Add Triangles.scad as a core library
This commit is contained in:
parent
0ca7062958
commit
807eca36e7
|
|
@ -0,0 +1,215 @@
|
|||
/*
|
||||
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");
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue