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Moved trig functions to trigonometry.scad

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Garth Minette 2021-09-11 02:29:07 -07:00
parent 4c19981e97
commit 444fc57267
5 changed files with 433 additions and 483 deletions
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408
geometry.scad
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@ -334,414 +334,6 @@ function line_from_points(points, fast=false, eps=EPSILON) =
// Section: 2D Triangles
// Function: law_of_cosines()
// Usage:
// C = law_of_cosines(a, b, c);
// c = law_of_cosines(a, b, C);
// Topics: Geometry, Triangles
// Description:
// Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the
// angle in degrees for the corner opposite of the third side. Given two side lengths, and the
// angle between them, returns the length of the third side.
// Figure(2D):
// stroke([[-50,0], [10,60], [50,0]], closed=true);
// color("black") {
// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center");
// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center");
// translate([-22,35]) text(text="c", size=8, halign="center", valign="center");
// }
// color("blue") {
// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center");
// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center");
// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center");
// }
// Arguments:
// a = The length of the first side.
// b = The length of the second side.
// c = The length of the third side.
// C = The angle in degrees of the corner opposite of the third side.
function law_of_cosines(a, b, c, C) =
// Triangle Law of Cosines:
// c^2 = a^2 + b^2 - 2*a*b*cos(C)
assert(num_defined([c,C]) == 1, "Must give exactly one of c= or C=.")
is_undef(c) ? sqrt(a*a + b*b - 2*a*b*cos(C)) :
acos(constrain((a*a + b*b - c*c) / (2*a*b), -1, 1));
// Function: law_of_sines()
// Usage:
// B = law_of_sines(a, A, b);
// b = law_of_sines(a, A, B);
// Topics: Geometry, Triangles
// Description:
// Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the
// angle between them, returns the angle of the corner opposite of the second side. Given a side
// length, the opposing angle, and a second angle, returns the length of the side opposite of the
// second angle.
// Figure(2D):
// stroke([[-50,0], [10,60], [50,0]], closed=true);
// color("black") {
// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center");
// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center");
// translate([-22,35]) text(text="c", size=8, halign="center", valign="center");
// }
// color("blue") {
// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center");
// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center");
// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center");
// }
// Arguments:
// a = The length of the first side.
// A = The angle in degrees of the corner opposite of the first side.
// b = The length of the second side.
// B = The angle in degrees of the corner opposite of the second side.
function law_of_sines(a, A, b, B) =
// Triangle Law of Sines:
// a/sin(A) = b/sin(B) = c/sin(C)
assert(num_defined([b,B]) == 1, "Must give exactly one of b= or B=.")
let( r = a/sin(A) )
is_undef(b) ? r*sin(B) :
asin(constrain(b/r, -1, 1));
// Function: tri_calc()
// Usage:
// triangle = tri_calc(ang,ang2,adj,opp,hyp);
// Topics: Geometry, Triangles
// Description:
// Given a side length and an angle, or two side lengths, calculates the rest of the side lengths
// and angles of a right triangle. Returns [ADJACENT, OPPOSITE, HYPOTENUSE, ANGLE, ANGLE2] where
// ADJACENT is the length of the side adjacent to ANGLE, and OPPOSITE is the length of the side
// opposite of ANGLE and adjacent to ANGLE2. ANGLE and ANGLE2 are measured in degrees.
// This is certainly more verbose and slower than writing your own calculations, but has the nice
// benefit that you can just specify the info you have, and don't have to figure out which trig
// formulas you need to use.
// Figure(2D,NoAxes):
// color("#ccc") {
// stroke(closed=false, width=0.5, [[45,0], [45,5], [50,5]]);
// stroke(closed=false, width=0.5, arc(N=6, r=15, cp=[0,0], start=0, angle=30));
// stroke(closed=false, width=0.5, arc(N=6, r=14, cp=[50,30], start=212, angle=58));
// }
// color("black") stroke(closed=true, [[0,0], [50,30], [50,0]]);
// color("#0c0") {
// translate([10.5,2.5]) text(size=3,text="ang",halign="center",valign="center");
// translate([44.5,22]) text(size=3,text="ang2",halign="center",valign="center");
// }
// color("blue") {
// translate([25,-3]) text(size=3,text="Adjacent",halign="center",valign="center");
// translate([53,15]) rotate(-90) text(size=3,text="Opposite",halign="center",valign="center");
// translate([25,18]) rotate(30) text(size=3,text="Hypotenuse",halign="center",valign="center");
// }
// Arguments:
// ang = The angle in degrees of the primary corner of the triangle.
// ang2 = The angle in degrees of the other non-right corner of the triangle.
// adj = The length of the side adjacent to the primary corner.
// opp = The length of the side opposite to the primary corner.
// hyp = The length of the hypotenuse.
// Example:
// tri = tri_calc(opp=15,hyp=30);
// echo(adjacent=tri[0], opposite=tri[1], hypotenuse=tri[2], angle=tri[3], angle2=tri[4]);
// Examples:
// adj = tri_calc(ang=30,opp=10)[0];
// opp = tri_calc(ang=20,hyp=30)[1];
// hyp = tri_calc(ang2=50,adj=20)[2];
// ang = tri_calc(adj=20,hyp=30)[3];
// ang2 = tri_calc(adj=20,hyp=40)[4];
function tri_calc(ang,ang2,adj,opp,hyp) =
assert(ang==undef || ang2==undef,"At most one angle is allowed.")
assert(num_defined([ang,ang2,adj,opp,hyp])==2, "Exactly two arguments must be given.")
let(
ang = ang!=undef
? assert(ang>0&&ang<90, "The input angles should be acute angles." ) ang
: ang2!=undef ? (90-ang2)
: adj==undef ? asin(constrain(opp/hyp,-1,1))
: opp==undef ? acos(constrain(adj/hyp,-1,1))
: atan2(opp,adj),
ang2 = ang2!=undef
? assert(ang2>0&&ang2<90, "The input angles should be acute angles." ) ang2
: (90-ang),
adj = adj!=undef
? assert(adj>0, "Triangle side lengths should be positive." ) adj
: (opp!=undef? (opp/tan(ang)) : (hyp*cos(ang))),
opp = opp!=undef
? assert(opp>0, "Triangle side lengths should be positive." ) opp
: (adj!=undef? (adj*tan(ang)) : (hyp*sin(ang))),
hyp = hyp!=undef
? assert(hyp>0, "Triangle side lengths should be positive." )
assert(adj<hyp && opp<hyp, "Hyphotenuse length should be greater than the other sides." )
hyp
: (adj!=undef? (adj/cos(ang))
: (opp/sin(ang)))
) [adj, opp, hyp, ang, ang2];
// Function: hyp_opp_to_adj()
// Alias: opp_hyp_to_adj()
// Usage:
// adj = hyp_opp_to_adj(hyp,opp);
// Topics: Geometry, Triangles
// Description:
// Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length
// of the adjacent side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// hyp = hyp_opp_to_adj(5,3); // Returns: 4
function hyp_opp_to_adj(hyp,opp) =
assert(is_finite(hyp+opp) && hyp>=0 && opp>=0,
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-opp*opp);
function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
// Function: hyp_ang_to_adj()
// Alias: ang_hyp_to_adj()
// Usage:
// adj = hyp_ang_to_adj(hyp,ang);
// Topics: Geometry, Triangles
// Description:
// Given the length of the hypotenuse and the angle of the primary corner of a right triangle,
// returns the length of the adjacent side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// adj = hyp_ang_to_adj(8,60); // Returns: 4
function hyp_ang_to_adj(hyp,ang) =
assert(is_finite(hyp) && hyp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*cos(ang);
function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
// Function: opp_ang_to_adj()
// Alias: ang_opp_to_adj()
// Usage:
// adj = opp_ang_to_adj(opp,ang);
// Topics: Geometry, Triangles
// Description:
// Given the angle of the primary corner of a right triangle, and the length of the side opposite of it,
// returns the length of the adjacent side.
// Arguments:
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// adj = opp_ang_to_adj(8,30); // Returns: 4
function opp_ang_to_adj(opp,ang) =
assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/tan(ang);
function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
// Function: hyp_adj_to_opp()
// Alias: adj_hyp_to_opp()
// Usage:
// opp = hyp_adj_to_opp(hyp,adj);
// Topics: Geometry, Triangles
// Description:
// Given the length of the hypotenuse and the adjacent side, returns the length of the opposite side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// Example:
// opp = hyp_adj_to_opp(5,4); // Returns: 3
function hyp_adj_to_opp(hyp,adj) =
assert(is_finite(hyp) && hyp>=0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-adj*adj);
function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
// Function: hyp_ang_to_opp()
// Alias: ang_hyp_to_opp()
// Usage:
// opp = hyp_ang_to_opp(hyp,adj);
// Topics: Geometry, Triangles
// Description:
// Given the length of the hypotenuse of a right triangle, and the angle of the corner, returns the length of the opposite side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// opp = hyp_ang_to_opp(8,30); // Returns: 4
function hyp_ang_to_opp(hyp,ang) =
assert(is_finite(hyp)&&hyp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*sin(ang);
function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
// Function: adj_ang_to_opp()
// Alias: ang_adj_to_opp()
// Usage:
// opp = adj_ang_to_opp(adj,ang);
// Topics: Geometry, Triangles
// Description:
// Given the length of the adjacent side of a right triangle, and the angle of the corner, returns the length of the opposite side.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// opp = adj_ang_to_opp(8,45); // Returns: 8
function adj_ang_to_opp(adj,ang) =
assert(is_finite(adj)&&adj>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj*tan(ang);
function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
// Function: adj_opp_to_hyp()
// Alias: opp_adj_to_hyp()
// Usage:
// hyp = adj_opp_to_hyp(adj,opp);
// Topics: Geometry, Triangles
// Description:
// Given the length of the adjacent and opposite sides of a right triangle, returns the length of thee hypotenuse.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// hyp = adj_opp_to_hyp(3,4); // Returns: 5
function adj_opp_to_hyp(adj,opp) =
assert(is_finite(opp) && opp>=0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be a positive numbers." )
norm([opp,adj]);
function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
// Function: adj_ang_to_hyp()
// Alias: ang_adj_to_hyp()
// Usage:
// hyp = adj_ang_to_hyp(adj,ang);
// Topics: Geometry, Triangles
// Description:
// For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// hyp = adj_ang_to_hyp(4,60); // Returns: 8
function adj_ang_to_hyp(adj,ang) =
assert(is_finite(adj) && adj>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj/cos(ang);
function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
// Function: opp_ang_to_hyp()
// Alias: ang_opp_to_hyp()
// Usage:
// hyp = opp_ang_to_hyp(opp,ang);
// Topics: Geometry, Triangles
// Description:
// For a right triangle, given the length of the opposite side, and the corner angle, returns the length of the hypotenuse.
// Arguments:
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// hyp = opp_ang_to_hyp(4,30); // Returns: 8
function opp_ang_to_hyp(opp,ang) =
assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/sin(ang);
function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang);
// Function: hyp_adj_to_ang()
// Alias: adj_hyp_to_ang()
// Usage:
// ang = hyp_adj_to_ang(hyp,adj);
// Description:
// For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the corner.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// Example:
// ang = hyp_adj_to_ang(8,4); // Returns: 60 degrees
function hyp_adj_to_ang(hyp,adj) =
assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be positive numbers." )
acos(adj/hyp);
function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
// Function: hyp_opp_to_ang()
// Alias: opp_hyp_to_ang()
// Usage:
// ang = hyp_opp_to_ang(hyp,opp);
// Topics: Geometry, Triangles
// Description:
// For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the corner.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// ang = hyp_opp_to_ang(8,4); // Returns: 30 degrees
function hyp_opp_to_ang(hyp,opp) =
assert(is_finite(hyp+opp) && hyp>0 && opp>=0,
"Triangle side lengths should be positive numbers." )
asin(opp/hyp);
function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
// Function: adj_opp_to_ang()
// Alias: opp_adj_to_ang()
// Usage:
// ang = adj_opp_to_ang(adj,opp);
// Topics: Geometry, Triangles
// Description:
// For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// ang = adj_opp_to_ang(sqrt(3)/2,0.5); // Returns: 30 degrees
function adj_opp_to_ang(adj,opp) =
assert(is_finite(adj+opp) && adj>0 && opp>=0,
"Triangle side lengths should be positive numbers." )
atan2(opp,adj);
function opp_adj_to_ang(opp,adj) = adj_opp_to_ang(adj,opp);
// Function: triangle_area()
// Usage:
// area = triangle_area(a,b,c);
// Topics: Geometry, Triangles, Area
// Description:
// Returns the area of a triangle formed between three 2D or 3D vertices.
// Result will be negative if the points are 2D and in clockwise order.
// Arguments:
// a = The first vertex of the triangle.
// b = The second vertex of the triangle.
// c = The third vertex of the triangle.
// Examples:
// triangle_area([0,0], [5,10], [10,0]); // Returns -50
// triangle_area([10,0], [5,10], [0,0]); // Returns 50
function triangle_area(a,b,c) =
assert( is_path([a,b,c]), "Invalid points or incompatible dimensions." )
len(a)==3
? 0.5*norm(cross(c-a,c-b))
: 0.5*cross(c-a,c-b);
// Section: Planes

1
std.scad
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@ -22,6 +22,7 @@ include <paths.scad>
include <edges.scad>
include <arrays.scad>
include <math.scad>
include <trigonometry.scad>
include <vectors.scad>
include <quaternions.scad>
include <affine.scad>

75
tests/test_geometry.scad
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@ -19,19 +19,6 @@ test_line_intersection();
test_line_closest_point();
//test_ray_closest_point(); // should add this type of case
test_line_from_points();
test_tri_calc();
//test_hyp_opp_to_adj();
//test_hyp_ang_to_adj();
//test_opp_ang_to_adj();
//test_hyp_adj_to_opp();
//test_hyp_ang_to_opp();
//test_adj_ang_to_opp();
//test_adj_opp_to_hyp();
//test_adj_ang_to_hyp();
//test_opp_ang_to_hyp();
//test_hyp_adj_to_ang();
//test_hyp_opp_to_ang();
//test_adj_opp_to_ang();
test_plane3pt();
test_plane3pt_indexed();
test_plane_from_normal();
@ -587,68 +574,6 @@ module test_circle_point_tangents() {
*test_circle_point_tangents();
module test_tri_calc() {
sides = rands(1,100,100,seed_value=8888);
for (p=pair(sides,true)) {
opp = p[0];
adj = p[1];
hyp = norm([opp,adj]);
ang = acos(adj/hyp);
ang2 = 90-ang;
expected = [adj, opp, hyp, ang, ang2];
assert(approx(tri_calc(adj=adj, hyp=hyp), expected));
assert(approx(tri_calc(opp=opp, hyp=hyp), expected));
assert(approx(tri_calc(adj=adj, opp=opp), expected));
assert(approx(tri_calc(adj=adj, ang=ang), expected));
assert(approx(tri_calc(opp=opp, ang=ang), expected, eps=1e-8));
assert(approx(tri_calc(hyp=hyp, ang=ang), expected));
assert(approx(tri_calc(adj=adj, ang2=ang2), expected));
assert(approx(tri_calc(opp=opp, ang2=ang2), expected, eps=1e-8));
assert(approx(tri_calc(hyp=hyp, ang2=ang2), expected));
}
}
*test_tri_calc();
module test_tri_functions() {
sides = rands(1,100,100,seed_value=8181);
for (p = pair(sides,true)) {
adj = p.x;
opp = p.y;
hyp = norm([opp,adj]);
ang = atan2(opp,adj);
assert_approx(hyp_opp_to_adj(hyp,opp), adj);
assert_approx(hyp_ang_to_adj(hyp,ang), adj);
assert_approx(opp_ang_to_adj(opp,ang), adj);
assert_approx(hyp_adj_to_opp(hyp,adj), opp);
assert_approx(hyp_ang_to_opp(hyp,ang), opp);
assert_approx(adj_ang_to_opp(adj,ang), opp);
assert_approx(adj_opp_to_hyp(adj,opp), hyp);
assert_approx(adj_ang_to_hyp(adj,ang), hyp);
assert_approx(opp_ang_to_hyp(opp,ang), hyp);
assert_approx(hyp_adj_to_ang(hyp,adj), ang);
assert_approx(hyp_opp_to_ang(hyp,opp), ang);
assert_approx(adj_opp_to_ang(adj,opp), ang);
}
}
*test_tri_functions();
module test_hyp_opp_to_adj() nil(); // Covered in test_tri_functions()
module test_hyp_ang_to_adj() nil(); // Covered in test_tri_functions()
module test_opp_ang_to_adj() nil(); // Covered in test_tri_functions()
module test_hyp_adj_to_opp() nil(); // Covered in test_tri_functions()
module test_hyp_ang_to_opp() nil(); // Covered in test_tri_functions()
module test_adj_ang_to_opp() nil(); // Covered in test_tri_functions()
module test_adj_opp_to_hyp() nil(); // Covered in test_tri_functions()
module test_adj_ang_to_hyp() nil(); // Covered in test_tri_functions()
module test_opp_ang_to_hyp() nil(); // Covered in test_tri_functions()
module test_hyp_adj_to_ang() nil(); // Covered in test_tri_functions()
module test_hyp_opp_to_ang() nil(); // Covered in test_tri_functions()
module test_adj_opp_to_ang() nil(); // Covered in test_tri_functions()
module test_plane3pt() {
assert_approx(plane3pt([0,0,20], [0,10,10], [0,0,0]), [1,0,0,0]);
assert_approx(plane3pt([2,0,20], [2,10,10], [2,0,0]), [1,0,0,2]);

42
tests/test_trigonometry.scad Normal file
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@ -0,0 +1,42 @@
include <../std.scad>
module test_tri_functions() {
sides = rands(1,100,100,seed_value=8181);
for (p = pair(sides,true)) {
adj = p.x;
opp = p.y;
hyp = norm([opp,adj]);
ang = atan2(opp,adj);
assert_approx(hyp_ang_to_adj(hyp,ang), adj);
assert_approx(opp_ang_to_adj(opp,ang), adj);
assert_approx(hyp_adj_to_opp(hyp,adj), opp);
assert_approx(hyp_ang_to_opp(hyp,ang), opp);
assert_approx(adj_ang_to_opp(adj,ang), opp);
assert_approx(adj_opp_to_hyp(adj,opp), hyp);
assert_approx(adj_ang_to_hyp(adj,ang), hyp);
assert_approx(opp_ang_to_hyp(opp,ang), hyp);
assert_approx(hyp_adj_to_ang(hyp,adj), ang);
assert_approx(hyp_opp_to_ang(hyp,opp), ang);
assert_approx(adj_opp_to_ang(adj,opp), ang);
}
}
*test_tri_functions();
module test_hyp_opp_to_adj() nil(); // Covered in test_tri_functions()
module test_hyp_ang_to_adj() nil(); // Covered in test_tri_functions()
module test_opp_ang_to_adj() nil(); // Covered in test_tri_functions()
module test_hyp_adj_to_opp() nil(); // Covered in test_tri_functions()
module test_hyp_ang_to_opp() nil(); // Covered in test_tri_functions()
module test_adj_ang_to_opp() nil(); // Covered in test_tri_functions()
module test_adj_opp_to_hyp() nil(); // Covered in test_tri_functions()
module test_adj_ang_to_hyp() nil(); // Covered in test_tri_functions()
module test_opp_ang_to_hyp() nil(); // Covered in test_tri_functions()
module test_hyp_adj_to_ang() nil(); // Covered in test_tri_functions()
module test_hyp_opp_to_ang() nil(); // Covered in test_tri_functions()
module test_adj_opp_to_ang() nil(); // Covered in test_tri_functions()
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

390
trigonometry.scad Normal file
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@ -0,0 +1,390 @@
//////////////////////////////////////////////////////////////////////
// LibFile: trigonometry.scad
// Trigonometry shortcuts for people who can't be bothered to remember
// all the function relations, or silly acronyms like SOHCAHTOA.
// Includes:
// include <BOSL2/std.scad>
//////////////////////////////////////////////////////////////////////
// Section: 2D General Triangle Functions
// Function: law_of_cosines()
// Usage:
// C = law_of_cosines(a, b, c);
// c = law_of_cosines(a, b, C=);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the
// angle in degrees for the corner opposite of the third side. Given two side lengths, and the
// angle between them, returns the length of the third side.
// Figure(2D):
// stroke([[-50,0], [10,60], [50,0]], closed=true);
// color("black") {
// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center");
// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center");
// translate([-22,35]) text(text="c", size=8, halign="center", valign="center");
// }
// color("blue") {
// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center");
// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center");
// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center");
// }
// Arguments:
// a = The length of the first side.
// b = The length of the second side.
// c = The length of the third side.
// ---
// C = The angle in degrees of the corner opposite of the third side.
// See Also: law_of_sines()
function law_of_cosines(a, b, c, C) =
// Triangle Law of Cosines:
// c^2 = a^2 + b^2 - 2*a*b*cos(C)
assert(num_defined([c,C]) == 1, "Must give exactly one of c= or C=.")
is_undef(c) ? sqrt(a*a + b*b - 2*a*b*cos(C)) :
acos(constrain((a*a + b*b - c*c) / (2*a*b), -1, 1));
// Function: law_of_sines()
// Usage:
// B = law_of_sines(a, A, b);
// b = law_of_sines(a, A, B=);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the
// angle between them, returns the angle of the corner opposite of the second side. Given a side
// length, the opposing angle, and a second angle, returns the length of the side opposite of the
// second angle.
// Figure(2D):
// stroke([[-50,0], [10,60], [50,0]], closed=true);
// color("black") {
// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center");
// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center");
// translate([-22,35]) text(text="c", size=8, halign="center", valign="center");
// }
// color("blue") {
// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center");
// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center");
// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center");
// }
// Arguments:
// a = The length of the first side.
// A = The angle in degrees of the corner opposite of the first side.
// b = The length of the second side.
// ---
// B = The angle in degrees of the corner opposite of the second side.
// See Also: law_of_cosines()
function law_of_sines(a, A, b, B) =
// Triangle Law of Sines:
// a/sin(A) = b/sin(B) = c/sin(C)
assert(num_defined([b,B]) == 1, "Must give exactly one of b= or B=.")
let( r = a/sin(A) )
is_undef(b) ? r*sin(B) :
asin(constrain(b/r, -1, 1));
// Function: triangle_area()
// Usage:
// area = triangle_area(p1,p2,p3);
// Topics: Geometry, Trigonometry, Triangles, Area
// Description:
// Returns the area of a triangle formed between three 2D or 3D vertices.
// Result will be negative if the points are 2D and in clockwise order.
// Arguments:
// p1 = The first vertex of the triangle.
// p2 = The second vertex of the triangle.
// p3 = The third vertex of the triangle.
// Examples:
// triangle_area([0,0], [5,10], [10,0]); // Returns -50
// triangle_area([10,0], [5,10], [0,0]); // Returns 50
function triangle_area(p1,p2,p3) =
assert( is_path([p1,p2,p3]), "Invalid points or incompatible dimensions." )
len(p1)==3
? 0.5*norm(cross(p3-p1,p3-p2))
: 0.5*cross(p3-p1,p3-p2);
// Section: 2D Right Triangle Functions
// This is a set of functions to make it easier to perform trig calculations on right triangles.
