca842d2 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -444,7 +444,10 @@ end """ get_external_cycle(V, EV, FE) -More goes HERE... +Evaluates the index of the external 3D-cell. + +This method looks for and retrieve the external cycle of the model `(V, EV, FE)`. +If the cell does not exist then it return a `Nothing` element. See also: [`Lar.Arrangement.componentgraph`](@ref). @@ -452,7 +455,28 @@ See also: [`Lar.Arrangement.componentgraph`](@ref). # Examples ```jldoctest - +# ``K^4`` graph +julia> V = [0.0 0.0; 4.0 0.0; 2.0 3.0; 2.0 1.5]; +julia> EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0] #1 -> 1,2 + [0 1 1 0] #2 -> 2,3 + [1 0 1 0] #3 -> 3,1 + [1 0 0 1] #4 -> 1,2 + [0 1 0 1] #5 -> 2,3 + [0 0 1 1] #6 -> 3,1 + ])); +julia> FE = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 0 1 1 0] #1 -> 1,4,5 + [0 1 0 0 1 1] #2 -> 2,5,6 + [0 0 1 1 0 1] #3 -> 3,4,6 + [1 1 1 0 0 0] #4 -> 1,2,3 External + ])); + +julia> Lar.Arrangement.get_external_cycle(V, EV, FE) +4 + +julia> typeof(Lar.Arrangement.get_external_cycle(V, EV, FV[1:3,:])) +Nothing ``` """ function get_external_cycle(V::Lar.Points, EV::Lar.ChainOp, FE::Lar.ChainOp) From 09b184c97f9f4895044ffc255e7377e5fb877e83 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 12:01:45 +0200 Subject: [PATCH 21/36] Some Test + pre_containment_test Docs --- src/arrangement/planar_arrangement.jl | 19 +++++--- test/refactor_planar_arrangement.jl | 64 +++++++++++++++++++++++++++ 2 files changed, 77 insertions(+), 6 deletions(-) diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index eca842d2..a93a24e2 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -516,9 +516,16 @@ end """ pre_containment_test(bboxes) -More goes HERE... +Generate the containment graph associated to `bboxes`. -See also: [`Lar.Arrangement.componentgraph`](@ref). +The function evaluate a `SparseArrays{Int8, n, n}` PRE-containmnet graph in the sense +that it contains redundancies that must be pruned (where `n = length(bboxes)`) + +The graph element `(i, j)` is **1** if the axis aligned bounding box of `bboxes[j]` contains `bboxes[i]`. + +See also: + - [`Lar.Arrangement.componentgraph`](@ref). + - [`Lar.bbox_contains`](@ref). --- @@ -529,7 +536,7 @@ See also: [`Lar.Arrangement.componentgraph`](@ref). """ function pre_containment_test(bboxes) n = length(bboxes) - containment_graph = spzeros(Int8, n, n) + containment_graph = SparseArrays.spzeros(Int8, n, n) for i in 1:n for j in 1:n @@ -691,13 +698,13 @@ Topological Gift Wrapping algorithm on 2D skeletons. This is the offline part of the TGW algorithm. It takes in input a model and its biconnected components mapping and evaluates usefull informations: - - number of biconnected components - - ? + - Number of biconnected components. + - Component Graph of the biconnected structure. - The 1-cells structure (UNMODIFIED). <----------------------------- Could be removed? - Association between non-dangling 2-cells and their orientation. - Association between 3-cells and 2-cells (with orientation). - Association between 3-cells and their orientation. - - Shell bounding boxes + - Shell bounding boxes of the components. See also: [`Lar.Arrangement.planar_arrangement_2`](@ref) for the TGW. diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index 6faae1de..e00f3829 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -63,6 +63,8 @@ Lara = LinearAlgebraicRepresentation.Arrangement end end +#--------------------------------------------------------------------------------------------------------------------------------#-------------------------------------------------------------------------------------------------------------------------------- + @testset "Biconnected Components" begin @testset "Normal Execution" begin EV = SparseArrays.sparse(Array{Int8, 2}([ @@ -106,4 +108,66 @@ end @test length(Lara.biconnected_components(EV)) == 1; @test sort(Lara.biconnected_components(EV)[1]) == [1, 2]; end +end + +#-------------------------------------------------------------------------------------------------------------------------------- + +@testset "Pipeline Arrangement 2 over K^4" begin + + # K^4 + edge + V = [0.0 0.0; 4.0 0.0; 2.0 3.0; 2.0 1.5]; + EV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0] #1 -> 1,2 + [0 1 1 0] #2 -> 2,3 + [1 0 1 0] #3 -> 3,1 + [1 0 0 1] #4 -> 1,2 + [0 1 0 1] #5 -> 2,3 + [0 0 1 1] #6 -> 3,1 + ])); + + EVs = [SparseArrays.sparse(Array{Int8, 2}([ + [-1 1 0 0] #1 -> 1,2 + [ 0 -1 1 0] #2 -> 2,3 + [-1 0 1 0] #3 -> 3,1 + [-1 0 0 1] #4 -> 1,2 + [ 0 -1 0 1] #5 -> 2,3 + [ 0 0 -1 1] #6 -> 3,1 + ]))]; + + FE = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 0 1 1 0] #1 -> 1,4,5 + [0 1 0 0 1 1] #2 -> 2,5,6 + [0 0 1 1 0 1] #3 -> 3,4,6 + [1 1 1 0 0 0] #4 -> 1,2,3 External + ])); + + boundaries = [SparseArrays.sparse(Array{Int8, 2}([ + [ 1 0 0 -1 1 0] #1 -> 1,4,5 + [ 0 1 0 0 -1 1] #2 -> 2,5,6 + [ 0 0 -1 1 0 -1] #3 -> 3,4,6 + ]))]; + + bicon_comps = [[1, 2, 3, 4, 5, 6]]; + + @testset "get_external_cycle" begin + @test Lara.get_external_cycle(V, EV, FE) == 4; + @test typeof(Lara.get_external_cycle(V, EV, FV[1:3,:])) == Nothing + end + + @testset "Biconnected Components 2" begin + @test length(Lara.biconnected_components(EV)) == 1; + @test sort(Lara.biconnected_components(EV)[1]) == bicon_comps; + end + + + + @test Lara.componentgraph(V, copEV, bicon_comps)[1] == 1; + @test Lara.componentgraph(V, copEV, bicon_comps)[2] == (1, 1); + @test Lara.componentgraph(V, copEV, bicon_comps)[3] == V; + @test Lara.componentgraph(V, copEV, bicon_comps)[4] == EVs; + @test Lara.componentgraph(V, copEV, bicon_comps)[5] == boundaries; + @test Lara.componentgraph(V, copEV, bicon_comps)[6] == [sparse(Array{Int8}([-1; -1; 1; 0; 0; 0]))]; + @test Lara.componentgraph(V, copEV, bicon_comps)[7] == [([0.0 0.0], [4.0 3.0])]; + + end \ No newline at end of file From 16b62b0b13180133a3e83bb9d7dba7ef4a24ffc1 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 16:22:57 +0200 Subject: [PATCH 22/36] Documentation Add --- docs/src/planar_arrangement.md | 7 +- src/arrangement/planar_arrangement.jl | 165 ++++++++++++++++++++------ 2 files changed, 133 insertions(+), 39 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 2febc745..96f9ba1d 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -7,11 +7,12 @@ Lar.planar_arrangement ``` In general we recall the notation we have used in source code: - - `V::Lar.Poins` is the 1-cells (Vertices) complex. + - `V::Lar.Points` is the 1-cells (Vertices) complex by Columns. + - `W::Lar.Points` is the 1-cells (Vertices) complex by Rows. - `EV::Lar.Cells` is the 2-cells (Edges) complex. - - `FV::Lar.` is the 3-cells (Faces) complex. + - `FV::Lar.Cells` is the 3-cells (Faces) complex. - `copEV::Lar.ChainOp`: is the Chain Coboundary of the 2-cells. - - `copFE::Lar.`: is the Chain Coboundary of the 3-cells. + - `copFE::Lar.ChainOp`: is the Chain Coboundary of the 3-cells. - `bigPI::Array{Array{Int64,1},1}`: is the bounding box intersection array: each row is associated to a 2-cell and contains the indices of the other 2-cells intersecting its bounding box. diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index a93a24e2..21e8b985 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -1,5 +1,6 @@ using LinearAlgebraicRepresentation Lar = LinearAlgebraicRepresentation +Lara = Lar.Arrangement #-------------------------------------------------------------------------------------------------------------------------------- @@ -57,11 +58,11 @@ julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0; 1.0 1.0]; # By Rows! julia> EV = [[1, 2], [2, 5], [3, 4], [4, 5]]; -julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); +julia> copEV = Lar.coboundary_0(EV::Lar.Cells); julia> bigPI = Lar.spaceindex((convert(Lar.Points, V'), EV)); -julia> Lar.Arrangement.frag_edge(V, cop_EV, 1, bigPI)[1] +julia> Lara.frag_edge(V, copEV, 1, bigPI)[1] 5×2 Array{Float64,2}: 1.0 0.0 0.0 1.0 @@ -69,7 +70,7 @@ julia> Lar.Arrangement.frag_edge(V, cop_EV, 1, bigPI)[1] 0.25 0.75 0.0 1.0 -julia> Lar.Arrangement.frag_edge(V, cop_EV, 1, bigPI)[2] +julia> Lara.frag_edge(V, copEV, 1, bigPI)[2] 2×5 SparseMatrixCSC{Int8,Int64} with 4 stored entries: [1, 1] = 1 [2, 2] = 1 @@ -117,30 +118,32 @@ See also: [`Lar.Arrangement.frag_edge`](@ref) # Examples ```jldoctest +# Cross julia> V = [1.0 0.0; 0.0 1.0; 0.0 0.5; 0.5 1.0]; # By Rows! julia> EV = [[1, 2], [3, 4]]; -julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); +julia> copEV = Lar.coboundary_0(EV::Lar.Cells); -julia> Lar.Arrangement.intersect_edges(V, cop_EV[1, :], cop_EV[2, :]) +julia> Lara.intersect_edges(V, copEV[1, :], copEV[2, :]) 1-element Array{Tuple{Array{T,2} where T,Float64},1}: ([0.25 0.75], 0.75) ``` ```jldoctest +# Collinear julia> V = [1.0 0.0; 0.0 1.0; 0.75 0.25; 0.5 0.5]; # By Rows! julia> EV = [[1, 2], [3, 4]]; -julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); +julia> copEV = Lar.coboundary_0(EV::Lar.Cells); -julia> Lar.Arrangement.intersect_edges(V, cop_EV[1, :], cop_EV[2, :]) +julia> Lar.Arrangement.intersect_edges(V, copEV[1, :], copEV[2, :]) 2-element Array{Tuple{Array{T,2} where T,Float64},1}: ([0.75 0.25], 0.25) ([0.5 0.5], 0.5) -julia> Lar.Arrangement.intersect_edges(V, cop_EV[2, :], cop_EV[1, :]) +julia> Lar.Arrangement.intersect_edges(V, copEV[2, :], copEV[1, :]) 0-element Array{Tuple{Array{T,2} where T,Float64},1} ``` """ @@ -205,19 +208,20 @@ See also: [`Lar.Arrangement.planar_arrangement_1`](@ref) # Examples ```jldoctest +# Collinear julia> V = [0.5 0.5; 0.0 0.0; 0.5 0.5; 1.0 1.0; 0.5 0.5; 1.0 1.0]; # By Rows! julia> EV = [[1, 4], [3, 2], [5, 6], [1, 6], [5, 3]]; -julia> cop_EV = Lar.coboundary_0(EV::Lar.Cells); +julia> copEV = Lar.coboundary_0(EV::Lar.Cells); -julia> Lar.Arrangement.merge_vertices!(V, cop_EV)[1] +julia> Lara.merge_vertices!(V, copEV)[1] 3×2 Array{Float64,2}: 0.5 0.5 0.0 0.0 1.0 1.0 -julia> Lar.Arrangement.merge_vertices!(V, cop_EV)[2] +julia> Lara.merge_vertices!(V, copEV)[2] 2×3 SparseArrays.SparseMatrixCSC{Int8,Int64} with 4 stored entries: [1, 1] = 1 [2, 1] = 1 @@ -313,7 +317,7 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. # Examples ```jldoctest -julia> EV = SparseArrays.sparse(Array{Int8, 2}([ +julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ [1 1 0 0 0 0] #1 -> 1,2 | [1 0 1 0 0 0] #2 -> 1,3 | [1 0 0 1 0 0] #3 -> 1,4 | @@ -322,19 +326,19 @@ julia> EV = SparseArrays.sparse(Array{Int8, 2}([ [0 1 1 0 0 0] #6 -> 2,3 | [0 0 0 1 1 0] #7 -> 4,5 | ])); -julia> Lar.Arrangement.biconnected_components(EV) +julia> Lara.biconnected_components(copEV) 2-element Array{Array{Int64,1},1}: [2, 6, 1] [4, 7, 3] ``` ```jldoctest -julia> EV = SparseArrays.sparse(Array{Int8, 2}([ +julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ [1 1 0] #1 -> 1,2 | [1 1 0] #2 -> 1,2 | [1 0 1] #3 -> 1,2 ])); -julia> Lar.Arrangement.biconnected_components(EV) +julia> Lara.biconnected_components(copEV) 1-element Array{Array{Int64,1},1}: [2, 1] ``` @@ -457,7 +461,7 @@ See also: [`Lar.Arrangement.componentgraph`](@ref). ```jldoctest # ``K^4`` graph julia> V = [0.0 0.0; 4.0 0.0; 2.0 3.0; 2.0 1.5]; -julia> EV = SparseArrays.sparse(Array{Int8, 2}([ +julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ [1 1 0 0] #1 -> 1,2 [0 1 1 0] #2 -> 2,3 [1 0 1 0] #3 -> 3,1 @@ -465,17 +469,17 @@ julia> EV = SparseArrays.sparse(Array{Int8, 2}([ [0 1 0 1] #5 -> 2,3 [0 0 1 1] #6 -> 3,1 ])); -julia> FE = SparseArrays.sparse(Array{Int8, 2}([ +julia> copFE = SparseArrays.sparse(Array{Int8, 2}([ [1 0 0 1 1 0] #1 -> 1,4,5 [0 1 0 0 1 1] #2 -> 2,5,6 [0 0 1 1 0 1] #3 -> 3,4,6 [1 1 1 0 0 0] #4 -> 1,2,3 External ])); -julia> Lar.Arrangement.get_external_cycle(V, EV, FE) +julia> Lara.get_external_cycle(V, copEV, copFE) 4 -julia> typeof(Lar.Arrangement.get_external_cycle(V, EV, FV[1:3,:])) +julia> typeof(Lara.get_external_cycle(V, copEV, copFE[1:3,:])) Nothing ``` """ @@ -531,7 +535,22 @@ See also: # Examples ```jldoctest - +# Planar Tiles +julia> bboxes = [ + ([0.0 0.0], [1.0 1.0]) + ([0.0 0.0], [0.4 0.4]) + ([0.6 0.0], [1.0 0.4]) + ([0.0 0.6], [0.4 1.0]) + ([0.6 0.6], [1.0 1.0]) + ([2.0 3.0], [2.0 3.0]) # no intersection + ]; + +julia> Lara.pre_containment_test(bboxes) +5×5 SparseMatrixCSC{Int8,Int64} with 4 stored entries: + [2, 1] = 1 + [3, 1] = 1 + [4, 1] = 1 + [5, 1] = 1 ``` """ function pre_containment_test(bboxes) @@ -553,9 +572,17 @@ end """ prune_containment_graph(n, V, EVs, shells, graph) -More goes HERE... +Prunes the containment `graph` from the non-intersecting faces. -See also: [`Lar.Arrangement.componentgraph`](@ref). +This method prunes the containment graph eliminating the intersecting bouning boxes +that not corresponds to intersectring faces. + +Do note that this method expects to work on biconnectet clusters of faces; in fact +it only checks for one point to see if the faces are intersecting. + +See also: + - [`Lar.Arrangement.componentgraph`](@ref). + - [`Lar.point_in_face`](@ref). --- @@ -698,13 +725,13 @@ Topological Gift Wrapping algorithm on 2D skeletons. This is the offline part of the TGW algorithm. It takes in input a model and its biconnected components mapping and evaluates usefull informations: - - Number of biconnected components. - - Component Graph of the biconnected structure. - - The 1-cells structure (UNMODIFIED). <----------------------------- Could be removed? - - Association between non-dangling 2-cells and their orientation. - - Association between 3-cells and 2-cells (with orientation). - - Association between 3-cells and their orientation. - - Shell bounding boxes of the components. + 1. Number of biconnected components. + 2. Component Graph of the biconnected structure. + 3. The 1-cells structure (UNMODIFIED). <----------------------------- Could be removed? + 4. Association between non-dangling 2-cells and their orientation (for each component). + 5. Association between 3-cells and 2-cells (with orientation, for each component). + 6. Association between 3-cells and their orientation (for each component). + 7. Shell bounding boxes of the components. See also: [`Lar.Arrangement.planar_arrangement_2`](@ref) for the TGW. @@ -713,7 +740,73 @@ See also: [`Lar.Arrangement.planar_arrangement_2`](@ref) for the TGW. # Examples ```jldoctest +# Papillon +julia> V = [0.0 0.0; 0.0 3.0; 2.0 1.5; 4.0 0.0; 4.0 3.0]; + +julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0] #1 -> 1,2 + [0 1 1 0 0] #2 -> 2,3 + [1 0 1 0 0] #3 -> 3,1 + [0 0 1 1 0] #4 -> 3,4 + [0 0 0 1 1] #5 -> 4,5 + [0 0 1 0 1] #6 -> 3,5 + ])); +julia> copFE = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 1 0 0 0] #1 -> 1,2,3 + [0 0 0 1 1 1] #2 -> 4,5,6 + [1 1 1 1 1 1] #3 -> 1,2,3,4,5,6 External + ])); + +julia> bicon_comps = [[1, 2, 3], [4, 5, 6]]; + +julia> Lara.componentgraph(V, copEV, bicon_comps)[1] +2 + +julia> Lara.componentgraph(V, copEV, bicon_comps)[2] +2×2 SparseMatrixCSC{Int8,Int64} with 0 stored entries + +julia> Lara.componentgraph(V, copEV, bicon_comps)[4] +2-element Array{SparseMatrixCSC{Int8,Int64},1}: + + [1, 1] = -1 + [3, 1] = -1 + [1, 2] = 1 + [2, 2] = -1 + [2, 3] = 1 + [3, 3] = 1 + + [1, 3] = -1 + [3, 3] = -1 + [1, 4] = 1 + [2, 4] = -1 + [2, 5] = 1 + [3, 5] = 1 + +julia> Lara.componentgraph(V, copEV, bicon_comps)[5] +2-element Array{SparseMatrixCSC{Int8,Int64},1}: + + [1, 1] = -1 + [1, 2] = -1 + [1, 3] = 1 + + [1, 1] = 1 + [1, 2] = 1 + [1, 3] = -1 + +julia> Lara.componentgraph(V, copEV, bicon_comps)[6] +2-element Array{SparseVector{Int8,Int64},1}: + [1] = 1 + [2] = 1 + [3] = -1 + [1] = -1 + [2] = -1 + [3] = 1 + +julia> Lara.componentgraph(V, copEV, bicon_comps)[7] +2-element Array{Any,1}: + ([0.0 0.0], [2.0 3.0]) + ([2.0 0.0], [4.0 3.0]) ``` """ function componentgraph(V, copEV, bicon_comps) @@ -776,9 +869,10 @@ gives back the dropped model and and a vector `todel` of the 2-cells to drop. # Examples ```jldoctest +# Nested Triangles julia> V = [0.0 0.0; 2.0 0.0; 4.0 0.0; 1.0 1.5; 3.0 1.5; 2.0 3.0; 2.0 -3.; -2. 3.0; 6.0 3.0]; -julia> EV = SparseArrays.sparse(Array{Int8, 2}([ +julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ [1 0 1 0 0 0 0 0 0] #1 -> 1,3 [1 0 0 0 0 1 0 0 0] #2 -> 1,6 [0 0 1 0 0 1 0 0 0] #3 -> 3,6 @@ -792,9 +886,9 @@ julia> EV = SparseArrays.sparse(Array{Int8, 2}([ julia> σ = SparseArrays.sparse([0; 0; 0; 1; 1; 1; 0; 0; 0]); -todel, V, EV = Lar.Arrangement.cleandecomposition(V, EV, convert(Lar.Chain, σ)) +todel, V, copEV = Lara.cleandecomposition(V, copEV, convert(Lar.Chain, σ)) -Plasm.view(convert(Lar.Points, V'), Lar.cop2lar(EV)); +Plasm.view(convert(Lar.Points, V'), Lar.cop2lar(copEV)); ``` """ function cleandecomposition(V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain) @@ -878,8 +972,6 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. # Examples ```jldoctest -julia> using Plasm - julia> EV = [[1, 2], [3, 4], [1, 3], [2, 4], [5, 6], [7, 8], [5, 7], [6, 8]]; julia> V = [ @@ -911,7 +1003,7 @@ julia> Plasm.view(Plasm.numbering(0.1)((V1,[[[k] for k=1:size(V1,2)], EV1]))); ``` """ function planar_arrangement_1(V::Lar.Points, copEV::Lar.ChainOp, - sigma::Lar.Chain=spzeros(Int8, 0), + sigma::Lar.Chain=SparseArrays.spzeros(Int8, 0), return_edge_map::Bool=false, multiproc::Bool=false) @@ -993,6 +1085,7 @@ See also: [`Lar.planar_arrangement`](@ref) for the complete pipeline. # Examples ```jldoctest +# Triforce julia> V = [0.0 0.0; 2.0 0.0; 4.0 0.0; 1.0 1.5; 3.0 1.5; 2.0 3.0; 3.0 3.0]; julia> W = convert(Lar.Points, V'); julia> EV = SparseArrays.sparse(Array{Int8, 2}([ @@ -1065,7 +1158,7 @@ See also: maps the edges of the imput to the one of the output. Defaults to `false`. - `multiproc::Bool`: Runs the computation in parallel mode. Defaults to `false`. -Many examples could be found in Lar Documentation. +Many examples could be found in Lar Documentation and `examples` directory. """ function planar_arrangement( V::Lar.Points, copEV::Lar.ChainOp, sigma::Lar.Chain=spzeros(Int8, 0), From 590ca85fde3c1efc05b44f8237f04341c5e3707c Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 16:23:18 +0200 Subject: [PATCH 23/36] Adding new Examples --- examples/2d/planar_arrangement/Triforce.jl | 61 ++++++++++++ examples/2d/planar_arrangement/planar_tile.jl | 97 +++++++++++++++++++ .../2d/planar_arrangement/triangulation.jl | 57 +++++++++++ 3 files changed, 215 insertions(+) create mode 100644 examples/2d/planar_arrangement/Triforce.jl create mode 100644 examples/2d/planar_arrangement/planar_tile.jl create mode 100644 examples/2d/planar_arrangement/triangulation.jl diff --git a/examples/2d/planar_arrangement/Triforce.jl b/examples/2d/planar_arrangement/Triforce.jl new file mode 100644 index 00000000..fc7bf50e --- /dev/null +++ b/examples/2d/planar_arrangement/Triforce.jl @@ -0,0 +1,61 @@ +using LinearAlgebraicRepresentation +using Plasm +using SparseArrays +Lar = LinearAlgebraicRepresentation +Lara = Lar.Arrangement + +# Data Reading +V = [ + 0.0 1.5 3.0 0.0 3.0 0.0 1.5 3.0; + 0.0 0.0 0.0 1.5 1.5 3.0 3.0 3.0 + ]; +EV = [ + [1, 3], [4, 5], # Orizontal + [1, 7], [2, 8], # Diag 1 + [2, 6], [3, 7] # Diag 2 + ]; + +## 1 - Input Reading +Plasm.view(Plasm.numbering(0.5)((V,[[[k] for k=1:size(V,2)], EV]))); + +# Planar Arrangement 1 +W = convert(Lar.Points, V'); # Infering type for W = V' +copEV = Lar.coboundary_0(EV::Lar.Cells); +W1, copEV1 = Lar.planar_arrangement_1(W::Lar.Points, copEV::Lar.ChainOp); + +## 2 - 2-cells fragmentation +EV1 = Lar.cop2lar(copEV1); +V1 = convert(Lar.Points, W1'); +Plasm.view(Plasm.numbering(0.5)((V1,[[[k] for k=1:size(V1,2)], EV1]))); + +# Biconnected COmponent Evaluation +bicon_comps = Lar.Arrangement.biconnected_components(copEV1); + +## 3 - Biconnected Components +hpcs = [ Plasm.lar2hpc(V1,[EV1[e] for e in comp]) for comp in bicon_comps ] +Plasm.view([ + Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) + for k = 1 : (length(hpcs)) +]) + +# computation of 2-cells and 2-boundary +W2, copEV2, copFE2 = Lar.planar_arrangement_2(W1, copEV1, bicon_comps) + +## 4 - 3-cells identification & dangling 1-cells elimination +Plasm.view( Plasm.numbering1(0.5)((W2, copEV2, copFE2)) ) + + +# 5 - Colorfull Representation +triangulated_faces = Lar.triangulate2D(W2, [copEV2, copFE2]) +V2 = convert(Lar.Points, W2') +FVs2 = convert(Array{Lar.Cells}, triangulated_faces) +Plasm.viewcolor(V2::Lar.Points, FVs2::Array{Lar.Cells}) + +# polygonal face boundaries +EVs2 = Lar.FV2EVs(copEV2, copFE2) +EVs2 = convert(Array{Array{Array{Int64,1},1},1}, EVs2) +Plasm.viewcolor(V2::Lar.Points, EVs2::Array{Lar.Cells}) + +# 6 - Exploded Representation +model = V2,EVs2 +Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) \ No newline at end of file diff --git a/examples/2d/planar_arrangement/planar_tile.jl b/examples/2d/planar_arrangement/planar_tile.jl new file mode 100644 index 00000000..02717f97 --- /dev/null +++ b/examples/2d/planar_arrangement/planar_tile.jl @@ -0,0 +1,97 @@ +using LinearAlgebraicRepresentation +using Plasm +using SparseArrays +Lar = LinearAlgebraicRepresentation +Lara = Lar.Arrangement + + +V = [ + 0.0 0.4 0.5 0.6 1.0 0.0 1.0 0.0 1.0 0.0 1.0 0.0 0.4 0.5 0.6 1.0; + 0.0 0.0 0.0 0.0 0.0 0.4 0.4 0.5 0.5 0.6 0.6 1.0 1.0 1.0 1.0 1.0 +] + +EV = [ + [ 1, 2], [ 1, 6], [ 2, 6], + [ 4, 5], [ 4, 7], [ 5, 7], + [10, 12], [10, 13], [12, 13], + [11, 15], [11, 16], [15, 16], + [ 3, 8], [ 3, 9], [ 3, 14], [ 8, 9], [ 8, 14], [ 9, 14] +] + +## 1 - Input Reading +Plasm.view(Plasm.numbering(0.5)((V,[[[k] for k=1:size(V,2)], EV]))); + + +# Planar Arrangement 1 +W = convert(Lar.Points, V'); # Infering type for W = V' +copEV = Lar.coboundary_0(EV::Lar.Cells); +W1, copEV1 = Lar.planar_arrangement_1(W::Lar.Points, copEV::Lar.ChainOp); + + +## 2 - 2-cells fragmentation +EV1 = Lar.cop2lar(copEV1); +V1 = convert(Lar.Points, W1'); +Plasm.view(Plasm.numbering(0.5)((V1,[[[k] for k=1:size(V1,2)], EV1]))); + + +# Biconnected COmponent Evaluation +bicon_comps = Lar.Arrangement.biconnected_components(copEV1); + + +## 3 - Biconnected Components +hpcs = [ Plasm.lar2hpc(V1,[EV1[e] for e in comp]) for comp in bicon_comps ] +Plasm.view([ + Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) + for k = 1 : (length(hpcs)) +]) + + +# computation of 2-cells and 2-boundary + +# n, containment_graph, W2, EVs, boundaries, shells, shell_bboxes = Lara.componentgraph(W1, copEV1, bicon_comps) + +n = size(bicon_comps, 1) +shells = Array{Lar.Chain, 1}(undef, n) +boundaries = Array{Lar.ChainOp, 1}(undef, n) +EVs = Array{Lar.ChainOp, 1}(undef, n) +# for each component +for p=1:n + ev = copEV1[sort(bicon_comps[p]), :] + fe = Lara.minimal_2cycles(W1, ev) + global shell_num = Lara.get_external_cycle(W1, ev, fe) + EVs[p] = ev + global tokeep = setdiff(1:fe.m, shell_num) + boundaries[p] = fe[tokeep, :] + shells[p] = fe[shell_num, :] +end + +shell_bboxes = [] +for i in 1:n + vs_indexes = (abs.(EVs[i]')*abs.(shells[i])).nzind + push!(shell_bboxes, Lar.bbox(W1[vs_indexes, :])) +end + +containment_graph = Lara.pre_containment_test(shell_bboxes) +containment_graph = Lara.prune_containment_graph(n, W1, EVs, shells, containment_graph) +Lara.transitive_reduction!(containment_graph) +copEV2, copFE2 = Lara.cell_merging(n, containment_graph, W2, EVs, boundaries, shells, shell_bboxes) + + +## 4 - 3-cells identification & dangling 1-cells elimination +Plasm.view( Plasm.numbering1(0.5)((W2, copEV2, copFE2)) ) + + +# 5 - Colorfull Representation +triangulated_faces = Lar.triangulate2D(W2, [copEV2, copFE2]) +V2 = convert(Lar.Points, W2') +FVs2 = convert(Array{Lar.Cells}, triangulated_faces) +Plasm.viewcolor(V2::Lar.Points, FVs2::Array{Lar.Cells}) + +# polygonal face boundaries +EVs2 = Lar.FV2EVs(copEV2, copFE2) +EVs2 = convert(Array{Array{Array{Int64,1},1},1}, EVs2) +Plasm.viewcolor(V2::Lar.Points, EVs2::Array{Lar.Cells}) + +# 6 - Exploded Representation +model = V2,EVs2 +Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) \ No newline at end of file diff --git a/examples/2d/planar_arrangement/triangulation.jl b/examples/2d/planar_arrangement/triangulation.jl new file mode 100644 index 00000000..887e1e38 --- /dev/null +++ b/examples/2d/planar_arrangement/triangulation.jl @@ -0,0 +1,57 @@ +using LinearAlgebraicRepresentation +using Plasm +using SparseArrays +Lar = LinearAlgebraicRepresentation +Lara = Lar.Arrangement + +# Data Reading +V = [ + 0.0 0.5 3.0 5.0 2.0 2.0 0.0 1.0 0.0 3.0; + 1.0 1.0 1.0 1.0 2.0 0.0 3.0 1.5 0.0 1.5 + ]; +EV = [[1, 4], [2, 3], [5, 6], [2, 5], [3, 6], [7, 10], [8, 10], [9, 10]]; + +## 1 - Input Reading +Plasm.view(Plasm.numbering(0.5)((V,[[[k] for k=1:size(V,2)], EV]))); + +# Planar Arrangement 1 +W = convert(Lar.Points, V'); # Infering type for W = V' +copEV = Lar.coboundary_0(EV::Lar.Cells); +W1, copEV1 = Lar.planar_arrangement_1(W::Lar.Points, copEV::Lar.ChainOp); + +## 2 - 2-cells fragmentation +EV1 = Lar.cop2lar(copEV1); +V1 = convert(Lar.Points, W1'); +Plasm.view(Plasm.numbering(0.5)((V1,[[[k] for k=1:size(V1,2)], EV1]))); + +# Biconnected COmponent Evaluation +bicon_comps = Lar.Arrangement.biconnected_components(copEV1); + +## 3 - Biconnected Components +hpcs = [ Plasm.lar2hpc(V1,[EV1[e] for e in comp]) for comp in bicon_comps ] +Plasm.view([ + Plasm.color(Plasm.colorkey[(k%12)==0 ? 12 : k%12])(hpcs[k]) + for k = 1 : (length(hpcs)) +]) + +# computation of 2-cells and 2-boundary +W2, copEV2, copFE2 = Lar.planar_arrangement_2(W1, copEV1, bicon_comps) + +## 4 - 3-cells identification & dangling 1-cells elimination +Plasm.view( Plasm.numbering1(0.5)((W2, copEV2, copFE2)) ) + + +# 5 - Colorfull Representation +triangulated_faces = Lar.triangulate2D(W2, [copEV2, copFE2]) +V2 = convert(Lar.Points, W2') +FVs2 = convert(Array{Lar.Cells}, triangulated_faces) +Plasm.viewcolor(V2::Lar.Points, FVs2::Array{Lar.Cells}) + +# polygonal face boundaries +EVs2 = Lar.FV2EVs(copEV2, copFE2) +EVs2 = convert(Array{Array{Array{Int64,1},1},1}, EVs2) +Plasm.viewcolor(V2::Lar.Points, EVs2::Array{Lar.Cells}) + +# 6 - Exploded Representation +model = V2,EVs2 +Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) \ No newline at end of file From e2bc3f26093e4efb3475e061d95cd3c36954bb87 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 16:23:53 +0200 Subject: [PATCH 24/36] Adding new Test over Pipeline2 --- test/refactor_planar_arrangement.jl | 221 +++++++++++++++++++++------- 1 file changed, 170 insertions(+), 51 deletions(-) diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index e00f3829..47413199 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -63,7 +63,7 @@ Lara = LinearAlgebraicRepresentation.Arrangement end end -#--------------------------------------------------------------------------------------------------------------------------------#-------------------------------------------------------------------------------------------------------------------------------- +#-------------------------------------------------------------------------------------------------------------------------------- @testset "Biconnected Components" begin @testset "Normal Execution" begin @@ -112,62 +112,181 @@ end #-------------------------------------------------------------------------------------------------------------------------------- -@testset "Pipeline Arrangement 2 over K^4" begin +@testset "Pipeline Arrangement 2" begin - # K^4 + edge - V = [0.0 0.0; 4.0 0.0; 2.0 3.0; 2.0 1.5]; - EV = SparseArrays.sparse(Array{Int8, 2}([ - [1 1 0 0] #1 -> 1,2 - [0 1 1 0] #2 -> 2,3 - [1 0 1 0] #3 -> 3,1 - [1 0 0 1] #4 -> 1,2 - [0 1 0 1] #5 -> 2,3 - [0 0 1 1] #6 -> 3,1 - ])); - - EVs = [SparseArrays.sparse(Array{Int8, 2}([ - [-1 1 0 0] #1 -> 1,2 - [ 0 -1 1 0] #2 -> 2,3 - [-1 0 1 0] #3 -> 3,1 - [-1 0 0 1] #4 -> 1,2 - [ 0 -1 0 1] #5 -> 2,3 - [ 0 0 -1 1] #6 -> 3,1 - ]))]; - - FE = SparseArrays.sparse(Array{Int8, 2}([ - [1 0 0 1 1 0] #1 -> 1,4,5 - [0 1 0 0 1 1] #2 -> 2,5,6 - [0 0 1 1 0 1] #3 -> 3,4,6 - [1 1 1 0 0 0] #4 -> 1,2,3 External - ])); - - boundaries = [SparseArrays.sparse(Array{Int8, 2}([ - [ 1 0 0 -1 1 0] #1 -> 1,4,5 - [ 0 1 0 0 -1 1] #2 -> 2,5,6 - [ 0 0 -1 1 0 -1] #3 -> 3,4,6 - ]))]; - - bicon_comps = [[1, 2, 3, 4, 5, 6]]; - - @testset "get_external_cycle" begin - @test Lara.get_external_cycle(V, EV, FE) == 4; - @test typeof(Lara.get_external_cycle(V, EV, FV[1:3,:])) == Nothing + @testset "Containment Boxes on Nested Triangular" begin + V = [ + 0.0 8.0 4.0 2.0 6.0 4.0; + 0.0 0.0 6.0 2.0 2.0 5.0 + ]; + end - @testset "Biconnected Components 2" begin - @test length(Lara.biconnected_components(EV)) == 1; - @test sort(Lara.biconnected_components(EV)[1]) == bicon_comps; + @testset "Pipeline Arrangement 2 over K^4" begin + + # K^4 + edge + W = [0.0 0.0; 4.0 0.0; 2.0 3.0; 2.0 1.5]; + copEV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0] #1 -> 1,2 + [0 1 1 0] #2 -> 2,3 + [1 0 1 0] #3 -> 3,1 + [1 0 0 1] #4 -> 1,2 + [0 1 0 1] #5 -> 2,3 + [0 0 1 1] #6 -> 3,1 + ])); + + copFE = SparseArrays.sparse(Array{Int8, 2}([ + [1 0 0 1 1 0] #1 -> 1,4,5 + [0 1 0 0 1 1] #2 -> 2,5,6 + [0 0 1 1 0 1] #3 -> 3,4,6 + [1 1 1 0 0 0] #4 -> 1,2,3 External + ])); + + bicon_comps = [[1, 2, 3, 4, 5, 6]]; + + @testset "External Cycle" begin + @test Lara.get_external_cycle(W, copEV, copFE) == 4; + @test typeof(Lara.get_external_cycle(W, copEV, copFE[1:3,:])) == Nothing + end + + @testset "Biconnected Components" begin + @test length(Lara.biconnected_components(copEV)) == 1; + @test sort(Lara.biconnected_components(copEV)[1]) == bicon_comps; + end + + @testset "Complete Component Graph" begin + EVs = [SparseArrays.sparse(Array{Int8, 2}([ + [-1 1 0 0] #1 -> 1,2 + [ 0 -1 1 0] #2 -> 2,3 + [-1 0 1 0] #3 -> 3,1 + [-1 0 0 1] #4 -> 1,2 + [ 0 -1 0 1] #5 -> 2,3 + [ 0 0 -1 1] #6 -> 3,1 + ]))]; + + boundaries = [SparseArrays.sparse(Array{Int8, 2}([ + [ 1 0 0 -1 1 0] #1 -> 1,4,5 + [ 0 1 0 0 -1 1] #2 -> 2,5,6 + [ 0 0 -1 1 0 -1] #3 -> 3,4,6 + ]))]; + + @test Lara.componentgraph(W, copEV, bicon_comps)[1] == 1; + @test Lara.componentgraph(W, copEV, bicon_comps)[2] == (1, 1); + @test Lara.componentgraph(W, copEV, bicon_comps)[3] == V; + @test Lara.componentgraph(W, copEV, bicon_comps)[4] == EVs; + @test Lara.componentgraph(W, copEV, bicon_comps)[5] == boundaries; + @test Lara.componentgraph(W, copEV, bicon_comps)[6] == [sparse(Array{Int8}([-1; -1; 1; 0; 0; 0]))]; + @test Lara.componentgraph(W, copEV, bicon_comps)[7] == [([0.0 0.0], [4.0 3.0])]; + end end + @testset "Pipeline Arrangement 2 over planar_tile" begin + W = [ + 0.0 0.0; 0.4 0.0; 0.5 0.0; 0.6 0.0; 1.0 0.0; + 0.0 0.4; 1.0 0.4; + 0.0 0.5; 1.0 0.5; + 0.0 0.6; 1.0 0.6; + 0.0 1.0; 0.4 1.0; 0.5 1.0; 0.6 1.0; 1.0 1.0; + 0.5 0.5 + ]; + copEV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] #1 -> 1 2 + [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] #2 -> 1 6 + [0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] #3 -> 2 6 + [0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0] #4 -> 4 5 + [0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0] #5 -> 4 7 + [0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0] #6 -> 5 7 - @test Lara.componentgraph(V, copEV, bicon_comps)[1] == 1; - @test Lara.componentgraph(V, copEV, bicon_comps)[2] == (1, 1); - @test Lara.componentgraph(V, copEV, bicon_comps)[3] == V; - @test Lara.componentgraph(V, copEV, bicon_comps)[4] == EVs; - @test Lara.componentgraph(V, copEV, bicon_comps)[5] == boundaries; - @test Lara.componentgraph(V, copEV, bicon_comps)[6] == [sparse(Array{Int8}([-1; -1; 1; 0; 0; 0]))]; - @test Lara.componentgraph(V, copEV, bicon_comps)[7] == [([0.0 0.0], [4.0 3.0])]; - + [0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0] #7 -> 10 12 + [0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0] #8 -> 10 13 + [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0] #9 -> 12 13 + [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0] #10 -> 11 15 + [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0] #11 -> 11 16 + [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0] #12 -> 15 16 + + [0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0] #13 -> 3 8 + [0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0] #14 -> 3 9 + [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1] #15 -> 3 17 + [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1] #16 -> 8 17 + [0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0] #17 -> 8 14 + [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1] #18 -> 9 17 + [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0] #19 -> 9 14 + [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1] #20 -> 14 17 + ])); + + copFE = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] #1 -> 1,2,3 + [0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] #2 -> 4,5,6 + [0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0] #3 -> 7,8,9 + [0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0] #4 -> 10,11,12 + [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0] #5 -> 13,15,16 + [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0] #6 -> 14,15,18 + [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1] #7 -> 16,17,20 + [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1] #8 -> 18,19,20 + [1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0] #9 -> external + ])); + + bicon_comps = [ + [ 1, 2, 3], + [ 4, 5, 6], + [ 7, 8, 9], + [10, 11, 12], + [13, 14, 15, 16, 17, 18, 19, 20] + ]; + + bboxes = [ + ([0.0 0.0], [1.0 1.0]) + ([0.0 0.0], [0.4 0.4]) + ([0.6 0.0], [1.0 0.4]) + ([0.0 0.6], [0.4 1.0]) + ([0.6 0.6], [1.0 1.0]) + ]; + + @testset "External Cycle" begin + @test Lara.get_external_cycle(W, copEV, copFE) == 9; + @test typeof(Lara.get_external_cycle(W, copEV, copFE[1:8,:])) == Nothing + end + + @testset "Biconnected Components" begin + @test length(Lara.biconnected_components(copEV)) == 5; + @test sort(sort(Lara.biconnected_components(copEV))[1]) == bicon_comps[1]; + @test sort(sort(Lara.biconnected_components(copEV))[2]) == bicon_comps[2]; + @test sort(sort(Lara.biconnected_components(copEV))[3]) == bicon_comps[3]; + @test sort(sort(Lara.biconnected_components(copEV))[4]) == bicon_comps[4]; + @test sort(sort(Lara.biconnected_components(copEV))[5]) == bicon_comps[5]; + end + + @testset "Containment Boxes" begin + pre_containment = SparseArrays.sparse(Array{Int8, 2}([ + [0 0 0 0 0] + [1 0 0 0 0] + [1 0 0 0 0] + [1 0 0 0 0] + [1 0 0 0 0] + ])); + @test Lara.pre_containment_test(bboxes) == pre_containment; + end + + @testset "Complete Component Graph" begin + shells = [ + sparse(Array{Int8}([-1; 1; -1])), + sparse(Array{Int8}([-1; 1; -1])), + sparse(Array{Int8}([ 1; -1; 1])), + sparse(Array{Int8}([ 1; -1; 1])), + sparse(Array{Int8}([ 1; -1; 0; 0; 1; 0; -1; 0])) + ]; + + @test Lara.componentgraph(W, copEV, bicon_comps)[1] == 5; + @test Lara.componentgraph(W, copEV, bicon_comps)[2] == SparseArrays.spzeros(Int8, 5, 5); + @test Lara.componentgraph(W, copEV, bicon_comps)[3] == W; + # @test abs(Lara.componentgraph(W, copEV, bicon_comps)[4]) == EV; + # @test abs(Lara.componentgraph(W, copEV, bicon_comps)[5]) == boundaries; + @test Lara.componentgraph(W, copEV, bicon_comps)[6] == shells; + @test Lara.componentgraph(W, copEV, bicon_comps)[7] == bboxes; + end + + + end end \ No newline at end of file From 048eb81e145c9cbde531af4455aa3cfa8edf2e09 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 16:57:39 +0200 Subject: [PATCH 25/36] Updating Tests --- test/refactor_planar_arrangement.jl | 54 ++++++++++++++++++++++++++--- 1 file changed, 49 insertions(+), 5 deletions(-) diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index 47413199..8e69af19 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -115,11 +115,55 @@ end @testset "Pipeline Arrangement 2" begin @testset "Containment Boxes on Nested Triangular" begin - V = [ - 0.0 8.0 4.0 2.0 6.0 4.0; - 0.0 0.0 6.0 2.0 2.0 5.0 + W = [0.0 0.0; 8.0 0.0; 4.0 6.0; 2.0 2.0; 6.0 2.0; 4.0 5.0; 9.0 0.0; 13.0 0.0; 11.0 3.0]; + copEV = SparseArrays.sparse(Array{Int8, 2}([ + [1 1 0 0 0 0 0 0 0] #1 -> 1,2 + [0 1 1 0 0 0 0 0 0] #2 -> 2,3 + [1 0 1 0 0 0 0 0 0] #3 -> 3,1 + [0 0 0 1 1 0 0 0 0] #4 -> 4,5 + [0 0 0 0 1 1 0 0 0] #5 -> 5,6 + [0 0 0 1 0 1 0 0 0] #6 -> 4,6 + [0 0 0 0 0 0 1 1 0] #7 -> 7,8 + [0 0 0 0 0 0 0 1 1] #8 -> 8,9 + [0 0 0 0 0 0 1 0 1] #9 -> 7,9 + ])); + + EVs = [ + SparseArrays.sparse(Array{Int8, 2}([ + [-1 1 0 0 0 0 0 0 0] #1 -> 1,2 + [ 0 -1 1 0 0 0 0 0 0] #2 -> 2,3 + [-1 0 1 0 0 0 0 0 0] #3 -> 3,1 + ])), + SparseArrays.sparse(Array{Int8, 2}([ + [0 0 0 -1 1 0 0 0 0] #4 -> 4,5 + [0 0 0 0 -1 1 0 0 0] #5 -> 5,6 + [0 0 0 -1 0 1 0 0 0] #6 -> 4,6 + ])), + SparseArrays.sparse(Array{Int8, 2}([ + [0 0 0 0 0 0 -1 1 0] #7 -> 7,8 + [0 0 0 0 0 0 0 -1 1] #8 -> 8,9 + [0 0 0 0 0 0 -1 0 1] #9 -> 7,9 + ])) ]; - + + shells = [ + SparseArrays.sparse(Array{Int8}([-1; -1; 1])), + SparseArrays.sparse(Array{Int8}([-1; -1; 1])), + SparseArrays.sparse(Array{Int8}([-1; -1; 1])), + ]; + + bicon_comps = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]; + shell_bboxes = [([0.0 0.0], [8.0 6.0]), ([2.0 2.0], [6.0 5.0]), ([6.0 4.0], [8.0 6.0])]; + precontainment = sparse(Array{Int8,2}([[0 0 0]; [1 0 0]; [1 0 0]])); + containment_graph = sparse(Array{Int8,2}([[0 0 0]; [1 0 0]; [0 0 0]])); + transitive = containment_graph; + + @test Lara.pre_containment_test(shell_bboxes) == precontainment; + @test Lara.prune_containment_graph(3, W, EVs, shells, containment_graph) == containment_graph; + + Lar.Arrangement.transitive_reduction!(containment_graph) + + @test containment_graph == transitive; end @testset "Pipeline Arrangement 2 over K^4" begin @@ -151,7 +195,7 @@ end @testset "Biconnected Components" begin @test length(Lara.biconnected_components(copEV)) == 1; - @test sort(Lara.biconnected_components(copEV)[1]) == bicon_comps; + @test sort(Lara.biconnected_components(copEV)[1]) == bicon_comps[1]; end @testset "Complete Component Graph" begin From 745e07a2463398c912929dd04b0276758d63a7a2 Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 17:09:54 +0200 Subject: [PATCH 26/36] Fixing Tests Error --- test/refactor_planar_arrangement.jl | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index 8e69af19..e23edce5 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -215,8 +215,8 @@ end ]))]; @test Lara.componentgraph(W, copEV, bicon_comps)[1] == 1; - @test Lara.componentgraph(W, copEV, bicon_comps)[2] == (1, 1); - @test Lara.componentgraph(W, copEV, bicon_comps)[3] == V; + @test size(Lara.componentgraph(W, copEV, bicon_comps)[2]) == (1, 1); + @test Lara.componentgraph(W, copEV, bicon_comps)[3] == W; @test Lara.componentgraph(W, copEV, bicon_comps)[4] == EVs; @test Lara.componentgraph(W, copEV, bicon_comps)[5] == boundaries; @test Lara.componentgraph(W, copEV, bicon_comps)[6] == [sparse(Array{Int8}([-1; -1; 1; 0; 0; 0]))]; @@ -281,11 +281,11 @@ end ]; bboxes = [ - ([0.0 0.0], [1.0 1.0]) ([0.0 0.0], [0.4 0.4]) ([0.6 0.0], [1.0 0.4]) ([0.0 0.6], [0.4 1.0]) ([0.6 0.6], [1.0 1.0]) + ([0.0 0.0], [1.0 1.0]) ]; @testset "External Cycle" begin @@ -304,11 +304,11 @@ end @testset "Containment Boxes" begin pre_containment = SparseArrays.sparse(Array{Int8, 2}([ + [0 0 0 0 1] + [0 0 0 0 1] + [0 0 0 0 1] + [0 0 0 0 1] [0 0 0 0 0] - [1 0 0 0 0] - [1 0 0 0 0] - [1 0 0 0 0] - [1 0 0 0 0] ])); @test Lara.pre_containment_test(bboxes) == pre_containment; end From 63d2c2e8dc3a3827767e4662e662d2412d7f832d Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 18:16:58 +0200 Subject: [PATCH 27/36] Pre Submit --- docs/src/planar_arrangement.md | 29 ++++++++++ src/arrangement/planar_arrangement.jl | 50 +++++++++-------- test/refactor_planar_arrangement.jl | 81 +++++++++++++++++++-------- 3 files changed, 114 insertions(+), 46 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 96f9ba1d..4c7c7da8 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -155,10 +155,39 @@ Lar.Arrangement.cell_merging #### Component graph evaluation Component Graph evaluation relies on different functions that could be use separatelly in order to obtain different results. +First of all we use the following function on each biconnected component +in order to gain the faces of the complex: ```@docs Lar.Arrangement.get_external_cycle +``` + + + +Then a containment graph is build in order to clarify if some biconnected component +relies in another biconnected component. To do so, the approach is similiar to what +we did with the 2-cells decomposition. We firstly build the bounding box of each +component and we check whether they are one inside the other via: +```@docs Lar.Arrangement.pre_containment_test +``` + + + +Then we prune the resulting mapping using: +```@docs Lar.Arrangement.prune_containment_graph +``` +In order to do so we take each biconnected component ``\phi`` whose bounding box is inside +the bounding box of ``\psi`` (``\foreach \psi``) and we check if a point of ``phi`` is or is not +on the possible ``\psi`` 3-cells. +Do note that it is sufficient checking one single point since we know in advance +that each couple of biconnected components is intersection free. Therefore if a single +point of ``\phi`` is inside a biconnected component ``\psi`` then ``\phi \subset \psi``. + + +However if three or more faces are nested one into the other, then the mapping +is redundant. We therefore eliminate this redundany by applying: +```@docs Lar.Arrangement.transitive_reduction! ``` diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index 21e8b985..a19b8097 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -523,9 +523,8 @@ end Generate the containment graph associated to `bboxes`. The function evaluate a `SparseArrays{Int8, n, n}` PRE-containmnet graph in the sense -that it contains redundancies that must be pruned (where `n = length(bboxes)`) - -The graph element `(i, j)` is **1** if the axis aligned bounding box of `bboxes[j]` contains `bboxes[i]`. +that it stores `1` when the bbox associated to the `i`-th component contains entirely +the bbox associated to the `j`-th one. (where `n = length(bboxes)`) See also: - [`Lar.Arrangement.componentgraph`](@ref). @@ -572,23 +571,16 @@ end """ prune_containment_graph(n, V, EVs, shells, graph) -Prunes the containment `graph` from the non-intersecting faces. +Prunes the containment `graph` from the non-included faces. -This method prunes the containment graph eliminating the intersecting bouning boxes -that not corresponds to intersectring faces. +This method prunes the containment graph eliminating the included bouning boxes +that not corresponds to included faces. -Do note that this method expects to work on biconnectet clusters of faces; in fact -it only checks for one point to see if the faces are intersecting. +Do note that this method expects to work on biconnectet clusters of faces. See also: - [`Lar.Arrangement.componentgraph`](@ref). - [`Lar.point_in_face`](@ref). - ---- - -# Examples -```jldoctest - ``` """ function prune_containment_graph(n, V, EVs, shells, graph) @@ -619,7 +611,10 @@ end """ transitive_reduction!(graph) -More goes HERE... +Prune the redundancies in containment `graph`. + +The ``m``-layer containment `graph` is reduced to the 1-layer containment `graph` +where only the first level nested components are considered. See also: [`Lar.Arrangement.componentgraph`](@ref). @@ -627,7 +622,25 @@ See also: [`Lar.Arrangement.componentgraph`](@ref). # Examples ```jldoctest +julia> containment = [ + 0 0 0 0 0 0 + 0 0 0 0 0 0 + 1 0 0 0 0 0 + 1 0 0 0 0 0 + 1 0 1 0 0 0 + 1 0 1 0 1 0 + ]; +julia> transitive_reduction!(containment) + +julia> containment +6×6 Array{Int64,2}: + 0 0 0 0 0 0 + 0 0 0 0 0 0 + 1 0 0 0 0 0 + 1 0 0 0 0 0 + 0 0 1 0 0 0 + 0 0 0 0 1 0 ``` """ function transitive_reduction!(graph) @@ -654,13 +667,6 @@ Cells composing for the Topological Gift Wrapping algorithm. This is the online part of the TGW algorithm. See also: [`Lar.Arrangement.planar_arrangement_2`](@ref). - ---- - -# Examples -```jldoctest - -``` """ function cell_merging(n, containment_graph, V, EVs, boundaries, shells, shell_bboxes) function bboxes(V::Lar.Points, indexes::Lar.ChainOp) diff --git a/test/refactor_planar_arrangement.jl b/test/refactor_planar_arrangement.jl index e23edce5..3c743a7c 100644 --- a/test/refactor_planar_arrangement.jl +++ b/test/refactor_planar_arrangement.jl @@ -115,34 +115,46 @@ end @testset "Pipeline Arrangement 2" begin @testset "Containment Boxes on Nested Triangular" begin - W = [0.0 0.0; 8.0 0.0; 4.0 6.0; 2.0 2.0; 6.0 2.0; 4.0 5.0; 9.0 0.0; 13.0 0.0; 11.0 3.0]; + W = [ + 0.0 0.0; 8.0 0.0; 4.0 6.0; + 2.0 2.0; 6.0 2.0; 4.0 5.0; + 8.0 1.0; 5.0 6.0; 8.0 6.0; + 3.0 3.0; 5.0 3.0; 4.0 4.0]; copEV = SparseArrays.sparse(Array{Int8, 2}([ - [1 1 0 0 0 0 0 0 0] #1 -> 1,2 - [0 1 1 0 0 0 0 0 0] #2 -> 2,3 - [1 0 1 0 0 0 0 0 0] #3 -> 3,1 - [0 0 0 1 1 0 0 0 0] #4 -> 4,5 - [0 0 0 0 1 1 0 0 0] #5 -> 5,6 - [0 0 0 1 0 1 0 0 0] #6 -> 4,6 - [0 0 0 0 0 0 1 1 0] #7 -> 7,8 - [0 0 0 0 0 0 0 1 1] #8 -> 8,9 - [0 0 0 0 0 0 1 0 1] #9 -> 7,9 + [1 1 0 0 0 0 0 0 0 0 0 0] # 1 -> 1,2 + [0 1 1 0 0 0 0 0 0 0 0 0] # 2 -> 2,3 + [1 0 1 0 0 0 0 0 0 0 0 0] # 3 -> 3,1 + [0 0 0 1 1 0 0 0 0 0 0 0] # 4 -> 4,5 + [0 0 0 0 1 1 0 0 0 0 0 0] # 5 -> 5,6 + [0 0 0 1 0 1 0 0 0 0 0 0] # 6 -> 4,6 + [0 0 0 0 0 0 1 1 0 0 0 0] # 7 -> 7,8 + [0 0 0 0 0 0 0 1 1 0 0 0] # 8 -> 8,9 + [0 0 0 0 0 0 1 0 1 0 0 0] # 9 -> 7,9 + [0 0 0 0 0 0 0 0 0 1 1 0] #10 -> 10,11 + [0 0 0 0 0 0 0 0 0 0 1 1] #11 -> 11,12 + [0 0 0 0 0 0 0 0 0 1 0 1] #12 -> 10,12 ])); EVs = [ SparseArrays.sparse(Array{Int8, 2}([ - [-1 1 0 0 0 0 0 0 0] #1 -> 1,2 - [ 0 -1 1 0 0 0 0 0 0] #2 -> 2,3 - [-1 0 1 0 0 0 0 0 0] #3 -> 3,1 + [-1 1 0 0 0 0 0 0 0 0 0 0] #1 -> 1,2 + [ 0 -1 1 0 0 0 0 0 0 0 0 0] #2 -> 2,3 + [-1 0 1 0 0 0 0 0 0 0 0 0] #3 -> 3,1 + ])), + SparseArrays.sparse(Array{Int8, 2}([ + [0 0 0 -1 1 0 0 0 0 0 0 0] #4 -> 4,5 + [0 0 0 0 -1 1 0 0 0 0 0 0] #5 -> 5,6 + [0 0 0 -1 0 1 0 0 0 0 0 0] #6 -> 4,6 ])), SparseArrays.sparse(Array{Int8, 2}([ - [0 0 0 -1 1 0 0 0 0] #4 -> 4,5 - [0 0 0 0 -1 1 0 0 0] #5 -> 5,6 - [0 0 0 -1 0 1 0 0 0] #6 -> 4,6 + [0 0 0 0 0 0 -1 1 0 0 0 0] #7 -> 7,8 + [0 0 0 0 0 0 0 -1 1 0 0 0] #8 -> 8,9 + [0 0 0 0 0 0 -1 0 1 0 0 0] #9 -> 7,9 ])), SparseArrays.sparse(Array{Int8, 2}([ - [0 0 0 0 0 0 -1 1 0] #7 -> 7,8 - [0 0 0 0 0 0 0 -1 1] #8 -> 8,9 - [0 0 0 0 0 0 -1 0 1] #9 -> 7,9 + [0 0 0 0 0 0 0 0 0 -1 1 0] #10 -> 10,11 + [0 0 0 0 0 0 0 0 0 0 -1 1] #11 -> 11,12 + [0 0 0 0 0 0 0 0 0 -1 0 1] #12 -> 10,12 ])) ]; @@ -150,13 +162,34 @@ end SparseArrays.sparse(Array{Int8}([-1; -1; 1])), SparseArrays.sparse(Array{Int8}([-1; -1; 1])), SparseArrays.sparse(Array{Int8}([-1; -1; 1])), + SparseArrays.sparse(Array{Int8}([-1; -1; 1])), ]; - bicon_comps = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]; - shell_bboxes = [([0.0 0.0], [8.0 6.0]), ([2.0 2.0], [6.0 5.0]), ([6.0 4.0], [8.0 6.0])]; - precontainment = sparse(Array{Int8,2}([[0 0 0]; [1 0 0]; [1 0 0]])); - containment_graph = sparse(Array{Int8,2}([[0 0 0]; [1 0 0]; [0 0 0]])); - transitive = containment_graph; + bicon_comps = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]; + shell_bboxes = [ + ([0.0 0.0], [8.0 6.0]), + ([2.0 2.0], [6.0 5.0]), + ([5.0 1.0], [8.0 6.0]), + ([3.0 3.0], [5.0 4.0]) + ]; + precontainment = sparse(Array{Int8,2}([ + [0 0 0 0] + [1 0 0 0] + [1 0 0 0] + [1 1 0 0] + ])); + containment_graph = sparse(Array{Int8,2}([ + [0 0 0 0] + [1 0 0 0] + [0 0 0 0] + [1 1 0 0] + ])); + transitive = sparse(Array{Int8,2}([ + [0 0 0 0] + [1 0 0 0] + [0 0 0 0] + [0 1 0 0] + ])); @test Lara.pre_containment_test(shell_bboxes) == precontainment; @test Lara.prune_containment_graph(3, W, EVs, shells, containment_graph) == containment_graph; From 38bfc32bb400163ac732b2b9c4cb9021fcced5aa Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Tue, 23 Apr 2019 18:30:25 +0200 Subject: [PATCH 28/36] Last Step --- docs/src/planar_arrangement.md | 2 +- src/arrangement/planar_arrangement.jl | 19 ++++++++++++++----- 2 files changed, 15 insertions(+), 6 deletions(-) diff --git a/docs/src/planar_arrangement.md b/docs/src/planar_arrangement.md index 4c7c7da8..1e31c8c8 100644 --- a/docs/src/planar_arrangement.md +++ b/docs/src/planar_arrangement.md @@ -178,7 +178,7 @@ Then we prune the resulting mapping using: Lar.Arrangement.prune_containment_graph ``` In order to do so we take each biconnected component ``\phi`` whose bounding box is inside -the bounding box of ``\psi`` (``\foreach \psi``) and we check if a point of ``phi`` is or is not +the bounding box of ``\psi`` (``\forall \psi``) and we check if a point of ``phi`` is or is not on the possible ``\psi`` 3-cells. Do note that it is sufficient checking one single point since we know in advance that each couple of biconnected components is intersection free. Therefore if a single diff --git a/src/arrangement/planar_arrangement.jl b/src/arrangement/planar_arrangement.jl index a19b8097..a6af963e 100644 --- a/src/arrangement/planar_arrangement.jl +++ b/src/arrangement/planar_arrangement.jl @@ -876,7 +876,11 @@ gives back the dropped model and and a vector `todel` of the 2-cells to drop. # Examples ```jldoctest # Nested Triangles -julia> V = [0.0 0.0; 2.0 0.0; 4.0 0.0; 1.0 1.5; 3.0 1.5; 2.0 3.0; 2.0 -3.; -2. 3.0; 6.0 3.0]; +julia> V = [ + 0.0 0.0; 2.0 0.0; 4.0 0.0; + 1.0 1.5; 3.0 1.5; 2.0 3.0; + 2.0 -3.; -2. 3.0; 6.0 3.0 + ]; julia> copEV = SparseArrays.sparse(Array{Int8, 2}([ [1 0 1 0 0 0 0 0 0] #1 -> 1,3 @@ -1074,7 +1078,9 @@ end """ - function planar_arrangement_2(V, copEV, bicon_comps[, sigma[, return_edge_map[, multiproc]]]) + function planar_arrangement_2(V, copEV, bicon_comps + [, sigma[, return_edge_map[, multiproc]]] + ) Second part of arrangement's algorithmic pipeline. @@ -1107,7 +1113,9 @@ julia> EV = SparseArrays.sparse(Array{Int8, 2}([ [0 0 0 0 0 1 1] ])); -julia> Plasm.view(Plasm.numbering(0.5)((W,[[[k] for k=1:size(W,2)], Lar.cop2lar(EV)]))); +julia> Plasm.view(Plasm.numbering(0.5)( + (W,[[[k] for k=1:size(W,2)], Lar.cop2lar(EV)]) + )); julia> bicon_comps = Lar.Arrangement.biconnected_components(EV); @@ -1141,8 +1149,9 @@ end """ - planar_arrangement(V::Points, copEV::ChainOp - [, sigma::Chain[, return_edge_map::Bool[, multiproc::Bool]]]) + planar_arrangement(V::Points, copEV::ChainOp + [, sigma::Chain[, return_edge_map::Bool[, multiproc::Bool]]] + ) Compute the arrangement on the given cellular complex 1-skeleton in 2D. Whole arrangement's algorithmic pipeline. From 738f824087cde82b6c70608036f3160cab5b268a Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Tue, 23 Apr 2019 18:40:29 +0200 Subject: [PATCH 29/36] Update .travis.yml --- .travis.yml | 1 - 1 file changed, 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 7d6b2338..98fd0b72 100644 --- a/.travis.yml +++ b/.travis.yml @@ -16,7 +16,6 @@ julia: matrix: allow_failures: - julia: nightly - - julia: 0.7 notifications: email: false From b8a3e053afeae5664cba01c93f91f6ad6bfe01bc Mon Sep 17 00:00:00 2001 From: eOnofri04 Date: Fri, 26 Apr 2019 15:12:00 +0200 Subject: [PATCH 30/36] Fixing 2d example --- examples/2d/planar_arrangement/planar_tile.jl | 21 +++++++++++-------- 1 file changed, 12 insertions(+), 9 deletions(-) diff --git a/examples/2d/planar_arrangement/planar_tile.jl b/examples/2d/planar_arrangement/planar_tile.jl index 02717f97..8edcebd4 100644 --- a/examples/2d/planar_arrangement/planar_tile.jl +++ b/examples/2d/planar_arrangement/planar_tile.jl @@ -48,8 +48,6 @@ Plasm.view([ # computation of 2-cells and 2-boundary -# n, containment_graph, W2, EVs, boundaries, shells, shell_bboxes = Lara.componentgraph(W1, copEV1, bicon_comps) - n = size(bicon_comps, 1) shells = Array{Lar.Chain, 1}(undef, n) boundaries = Array{Lar.ChainOp, 1}(undef, n) @@ -57,9 +55,9 @@ EVs = Array{Lar.ChainOp, 1}(undef, n) # for each component for p=1:n ev = copEV1[sort(bicon_comps[p]), :] - fe = Lara.minimal_2cycles(W1, ev) + fe = Lara.minimal_2cycles(W1, ev) global shell_num = Lara.get_external_cycle(W1, ev, fe) - EVs[p] = ev + EVs[p] = ev global tokeep = setdiff(1:fe.m, shell_num) boundaries[p] = fe[tokeep, :] shells[p] = fe[shell_num, :] @@ -72,9 +70,14 @@ for i in 1:n end containment_graph = Lara.pre_containment_test(shell_bboxes) -containment_graph = Lara.prune_containment_graph(n, W1, EVs, shells, containment_graph) -Lara.transitive_reduction!(containment_graph) -copEV2, copFE2 = Lara.cell_merging(n, containment_graph, W2, EVs, boundaries, shells, shell_bboxes) +containment_graph = Lara.prune_containment_graph( + n, W1, EVs, shells, containment_graph +) +Lara.transitive_reduction!(containment_graph) +W2 = W1; +copEV2, copFE2 = Lara.cell_merging( + n, containment_graph, W2, EVs, boundaries, shells, shell_bboxes +) ## 4 - 3-cells identification & dangling 1-cells elimination @@ -88,10 +91,10 @@ FVs2 = convert(Array{Lar.Cells}, triangulated_faces) Plasm.viewcolor(V2::Lar.Points, FVs2::Array{Lar.Cells}) # polygonal face boundaries -EVs2 = Lar.FV2EVs(copEV2, copFE2) +EVs2 = Lar.FV2EVs(copEV2, copFE2) EVs2 = convert(Array{Array{Array{Int64,1},1},1}, EVs2) Plasm.viewcolor(V2::Lar.Points, EVs2::Array{Lar.Cells}) # 6 - Exploded Representation model = V2,EVs2 -Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) \ No newline at end of file +Plasm.view(Plasm.lar_exploded(model)(1.2,1.2,1.2)) From caa15fc4c2ad90b7ffa4d1d6c3ab6b0eb5bbb5fc Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 12:41:55 +0200 Subject: [PATCH 31/36] Update mapper.jl --- src/mapper.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/src/mapper.jl b/src/mapper.jl index cac677e3..0d398d59 100644 --- a/src/mapper.jl +++ b/src/mapper.jl @@ -1,4 +1,5 @@ using DataStructures +using Plasm Lar = LinearAlgebraicRepresentation cuboidGrid = larCuboids From 38b75a3111695fd84ef754aa812ba47c149c58de Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 12:45:28 +0200 Subject: [PATCH 32/36] Update REQUIRE --- REQUIRE | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/REQUIRE b/REQUIRE index ff1f67ea..ebaaed4a 100644 --- a/REQUIRE +++ b/REQUIRE @@ -2,4 +2,5 @@ julia 1.0 NearestNeighbors IntervalTrees DataStructures -Triangle \ No newline at end of file +Triangle +Plasm From f020c31e3866a33d5b7189b32037feee72fd4c06 Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 12:50:51 +0200 Subject: [PATCH 33/36] Update .travis.yml --- .travis.yml | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/.travis.yml b/.travis.yml index 98fd0b72..325443dc 100644 --- a/.travis.yml +++ b/.travis.yml @@ -20,6 +20,10 @@ matrix: notifications: email: false +install: + - if [[ "$TRAVIS_JULIA_VERSION" != "0.6.4" ]]; then + julia -e 'using Pkg; Pkg.add(PackageSpec(url="https://github.com/cvdlab/Plasm.jl", rev="julia-1.0"))'; + fi after_success: - julia -e 'using Pkg; Pkg.add("Documenter"); Pkg.add("Coverage");' - julia -e 'import LinearAlgebraicRepresentation; cd(dirname(dirname(pathof(LinearAlgebraicRepresentation)))); include(joinpath("docs", "make.jl"))' From ff6cc52228800faafbf7dc04274d03276a4150f9 Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 13:40:36 +0200 Subject: [PATCH 34/36] [ci skip] back1 --- REQUIRE | 1 - 1 file changed, 1 deletion(-) diff --git a/REQUIRE b/REQUIRE index ebaaed4a..672a74c0 100644 --- a/REQUIRE +++ b/REQUIRE @@ -3,4 +3,3 @@ NearestNeighbors IntervalTrees DataStructures Triangle -Plasm From 11b88bd5dead9346dee7749884779a35df80034c Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 13:41:11 +0200 Subject: [PATCH 35/36] Update mapper.jl --- src/mapper.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/src/mapper.jl b/src/mapper.jl index 0d398d59..cac677e3 100644 --- a/src/mapper.jl +++ b/src/mapper.jl @@ -1,5 +1,4 @@ using DataStructures -using Plasm Lar = LinearAlgebraicRepresentation cuboidGrid = larCuboids From 6ac6109f527f733ae697256b54fc591f6c318842 Mon Sep 17 00:00:00 2001 From: Elia Onofri <30669145+eOnofri04@users.noreply.github.com> Date: Mon, 3 Jun 2019 13:41:19 +0200 Subject: [PATCH 36/36] Update .travis.yml --- .travis.yml | 4 ---- 1 file changed, 4 deletions(-) diff --git a/.travis.yml b/.travis.yml index 325443dc..98fd0b72 100644 --- a/.travis.yml +++ b/.travis.yml @@ -20,10 +20,6 @@ matrix: notifications: email: false -install: - - if [[ "$TRAVIS_JULIA_VERSION" != "0.6.4" ]]; then - julia -e 'using Pkg; Pkg.add(PackageSpec(url="https://github.com/cvdlab/Plasm.jl", rev="julia-1.0"))'; - fi after_success: - julia -e 'using Pkg; Pkg.add("Documenter"); Pkg.add("Coverage");' - julia -e 'import LinearAlgebraicRepresentation; cd(dirname(dirname(pathof(LinearAlgebraicRepresentation)))); include(joinpath("docs", "make.jl"))'