Add missing file

openscad/triangles.scad

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+/*
+Triangles.scad
+ Author: Tim Koopman
+ https://github.com/tkoopman/Delta-Diamond/blob/master/OpenSCAD/Triangles.scad
+
+         angleCA
+           /|\
+        a / H \ c
+         /  |  \
+ angleAB ------- angleBC
+            b
+
+Standard Parameters
+	center: true/false
+		If true same as centerXYZ = [true, true, true]
+
+	centerXYZ: Vector of 3 true/false values [CenterX, CenterY, CenterZ]
+		center must be left undef
+
+	height: The 3D height of the Triangle. Ignored if heights defined
+
+	heights: Vector of 3 height values heights @ [angleAB, angleBC, angleCA]
+		If CenterZ is true each height will be centered individually, this means
+		the shape will be different depending on CenterZ. Most times you will want
+		CenterZ to be true to get the shape most people want.
+*/
+
+/* 
+Triangle
+	a: Length of side a
+	b: Length of side b
+	angle: angle at point angleAB
+*/
+module Triangle(
+			a, b, angle, height=1, heights=undef,
+			center=undef, centerXYZ=[false,false,false])
+{
+	// Calculate Heights at each point
+	heightAB = ((heights==undef) ? height : heights[0])/2;
+	heightBC = ((heights==undef) ? height : heights[1])/2;
+	heightCA = ((heights==undef) ? height : heights[2])/2;
+	centerZ = (center || (center==undef && centerXYZ[2]))?0:max(heightAB,heightBC,heightCA);
+
+	// Calculate Offsets for centering
+	offsetX = (center || (center==undef && centerXYZ[0]))?((cos(angle)*a)+b)/3:0;
+	offsetY = (center || (center==undef && centerXYZ[1]))?(sin(angle)*a)/3:0;
+
+	pointAB1 = [-offsetX,-offsetY, centerZ-heightAB];
+	pointAB2 = [-offsetX,-offsetY, centerZ+heightAB];
+	pointBC1 = [b-offsetX,-offsetY, centerZ-heightBC];
+	pointBC2 = [b-offsetX,-offsetY, centerZ+heightBC];
+	pointCA1 = [(cos(angle)*a)-offsetX,(sin(angle)*a)-offsetY, centerZ-heightCA];
+	pointCA2 = [(cos(angle)*a)-offsetX,(sin(angle)*a)-offsetY, centerZ+heightCA];
+
+	polyhedron(
+		points=[	pointAB1, pointBC1, pointCA1,
+					pointAB2, pointBC2, pointCA2 ],
+		triangles=[	
+			[0, 1, 2],
+			[3, 5, 4],
+			[0, 3, 1],
+			[1, 3, 4],
+			[1, 4, 2],
+			[2, 4, 5],
+			[2, 5, 0],
+			[0, 5, 3] ] );
+}
+
+/*
+Isosceles Triangle
+	Exactly 2 of the following paramaters must be defined.
+	If all 3 defined H will be ignored.
+	b: length of side b
+	angle: angle at points angleAB & angleBC.
+*/
+module Isosceles_Triangle(
+			b, angle, H=undef, height=1, heights=undef,
+			center=undef, centerXYZ=[true, false, false])
+{
+	valid = 	(angle!=undef)?((angle < 90) && (b!=undef||H!=undef)) : (b!=undef&&H!=undef);
+	ANGLE = (angle!=undef) ? angle : atan(H / (b/2));
+	a = (b==undef)?(H/sin((180-(angle*2))/2)) : 
+		 (b / cos(ANGLE))/2;
+	B = (b==undef)? (cos(angle)*a)*2:b;
+	if (valid)
+	{
+		Triangle(a=a, b=B, angle=ANGLE, height=height, heights=heights,
+					center=center, centerXYZ=centerXYZ);
+	} else {
+		echo("Invalid Isosceles_Triangle. Must specify any 2 of b, angle and H, and if angle used angle must be less than 90");
+	}
+}
+
+/*
+Right Angled Triangle
+	Create a Right Angled Triangle where the hypotenuse will be calculated.
+
+       |\
+      a| \
+       |  \
+       ----
+         b
+	a: length of side a
+	b: length of side b
+*/
+module Right_Angled_Triangle(
+			a, b, height=1, heights=undef,
+			center=undef, centerXYZ=[false, false, false])
+{
+	Triangle(a=a, b=b, angle=90, height=height, heights=heights,
+				center=center, centerXYZ=centerXYZ);
+}
+
+/*
+Wedge
+	Is same as Right Angled Triangle with 2 different heights, and rotated.
+	Good for creating support structures.