// In general, all these functions are named using these abbreviations:
// - *hyp*: The length of the Hypotenuse.
// - *adj*: The length of the side adjacent to the angle.
// - *opp*: The length of the side opposite to the angle.
// - *ang*: The angle size in degrees.
// If you know two of those, and want to know the value of a third, you will need to call a
// function named like `AAA_BBB_to_CCC()`. For example, if you know the length of the hypotenuse,
// and the length of the side adjacent to the angle, and want to learn the length of the side
// opposite to the angle, you will call `opp = hyp_adj_to_opp(hyp,adj);`.
// Figure(2D):
// color("brown") {
// stroke([[40,0], [40,10], [50,10]]);
// left(50) stroke(arc(r=37,angle=30));
// }
// color("lightgreen") stroke([[-50,0], [50,60], [50,0]], closed=true);
// color("black") {
// translate([ 62,25]) text(text="opp", size=8, halign="center", valign="center");
// translate([ 0,-6]) text(text="adj", size=8, halign="center", valign="center");
// translate([ 0,40]) text(text="hyp", size=8, halign="center", valign="center");
// translate([-25, 5]) text(text="ang", size=7, halign="center", valign="center");
// }
// Function: hyp_opp_to_adj()
// Alias: opp_hyp_to_adj()
// Usage:
// adj = hyp_opp_to_adj(hyp,opp);
// adj = opp_hyp_to_adj(opp,hyp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length
// of the adjacent side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// hyp = hyp_opp_to_adj(5,3); // Returns: 4
function hyp_opp_to_adj(hyp,opp) =
assert(is_finite(hyp+opp) && hyp>=0 && opp>=0,
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-opp*opp);
function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
// Function: hyp_ang_to_adj()
// Alias: ang_hyp_to_adj()
// Usage:
// adj = hyp_ang_to_adj(hyp,ang);
// adj = ang_hyp_to_adj(ang,hyp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the length of the hypotenuse and the angle of the primary corner of a right triangle,
// returns the length of the adjacent side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// adj = hyp_ang_to_adj(8,60); // Returns: 4
function hyp_ang_to_adj(hyp,ang) =
assert(is_finite(hyp) && hyp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*cos(ang);
function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
// Function: opp_ang_to_adj()
// Alias: ang_opp_to_adj()
// Usage:
// adj = opp_ang_to_adj(opp,ang);
// adj = ang_opp_to_adj(ang,opp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the angle of the primary corner of a right triangle, and the length of the side opposite of it,
// returns the length of the adjacent side.
// Arguments:
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// adj = opp_ang_to_adj(8,30); // Returns: 4
function opp_ang_to_adj(opp,ang) =
assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/tan(ang);
function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
// Function: hyp_adj_to_opp()
// Alias: adj_hyp_to_opp()
// Usage:
// opp = hyp_adj_to_opp(hyp,adj);
// opp = adj_hyp_to_opp(adj,hyp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the length of the hypotenuse and the adjacent side, returns the length of the opposite side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// Example:
// opp = hyp_adj_to_opp(5,4); // Returns: 3
function hyp_adj_to_opp(hyp,adj) =
assert(is_finite(hyp) && hyp>=0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-adj*adj);
function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
// Function: hyp_ang_to_opp()
// Alias: ang_hyp_to_opp()
// Usage:
// opp = hyp_ang_to_opp(hyp,ang);
// opp = ang_hyp_to_opp(ang,hyp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the length of the hypotenuse of a right triangle, and the angle of the corner, returns the length of the opposite side.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// opp = hyp_ang_to_opp(8,30); // Returns: 4
function hyp_ang_to_opp(hyp,ang) =
assert(is_finite(hyp)&&hyp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*sin(ang);
function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
// Function: adj_ang_to_opp()
// Alias: ang_adj_to_opp()
// Usage:
// opp = adj_ang_to_opp(adj,ang);
