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