+*/
+module Wedge(a, b, w1, w2)
+{
+	rotate([90,0,0])
+		Right_Angled_Triangle(a, b, heights=[w1, w2, w1], centerXYZ=[false, false, true]);
+}
+
+/*
+Equilateral Triangle
+	Create a Equilateral Triangle.
+
+	l: Length of all sides (a, b & c)
+	H: Triangle size will be based on the this 2D height
+		When using H, l is ignored.
+*/
+module Equilateral_Triangle(
+			l=10, H=undef, height=1, heights=undef,
+			center=undef, centerXYZ=[true,false,false])
+{
+	L = (H==undef)?l:H/sin(60);
+	Triangle(a=L,b=L,angle=60,height=height, heights=heights,
+				center=center, centerXYZ=centerXYZ);
+}
+
+/*
+Trapezoid
+	Create a Basic Trapezoid (Based on Isosceles_Triangle)
+
+            d
+          /----\
+         /  |   \
+     a  /   H    \ c
+       /    |     \
+ angle ------------ angle
+            b
+
+	b: Length of side b
+	angle: Angle at points angleAB & angleBC
+	H: The 2D height at which the triangle should be cut to create the trapezoid
+	heights: If vector of size 3 (Standard for triangles) both cd & da will be the same height, if vector have 4 values [ab,bc,cd,da] than each point can have different heights.
+*/
+module Trapezoid(
+			b, angle=60, H, height=1, heights=undef,
+			center=undef, centerXYZ=[true,false,false])
+{
+	validAngle = (angle < 90);
+	adX = H / tan(angle);
+
+	// Calculate Heights at each point
+	heightAB = ((heights==undef) ? height : heights[0])/2;
+	heightBC = ((heights==undef) ? height : heights[1])/2;
+	heightCD = ((heights==undef) ? height : heights[2])/2;
+	heightDA = ((heights==undef) ? height : ((len(heights) > 3)?heights[3]:heights[2]))/2;
+
+	// Centers
+	centerX = (center || (center==undef && centerXYZ[0]))?0:b/2;
+	centerY = (center || (center==undef && centerXYZ[1]))?0:H/2;
+	centerZ = (center || (center==undef && centerXYZ[2]))?0:max(heightAB,heightBC,heightCD,heightDA);
+
+	// Points
+	y = H/2;
+	bx = b/2;
+	dx = (b-(adX*2))/2;
+
+	pointAB1 = [centerX-bx, centerY-y, centerZ-heightAB];
+	pointAB2 = [centerX-bx, centerY-y, centerZ+heightAB];
+	pointBC1 = [centerX+bx, centerY-y, centerZ-heightBC];
+	pointBC2 = [centerX+bx, centerY-y, centerZ+heightBC];
+	pointCD1 = [centerX+dx, centerY+y, centerZ-heightCD];
+	pointCD2 = [centerX+dx, centerY+y, centerZ+heightCD];
+	pointDA1 = [centerX-dx, centerY+y, centerZ-heightDA];
+	pointDA2 = [centerX-dx, centerY+y, centerZ+heightDA];
+
+	validH = (adX < b/2);
+
+	if (validAngle && validH)
+	{
+		polyhedron(
+			points=[	pointAB1, pointBC1, pointCD1, pointDA1,
+						pointAB2, pointBC2, pointCD2, pointDA2 ],
+			triangles=[	
+				[0, 1, 2],
+				[0, 2, 3],
+				[4, 6, 5],
+				[4, 7, 6],
+				[0, 4, 1],
+				[1, 4, 5],
+				[1, 5, 2],
+				[2, 5, 6],
+				[2, 6, 3],
+				[3, 6, 7],
+				[3, 7, 0],
+				[0, 7, 4]	] );
+	} else {
+		if (!validAngle) echo("Trapezoid invalid, angle must be less than 90");
+		else echo("Trapezoid invalid, H is larger than triangle");
+	}
+}
+
+
+// Examples
+Triangle(a=5, b=15, angle=33, centerXYZ=[true,false,false]);
+translate([20,0,0]) Right_Angled_Triangle(a=5, b=20, centerXYZ=[false,true,false]);
+translate([45,0,0]) Wedge(a=5, b=20, w1=10, w2=5);
+translate([-20,0,0]) Trapezoid(b=20, angle=33, H=4, height=5, centerXYZ=[true,false,true]);
+
+translate([0,10,0]) Isosceles_Triangle(b=20, angle=33);
+translate([30,10,0]) Isosceles_Triangle(b=20, H=5);
+translate([-30,10,0]) Isosceles_Triangle(angle=33, H=5, center=true);
+
+translate([15,-25,0]) Equilateral_Triangle(l=20);
+translate([-15,-25,0]) Equilateral_Triangle(H=20);