// opp = ang_adj_to_opp(ang,adj);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the length of the adjacent side of a right triangle, and the angle of the corner, returns the length of the opposite side.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// opp = adj_ang_to_opp(8,45); // Returns: 8
function adj_ang_to_opp(adj,ang) =
assert(is_finite(adj)&&adj>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj*tan(ang);
function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
// Function: adj_opp_to_hyp()
// Alias: opp_adj_to_hyp()
// Usage:
// hyp = adj_opp_to_hyp(adj,opp);
// hyp = opp_adj_to_hyp(opp,adj);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// Given the length of the adjacent and opposite sides of a right triangle, returns the length of thee hypotenuse.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// hyp = adj_opp_to_hyp(3,4); // Returns: 5
function adj_opp_to_hyp(adj,opp) =
assert(is_finite(opp) && opp>=0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be a positive numbers." )
norm([opp,adj]);
function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
// Function: adj_ang_to_hyp()
// Alias: ang_adj_to_hyp()
// Usage:
// hyp = adj_ang_to_hyp(adj,ang);
// hyp = ang_adj_to_hyp(ang,adj);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// hyp = adj_ang_to_hyp(4,60); // Returns: 8
function adj_ang_to_hyp(adj,ang) =
assert(is_finite(adj) && adj>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj/cos(ang);
function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
// Function: opp_ang_to_hyp()
// Alias: ang_opp_to_hyp()
// Usage:
// hyp = opp_ang_to_hyp(opp,ang);
// hyp = ang_opp_to_hyp(ang,opp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// For a right triangle, given the length of the opposite side, and the corner angle, returns the length of the hypotenuse.
// Arguments:
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// ang = The angle in degrees of the primary corner of the right triangle.
// Example:
// hyp = opp_ang_to_hyp(4,30); // Returns: 8
function opp_ang_to_hyp(opp,ang) =
assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/sin(ang);
function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang);
// Function: hyp_adj_to_ang()
// Alias: adj_hyp_to_ang()
// Usage:
// ang = hyp_adj_to_ang(hyp,adj);
// ang = adj_hyp_to_ang(adj,hyp);
// Description:
// For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the corner.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// Example:
// ang = hyp_adj_to_ang(8,4); // Returns: 60 degrees
function hyp_adj_to_ang(hyp,adj) =
assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
"Triangle side lengths should be positive numbers." )
acos(adj/hyp);
function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
// Function: hyp_opp_to_ang()
// Alias: opp_hyp_to_ang()
// Usage:
// ang = hyp_opp_to_ang(hyp,opp);
// ang = opp_hyp_to_ang(opp,hyp);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the corner.
// Arguments:
// hyp = The length of the hypotenuse of the right triangle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// ang = hyp_opp_to_ang(8,4); // Returns: 30 degrees
function hyp_opp_to_ang(hyp,opp) =
assert(is_finite(hyp+opp) && hyp>0 && opp>=0,
"Triangle side lengths should be positive numbers." )
asin(opp/hyp);
function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
// Function: adj_opp_to_ang()
// Alias: opp_adj_to_ang()
// Usage:
// ang = adj_opp_to_ang(adj,opp);
// ang = opp_adj_to_ang(opp,adj);
// Topics: Geometry, Trigonometry, Triangles
// Description:
// For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner.
// Arguments:
// adj = The length of the side of the right triangle that is adjacent to the primary angle.
// opp = The length of the side of the right triangle that is opposite from the primary angle.
// Example:
// ang = adj_opp_to_ang(sqrt(3)/2,0.5); // Returns: 30 degrees
function adj_opp_to_ang(adj,opp) =
assert(is_finite(adj+opp) && adj>0 && opp>=0,
"Triangle side lengths should be positive numbers." )
atan2(opp,adj);
function opp_adj_to_ang(opp,adj) = adj_opp_to_ang(adj,opp);
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap