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Numerical algorithms implemented in Julia

Algorithms

Currently implemented:

  • Fitting a straight line in 2 dimensions using the method of least squares
  • Fitting a plane in 3 dimensions using the method of least squares
  • Savitzky-Golay filter for 2 dimensional values
  • Approximation of parametric curves using differential equation solvers
    • Chase (Chase.jl): An object is constantly moving in the direction of another object with a constant speed value.
    • Pull (Pull.jl): An object is being pulled or pushed by another moving object through a solid, inflexible beam with $d$ length that is attached to the pulled/pushed object in question.
  • Bézier-curves:
    • Custom generation with optional noise
    • Visualization
    • Degree elevation
    • Curve splitting
  • Bezier-surfaces
    • Custom generation with optional noise
    • Visualization

TODO:

  • Prey-Predator model
  • Perpendicular and parallel plane/line fitting
  • Implement Bezier-splines, and interactive Bezier-spline manipulation
  • Implement NURBS

Gallery

Chase.jl: "Dog chasing runner"

Chase.jl

Bézier-curves

Bézier-curve in 2D space

bezier2d.gif

Bézier-curve in 3D space

bezier3d.gif

Parametric surface defined through Bézier-curves