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BOSL2/tests/test_geometry.scad
Adrian Mariano 2cc5c39d64 fix doc bug in bottlecaps. 
knurling mask didn't pass parameters (so they were ignored)
2022-04-08 20:17:41 -04:00

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include <../std.scad>
//the commented lines are for tests to be written
//the tests are ordered as they appear in geometry.scad
test_is_point_on_line();
test_is_collinear();
test_point_line_distance();
test_segment_distance();
test_line_normal();
test_line_intersection();
//test_line_ray_intersection(); // should add this type of case
//test_ray_intersection(); // should add this type of case
//test_ray_segment_intersection(); // should add this type of case
test_line_closest_point();
//test_ray_closest_point(); // should add this type of case
test_line_from_points();
test_plane3pt();
test_plane3pt_indexed();
test_plane_from_normal();
test_plane_from_points();
test_plane_from_polygon();
test_plane_normal();
test_plane_offset();
test_plane_closest_point();
test_point_plane_distance();
test__general_plane_line_intersection();
test_plane_line_angle();
test_plane_line_intersection();
test_polygon_line_intersection();
test_plane_intersection();
test_is_coplanar();
test_are_points_on_plane();
test__is_point_above_plane();
test_circle_2tangents();
test_circle_3points();
test_circle_point_tangents();
test__noncollinear_triple();
test_polygon_area();
test_is_polygon_convex();
test_reindex_polygon();
test_align_polygon();
test_centroid();
test_point_in_polygon();
test_polygon_triangulate();
test_is_polygon_clockwise();
test_clockwise_polygon();
test_ccw_polygon();
test_reverse_polygon();
test_polygon_normal();
test_rot_decode();
//tests to migrate to other files
test_convex_distance();
test_convex_collision();
// to be used when there are two alternative symmetrical outcomes
// from a function like a plane output; v must be a vector
function standardize(v) =
v==[]? [] :
let( i = max_index([for(vi=v) abs(vi) ]),
s = sign(v[i]) )
v*s;
module assert_std(vc,ve,info) { assert_approx(standardize(vc),standardize(ve),info); }
function info_str(list,i=0,string=chr(10)) =
assert(i>=len(list) || (is_list(list[i])&&len(list[i])>=2), "Invalid list for info_str." )
i>=len(list)
? str(string)
: info_str(list,i+1,str(string,str(list[i][0],_valstr(list[i][1]),chr(10))));
module test_polygon_triangulate() {
poly0 = [ [0,0,1], [10,0,2], [10,10,0] ];
poly1 = [ [-10,0,-10], [10,0,10], [0,10,0], [-10,0,-10], [-4,4,-4], [4,4,4], [0,2,0], [-4,4,-4] ];
poly2 = [ [0,0], [5,5], [-5,5], [0,0], [-5,-5], [5,-5] ];
poly3 = [ [0,0], [10,0], [10,10], [10,13], [10,10], [0,10], [0,0], [3,3], [7,3], [7,7], [7,3], [3,3] ];
tris0 = (polygon_triangulate(poly0));
assert(approx(tris0, [[0, 1, 2]]));
tris1 = (polygon_triangulate(poly1));
assert(approx(tris1,( [[2, 3, 4], [6, 7, 0], [2, 4, 5], [6, 0, 1], [1, 2, 5], [5, 6, 1]])));
tris2 = (polygon_triangulate(poly2));
assert(approx(tris2,( [[3, 4, 5], [1, 2, 3]])));
tris3 = (polygon_triangulate(poly3));
assert(approx(tris3,( [[5, 6, 7], [11, 0, 1], [5, 7, 8], [10, 11, 1], [5, 8, 9], [10, 1, 2], [4, 5, 9], [9, 10, 2]])));
}
module test__normalize_plane(){
plane = rands(-5,5,4,seed=333)+[10,0,0,0];
plane2 = _normalize_plane(plane);
assert_approx(norm(point3d(plane2)),1);
assert_approx(plane*plane2[3],plane2*plane[3]);
}
test__normalize_plane();
module test_plane_line_intersection(){
line = [rands(-1,1,3,seed=74),rands(-1,1,3,seed=99)+[2,0,0]];
plane1 = plane_from_normal(line[1]-line[0],2*line[0]-line[1]); // plane disjoint from segment
plane2 = plane_from_normal(line[1]-line[0],(line[0]+line[1])/2); // through middle point of line
plane3 = plane3pt(line[1],line[0], rands(-1,1,3)+[0,3,0]); // containing line
plane4 = plane3pt(line[1],line[0], rands(-1,1,3)+[0,3,0])+[0,0,0,1]; // parallel to line
info1 = info_str([ ["line = ",line],["plane = ",plane1]]);
assert_approx(plane_line_intersection(plane1, line),2*line[0]-line[1],info1);
assert_approx(plane_line_intersection(plane1, line,[true,false]),undef,info1);
assert_approx(plane_line_intersection(plane1, line,[false,true]),2*line[0]-line[1],info1);
assert_approx(plane_line_intersection(plane1, line,[true, true]),undef,info1);
info2 = info_str([ ["line = ",line],["plane = ",plane2]]);
assert_approx(plane_line_intersection(plane2, line),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[true,false]),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[false,true]),(line[0]+line[1])/2,info2);
assert_approx(plane_line_intersection(plane2, line,[true, true]),(line[0]+line[1])/2,info2);
info3 = info_str([ ["line = ",line],["plane = ",plane3]]);
assert_approx(plane_line_intersection(plane3, line),line,info3);
assert_approx(plane_line_intersection(plane3, line,[true,false]),line,info3);
assert_approx(plane_line_intersection(plane3, line,[false,true]),line,info3);
assert_approx(plane_line_intersection(plane3, line,[true, true]),line,info3);
info4 = info_str([ ["line = ",line],["plane = ",plane4]]);
assert_approx(plane_line_intersection(plane4, line),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[true,false]),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[false,true]),undef,info4);
assert_approx(plane_line_intersection(plane4, line,[true, true]),undef,info4);
}
*test_plane_line_intersection();
module test_plane_intersection(){
line = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a valid line
pt0 = line[0]-[2,0,0]; // 2 points not on the line
pt1 = line[1]-[0,2,0];
plane01 = plane3pt(line[0],line[1],pt0);
plane02 = plane3pt(line[0],line[1],pt1);
plane03 = plane3pt(line[0],pt0,pt1);
info = info_str([["plane1 = ",plane01],["plane2 = ",plane02],["plane3 = ",plane03]]);
assert_approx(plane_intersection(plane01,plane02,plane03),line[0],info);
assert_approx(plane_intersection(plane01,2*plane01),undef,info);
lineInters = plane_intersection(plane01,plane02);
assert_approx(line_closest_point(lineInters,line[0]), line[0], info);
assert_approx(line_closest_point(lineInters,line[1]), line[1], info);
}
*test_plane_intersection();
module test_plane_offset(){
plane = rands(-1,1,4)+[2,0,0,0]; // a valid plane
info = info_str([["plane = ",plane]]);
assert_approx(plane_offset(plane), _normalize_plane(plane)[3],info);
assert_approx(plane_offset([1,1,1,1]), 1/sqrt(3),info);
}
*test_plane_offset();
module test_plane_from_polygon(){
poly1 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0], rands(-1,1,3)+[0,2,2] ];
poly2 = concat(poly1, [sum(poly1)/3] );
info = info_str([["poly1 = ",poly1],["poly2 = ",poly2]]);
assert_approx(plane_from_polygon(poly1),plane3pt(poly1[0],poly1[1],poly1[2]),info);
assert_approx(plane_from_polygon(poly2),plane3pt(poly1[0],poly1[1],poly1[2]),info);
}
*test_plane_from_polygon();
module test_plane_from_normal(){
normal = rands(-1,1,3)+[2,0,0];
point = rands(-1,1,3);
displ = normal*point;
info = info_str([["normal = ",normal],["point = ",point],["displ = ",displ]]);
assert_approx(plane_from_normal(normal,point)*[each point,-1],0,info);
assert_approx(plane_from_normal([1,1,1],[1,2,3]),[0.57735026919,0.57735026919,0.57735026919,3.46410161514]);
}
*test_plane_from_normal();
module test_plane_line_angle() {
angs = rands(0,360,3);
displ = rands(-1,1,1)[0];
info = info_str([["angs = ",angs],["displ = ",displ]]);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),displ],[[0,0,0],rot(angs,p=[0,0,1])]),90,info);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),displ],[[0,0,0],rot(angs,p=[0,1,1])]),45,info);
assert_approx(plane_line_angle([each rot(angs,p=[0,0,1]),0],[[0,0,0],rot(angs,p=[1,1,1])]),35.2643896828);
}
*test_plane_line_angle();
module test__general_plane_line_intersection() {
CRLF = chr(10);
// general line
plane1 = rands(-1,1,4)+[2,0,0,0]; // a random valid plane (normal!=0)
line1 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a random valid line (line1[0]!=line1[1])
inters1 = _general_plane_line_intersection(plane1, line1);
info1 = info_str([["line = ",line1],["plane = ",plane1]]);
if(inters1==undef) { // parallel to the plane ?
assert_approx( point3d(plane1)*(line1[1]-line1[0]), 0, info1);
assert( point3d(plane1)*line1[0]== plane1[3], info1); // not on the plane
}
if( inters1[1]==undef) { // on the plane ?
assert_approx( point3d(plane1)*(line1[1]-line1[0]), 0, info1);
assert_approx(point3d(plane1)*line1[0],plane1[3], info1) ; // on the plane
}
else {
interspoint = line1[0]+inters1[1]*(line1[1]-line1[0]);
assert_approx(inters1[0],interspoint, info1);
assert_approx(point3d(plane1)*inters1[0], plane1[3], info1); // interspoint on the plane
assert_approx(point_plane_distance(plane1, inters1[0]), 0, info1); // inters1[0] on the plane
}
// line parallel to the plane
line2 = [ rands(-1,1,3)+[0,2,0], rands(-1,1,3)+[2,0,0] ]; // a random valid line2
// not containing the origin
plane0 = plane_from_points([line2[0], line2[1], [0,0,0]]); // plane cointaining the line
plane2 = plane_from_normal(plane_normal(plane0), [5,5,5]);
inters2 = _general_plane_line_intersection(plane2, line2);
info2 = info_str([["line = ",line2],["plane = ",plane2]]);
assert(inters2==undef, info2);
// line on the plane
line3 = [ rands(-1,1,3), rands(-1,1,3)+[2,0,0] ]; // a random valid line
imax = max_index(line3[1]-line3[0]);
w = [for(j=[0:2]) imax==j? 0: 3 ];
p3 = line3[0] + cross(line3[1]-line3[0],w); // a point not on the line
plane3 = plane_from_points([line3[0], line3[1], p3]); // plane containing line
inters3 = _general_plane_line_intersection(plane3, line3);
info3 = info_str([["line = ",line3],["plane = ",plane3]]);
assert(!is_undef(inters3) && inters3[1]==undef, info3);
assert_approx(inters3[0], line3, info3);
}
*test__general_plane_line_intersection();
module test_are_points_on_plane() {
pts = [for(i=[0:40]) rands(-1,1,3) ];
dir = rands(-10,10,3);
normal0 = [1,2,3];
ang = rands(0,360,1)[0];
normal = rot(a=ang,p=normal0);
plane = [each normal, normal*dir];
prj_pts = plane_closest_point(plane,pts);
info = info_str([["pts = ",pts],["dir = ",dir],["ang = ",ang]]);
assert(are_points_on_plane(prj_pts,plane),info);
assert(!are_points_on_plane(concat(pts,[normal-dir]),plane),info);
}
*test_are_points_on_plane();
module test_plane_closest_point(){
ang = rands(0,360,1)[0];
dir = rands(-10,10,3);
normal0 = unit([1,2,3]);
normal = rot(a=ang,p=normal0);
plane0 = [each normal0, 0];
plane = [each normal, 0];
planem = [each normal, normal*dir];
pts = [for(i=[1:10]) rands(-1,1,3)];
info = info_str([["ang = ",ang],["dir = ",dir]]);
assert_approx( plane_closest_point(plane,pts),
plane_closest_point(plane,plane_closest_point(plane,pts)),info);
assert_approx( plane_closest_point(plane,pts),
rot(a=ang,p=plane_closest_point(plane0,rot(a=-ang,p=pts))),info);
assert_approx( move((-normal*dir)*normal,p=plane_closest_point(planem,pts)),
plane_closest_point(plane,pts),info);
assert_approx( move((normal*dir)*normal,p=plane_closest_point(plane,pts)),
plane_closest_point(planem,pts),info);
}
*test_plane_closest_point();
module test_line_from_points() {
assert_approx(line_from_points([[1,0],[0,0],[-1,0]]),[[-1,0],[1,0]]);
assert_approx(line_from_points([[1,1],[0,1],[-1,1]]),[[-1,1],[1,1]]);
assert(line_from_points([[1,1],[0,1],[-1,0]])==undef);
assert(line_from_points([[1,1],[0,1],[-1,0]],fast=true)== [[-1,0],[1,1]]);
}
*test_line_from_points();
module test_is_point_on_line() {
assert(is_point_on_line([-15,0], [[-10,0], [10,0]],SEGMENT) == false);
assert(is_point_on_line([-10,0], [[-10,0], [10,0]],SEGMENT) == true);
assert(is_point_on_line([-5,0], [[-10,0], [10,0]],SEGMENT) == true);
assert(is_point_on_line([0,0], [[-10,0], [10,0]],SEGMENT) == true);
assert(is_point_on_line([3,3], [[-10,0], [10,0]],SEGMENT) == false);
assert(is_point_on_line([5,0], [[-10,0], [10,0]],SEGMENT) == true);
assert(is_point_on_line([10,0], [[-10,0], [10,0]],SEGMENT) == true);
assert(is_point_on_line([15,0], [[-10,0], [10,0]],SEGMENT) == false);
assert(is_point_on_line([0,-15], [[0,-10], [0,10]],SEGMENT) == false);
assert(is_point_on_line([0,-10], [[0,-10], [0,10]],SEGMENT) == true);
assert(is_point_on_line([0, -5], [[0,-10], [0,10]],SEGMENT) == true);
assert(is_point_on_line([0, 0], [[0,-10], [0,10]],SEGMENT) == true);
assert(is_point_on_line([3, 3], [[0,-10], [0,10]],SEGMENT) == false);
assert(is_point_on_line([0, 5], [[0,-10], [0,10]],SEGMENT) == true);
assert(is_point_on_line([0, 10], [[0,-10], [0,10]],SEGMENT) == true);
assert(is_point_on_line([0, 15], [[0,-10], [0,10]],SEGMENT) == false);
assert(is_point_on_line([-15,-15], [[-10,-10], [10,10]],SEGMENT) == false);
assert(is_point_on_line([-10,-10], [[-10,-10], [10,10]],SEGMENT) == true);
assert(is_point_on_line([ -5, -5], [[-10,-10], [10,10]],SEGMENT) == true);
assert(is_point_on_line([ 0, 0], [[-10,-10], [10,10]],SEGMENT) == true);
assert(is_point_on_line([ 0, 3], [[-10,-10], [10,10]],SEGMENT) == false);
assert(is_point_on_line([ 5, 5], [[-10,-10], [10,10]],SEGMENT) == true);
assert(is_point_on_line([ 10, 10], [[-10,-10], [10,10]],SEGMENT) == true);
assert(is_point_on_line([ 15, 15], [[-10,-10], [10,10]],SEGMENT) == false);
assert(is_point_on_line([10,10], [[0,0],[5,5]]) == true);
assert(is_point_on_line([4,4], [[0,0],[5,5]]) == true);
assert(is_point_on_line([-2,-2], [[0,0],[5,5]]) == true);
assert(is_point_on_line([5,5], [[0,0],[5,5]]) == true);
assert(is_point_on_line([10,10], [[0,0],[5,5]],RAY) == true);
assert(is_point_on_line([0,0], [[0,0],[5,5]],RAY) == true);
assert(is_point_on_line([3,3], [[0,0],[5,5]],RAY) == true);
}
*test_is_point_on_line();
module test__point_left_of_line2d() {
assert(_point_left_of_line2d([ -3, 0], [[-10,-10], [10,10]]) > 0);
assert(_point_left_of_line2d([ 0, 0], [[-10,-10], [10,10]]) == 0);
assert(_point_left_of_line2d([ 3, 0], [[-10,-10], [10,10]]) < 0);
}
test__point_left_of_line2d();
module test_is_collinear() {
assert(is_collinear([-10,-10], [-15, -16], [10,10]) == false);
assert(is_collinear([[-10,-10], [-15, -16], [10,10]]) == false);
assert(is_collinear([-10,-10], [-15, -15], [10,10]) == true);
assert(is_collinear([[-10,-10], [-15, -15], [10,10]]) == true);
assert(is_collinear([-10,-10], [ -3, 0], [10,10]) == false);
assert(is_collinear([-10,-10], [ 0, 0], [10,10]) == true);
assert(is_collinear([-10,-10], [ 3, 0], [10,10]) == false);
assert(is_collinear([-10,-10], [ 15, 15], [10,10]) == true);
assert(is_collinear([-10,-10], [ 15, 16], [10,10]) == false);
}
*test_is_collinear();
module test_point_line_distance() {
assert_approx(point_line_distance([1,1,1], [[-10,-10,-10], [10,10,10]]), 0);
assert_approx(point_line_distance([-1,-1,-1], [[-10,-10,-10], [10,10,10]]), 0);
assert_approx(point_line_distance([1,-1,0], [[-10,-10,-10], [10,10,10]]), sqrt(2));
assert_approx(point_line_distance([8,-8,0], [[-10,-10,-10], [10,10,10]]), 8*sqrt(2));
assert_approx(point_line_distance([3,8], [[-10,0], [10,0]],SEGMENT), 8);
assert_approx(point_line_distance([14,3], [[-10,0], [10,0]],SEGMENT), 5);
}
*test_point_line_distance();
module test_segment_distance() {
assert_approx(segment_distance([[-14,3], [-14,9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[-14,3], [-15,9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[14,3], [14,9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[-14,-3], [-14,-9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[-14,-3], [-15,-9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[14,-3], [14,-9]], [[-10,0], [10,0]]), 5);
assert_approx(segment_distance([[14,3], [14,-3]], [[-10,0], [10,0]]), 4);
assert_approx(segment_distance([[-14,3], [-14,-3]], [[-10,0], [10,0]]), 4);
assert_approx(segment_distance([[-6,5], [4,-5]], [[-10,0], [10,0]]), 0);
assert_approx(segment_distance([[-5,5], [5,-5]], [[-10,3], [10,-3]]), 0);
}
*test_segment_distance();
module test_line_normal() {
assert(line_normal([0,0],[10,0]) == [0,1]);
assert(line_normal([0,0],[0,10]) == [-1,0]);
assert(line_normal([0,0],[-10,0]) == [0,-1]);
assert(line_normal([0,0],[0,-10]) == [1,0]);
assert(approx(line_normal([0,0],[10,10]), [-sqrt(2)/2,sqrt(2)/2]));
assert(line_normal([[0,0],[10,0]]) == [0,1]);
assert(line_normal([[0,0],[0,10]]) == [-1,0]);
assert(line_normal([[0,0],[-10,0]]) == [0,-1]);
assert(line_normal([[0,0],[0,-10]]) == [1,0]);
assert(approx(line_normal([[0,0],[10,10]]), [-sqrt(2)/2,sqrt(2)/2]));
pts = [for (p=pair(rands(-100,100,1000,seed_value=4312))) p];
for (p = pair(pts,true)) {
p1 = p.x;
p2 = p.y;
n = unit(p2-p1);
n1 = [-n.y, n.x];
n2 = line_normal(p1,p2);
assert(approx(n2, n1));
}
}
*test_line_normal();
module test_line_intersection() {
assert(line_intersection([[-10,-10], [ -1,-10]], [[ 10,-10], [ 1,-10]]) == undef);
assert(line_intersection([[-10, 0], [ -1, 0]], [[ 10, 0], [ 1, 0]]) == undef);
assert(line_intersection([[-10, 0], [ -1, 0]], [[ 1, 0], [ 10, 0]]) == undef);
assert(line_intersection([[-10, 0], [ 10, 0]], [[-10, 0], [ 10, 0]]) == undef);
assert(line_intersection([[-10, 10], [ 10, 10]], [[-10,-10], [ 10,-10]]) == undef);
assert(line_intersection([[-10,-10], [ -1, -1]], [[ 10,-10], [ 1, -1]]) == [0,0]);
assert(line_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [-10, 10]]) == [0,0]);
assert(line_intersection([[ -8, 0], [ 12, 4]], [[ 12, 0], [ -8, 4]]) == [2,2]);
assert(line_intersection([[-10,-10], [ -1,-10]], [[ 10,-10], [ 1,-10]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10, 0], [ -1, 0]], [[ 10, 0], [ 1, 0]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10, 0], [ -1, 0]], [[ 1, 0], [ 10, 0]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10, 0], [ 10, 0]], [[-10, 0], [ 10, 0]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10, 10], [ 10, 10]], [[-10,-10], [ 10,-10]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10,-10], [ -1, -1]], [[ 10,-10], [ 1, -1]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [-10, 10]],LINE,SEGMENT) == [0,0]);
assert(line_intersection([[ -8, 0], [ 12, 4]], [[ 12, 0], [ -8, 4]],LINE,SEGMENT) == [2,2]);
assert(line_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [ 1, -1]],LINE,SEGMENT) == undef);
assert(line_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [ -1, 1]],LINE,SEGMENT) == [0,0]);
}
*test_line_intersection();
module test_line_closest_point() {
assert(approx(line_closest_point([[-10,-10], [10,10]], [1,-1]), [0,0]));
assert(approx(line_closest_point([[-10,-10], [10,10]], [-1,1]), [0,0]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [1,2]+[-2,1]), [1,2]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [1,2]+[2,-1]), [1,2]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [13,31]), [15,30]));
assert(approx(line_closest_point([[-10,-10], [10,10]], [1,-1],SEGMENT), [0,0]));
assert(approx(line_closest_point([[-10,-10], [10,10]], [-1,1],SEGMENT), [0,0]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [1,2]+[-2,1],SEGMENT), [1,2]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [1,2]+[2,-1],SEGMENT), [1,2]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [13,31],SEGMENT), [10,20]));
assert(approx(line_closest_point([[-10,-20], [10,20]], [15,25],SEGMENT), [10,20]));
}
*test_line_closest_point();
module test_circle_2tangents() {
//** missing tests with arg tangent=true
assert(approx(circle_2tangents(10/sqrt(2),[10,10],[0,0],[10,-10])[0], [10,0]));
assert(approx(circle_2tangents(10/sqrt(2),[-10,10],[0,0],[-10,-10])[0], [-10,0]));
assert(approx(circle_2tangents(10/sqrt(2),[-10,10],[0,0],[10,10])[0], [0,10]));
assert(approx(circle_2tangents(10/sqrt(2),[-10,-10],[0,0],[10,-10])[0], [0,-10]));
assert(approx(circle_2tangents(10,[0,10],[0,0],[10,0])[0], [10,10]));
assert(approx(circle_2tangents(10,[10,0],[0,0],[0,-10])[0], [10,-10]));
assert(approx(circle_2tangents(10,[0,-10],[0,0],[-10,0])[0], [-10,-10]));
assert(approx(circle_2tangents(10,[-10,0],[0,0],[0,10])[0], [-10,10]));
assert_approx(circle_2tangents(10,polar_to_xy(10,60),[0,0],[10,0])[0], polar_to_xy(20,30));
}
*test_circle_2tangents();
module test_circle_3points() {
count = 200;
coords = rands(-100,100,count,seed_value=888);
radii = rands(10,100,count,seed_value=390);
angles = rands(0,360,count,seed_value=699);
// 2D tests.
for(i = count(count)) {
cp = select(coords,i,i+1);
r = radii[i];
angs = sort(select(angles,i,i+2));
pts = [for (a=angs) cp+polar_to_xy(r,a)];
res = circle_3points(pts);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[0], expected=cp, delta=res[0]-cp);
assert(approx(res[0], cp));
}
if (!approx(res[1], r)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[1], expected=r, delta=res[1]-r);
assert(approx(res[1], r));
}
if (!approx(res[2], UP)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[2], expected=UP, delta=res[2]-UP);
assert(approx(res[2], UP));
}
}
for(i = count(count)) {
cp = select(coords,i,i+1);
r = radii[i];
angs = sort(select(angles,i,i+2));
pts = [for (a=angs) cp+polar_to_xy(r,a)];
res = circle_3points(pts[0], pts[1], pts[2]);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[0], expected=cp, delta=res[0]-cp);
assert(approx(res[0], cp));
}
if (!approx(res[1], r)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[1], expected=r, delta=res[1]-r);
assert(approx(res[1], r));
}
if (!approx(res[2], UP)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
echo(got=res[2], expected=UP, delta=res[2]-UP);
assert(approx(res[2], UP));
}
}
// 3D tests.
for(i = count(count)) {
cp = select(coords,i,i+2);
r = radii[i];
nrm = unit(select(coords,i+10,i+12));
n = nrm.z<0? -nrm : nrm;
angs = sort(select(angles,i,i+2));
pts = translate(cp,p=rot(from=UP,to=n,p=[for (a=angs) point3d(polar_to_xy(r,a))]));
res = circle_3points(pts);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("CP:", got=res[0], expected=cp, delta=res[0]-cp);
assert(approx(res[0], cp));
}
if (!approx(res[1], r)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("R:", got=res[1], expected=r, delta=res[1]-r);
assert(approx(res[1], r));
}
if (!approx(res[2], n)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("NORMAL:", got=res[2], expected=n, delta=res[2]-n);
assert(approx(res[2], n));
}
}
for(i = count(count)) {
cp = select(coords,i,i+2);
r = radii[i];
nrm = unit(select(coords,i+10,i+12));
n = nrm.z<0? -nrm : nrm;
angs = sort(select(angles,i,i+2));
pts = translate(cp,p=rot(from=UP,to=n,p=[for (a=angs) point3d(polar_to_xy(r,a))]));
res = circle_3points(pts[0], pts[1], pts[2]);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("CENTER:", got=res[0], expected=cp, delta=res[0]-cp);
assert(approx(res[0], cp));
}
if (!approx(res[1], r)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("RADIUS:", got=res[1], expected=r, delta=res[1]-r);
assert(approx(res[1], r));
}
if (!approx(res[2], n)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
echo("NORMAL:", got=res[2], expected=n, delta=res[2]-n);
assert(approx(res[2], n));
}
}
}
*test_circle_3points();
module test_circle_point_tangents() {
testvals = [
// cp r pt expect
[[0,0], 50, [50*sqrt(2),0], [polar_to_xy(50,45), polar_to_xy(50,-45)]],
[[5,10], 50, [5+50*sqrt(2),10], [[5,10]+polar_to_xy(50,45), [5,10]+polar_to_xy(50,-45)]],
[[0,0], 50, [0,50*sqrt(2)], [polar_to_xy(50,135), polar_to_xy(50,45)]],
[[5,10], 50, [5,10+50*sqrt(2)], [[5,10]+polar_to_xy(50,135), [5,10]+polar_to_xy(50,45)]],
[[5,10], 50, [5,10+50*sqrt(2)], [[5,10]+polar_to_xy(50,135), [5,10]+polar_to_xy(50,45)]],
[[5,10], 50, [5, 60], [[5, 60]]],
[[5,10], 50, [5, 59], []],
];
for (v = testvals) {
cp = v[0]; r = v[1]; pt = v[2]; expect = v[3];
info = str("cp=",cp, ", r=",r, ", pt=",pt);
assert_approx(circle_point_tangents(r=r,cp=cp,pt=pt), expect, info);
}
}
*test_circle_point_tangents();
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]);
assert_approx(plane3pt([0,0,0], [10,0,10], [0,0,20]), [0,1,0,0]);
assert_approx(plane3pt([0,2,0], [10,2,10], [0,2,20]), [0,1,0,2]);
assert_approx(plane3pt([0,0,0], [10,10,0], [20,0,0]), [0,0,1,0]);
assert_approx(plane3pt([0,0,2], [10,10,2], [20,0,2]), [0,0,1,2]);
}
*test_plane3pt();
module test_plane3pt_indexed() {
pts = [ [0,0,0], [10,0,0], [0,10,0], [0,0,10] ];
s13 = sqrt(1/3);
assert_approx(plane3pt_indexed(pts, 0,3,2), [1,0,0,0]);
assert_approx(plane3pt_indexed(pts, 0,2,3), [-1,0,0,0]);
assert_approx(plane3pt_indexed(pts, 0,1,3), [0,1,0,0]);
assert_approx(plane3pt_indexed(pts, 0,3,1), [0,-1,0,0]);
assert_approx(plane3pt_indexed(pts, 0,2,1), [0,0,1,0]);
assert_approx(plane3pt_indexed(pts, 0,1,2), [0,0,-1,0]);
assert_approx(plane3pt_indexed(pts, 3,2,1), [s13,s13,s13,10*s13]);
assert_approx(plane3pt_indexed(pts, 1,2,3), [-s13,-s13,-s13,-10*s13]);
}
*test_plane3pt_indexed();
module test_plane_from_points() {
assert_std(plane_from_points([[0,0,20], [0,10,10], [0,0,0], [0,5,3]]), [1,0,0,0]);
assert_std(plane_from_points([[2,0,20], [2,10,10], [2,0,0], [2,3,4]]), [1,0,0,2]);
assert_std(plane_from_points([[0,0,0], [10,0,10], [0,0,20], [5,0,7]]), [0,1,0,0]);
assert_std(plane_from_points([[0,2,0], [10,2,10], [0,2,20], [4,2,3]]), [0,1,0,2]);
assert_std(plane_from_points([[0,0,0], [10,10,0], [20,0,0], [8,3,0]]), [0,0,1,0]);
assert_std(plane_from_points([[0,0,2], [10,10,2], [20,0,2], [3,4,2]]), [0,0,1,2]);
}
*test_plane_from_points();
module test_polygon_normal() {
circ = path3d(circle($fn=37, r=3));
assert_approx(polygon_normal(circ), UP);
assert_approx(polygon_normal(rot(from=UP,to=[1,2,3],p=circ)), unit([1,2,3]));
assert_approx(polygon_normal(rot(from=UP,to=[4,-2,3],p=reverse(circ))), -unit([4,-2,3]));
assert_approx(polygon_normal(path3d([[0,0], [10,10], [11,10], [0,-1], [-1,1]])), UP);
}
*test_polygon_normal();
module test_plane_normal() {
assert_approx(plane_normal(plane3pt([0,0,20], [0,10,10], [0,0,0])), [1,0,0]);
assert_approx(plane_normal(plane3pt([2,0,20], [2,10,10], [2,0,0])), [1,0,0]);
assert_approx(plane_normal(plane3pt([0,0,0], [10,0,10], [0,0,20])), [0,1,0]);
assert_approx(plane_normal(plane3pt([0,2,0], [10,2,10], [0,2,20])), [0,1,0]);
assert_approx(plane_normal(plane3pt([0,0,0], [10,10,0], [20,0,0])), [0,0,1]);
assert_approx(plane_normal(plane3pt([0,0,2], [10,10,2], [20,0,2])), [0,0,1]);
}
*test_plane_normal();
module test_point_plane_distance() {
plane1 = plane3pt([-10,0,0], [0,10,0], [10,0,0]);
assert(point_plane_distance(plane1, [0,0,5]) == 5);
assert(point_plane_distance(plane1, [5,5,8]) == 8);
}
*test_point_plane_distance();
module test_polygon_line_intersection() {
poly0 = [ [-10,-10, 0],[10,-10, 0],[10,10,0],[0,5,0],[-10,10,0] ];
line0 = [ [-3,7.5,0],[3,7.5,0] ]; // a segment on poly0 plane, out of poly0
angs = rands(0,360,3);
poly = rot(angs,p=poly0);
lineon = rot(angs,p=line0);
info = info_str([["angs = ",angs],["line = ",lineon],["poly = ",poly]]);
// line on polygon plane
assert_approx(polygon_line_intersection(poly,lineon,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[true,false]),
[rot(angs,p=[[5,7.5,0],[10,7.5,0]])], info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[false,true]),
[rot(angs,p=[[-10,7.5,0],[-5,7.5,0]])], info);
assert_approx(polygon_line_intersection(poly,lineon,bounded=[false,false]),
rot(angs,p=[[[-10,7.5,0],[-5,7.5,0]],[[5,7.5,0],[10,7.5,0]]]), info);
// line parallel to polygon plane
linepll = move([0,0,1],lineon);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[true,false]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[false,true]),
undef, info);
assert_approx(polygon_line_intersection(poly,linepll,bounded=[false,false]),
undef, info);
// general case
trnsl = [0,0,1];
linegnr = move(trnsl,rot(angs,p=[[5,5,5],[3,3,3]]));
polygnr = move(trnsl,rot(angs,p=poly0));
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[true,true]),
undef, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[true,false]),
trnsl, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[false,true]),
undef, info);
assert_approx(polygon_line_intersection(polygnr,linegnr,bounded=[false,false]),
trnsl, info);
sq = path3d(square(10));
pentagram = 10*path3d(turtle(["move",10,"left",144], repeat=4));
for (tran = [ident(4), skew(sxy=1.2)*scale([.9,1,1.2])*yrot(14)*zrot(37)*xrot(9)])
{
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[5,5,-1], [5,5,10]])), apply(tran, [5,5,0]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[5,5,1], [5,5,10]])), apply(tran, [5,5,0]));
assert(undef==polygon_line_intersection(apply(tran,sq),apply(tran,[[5,5,1], [5,5,10]]),RAY));
assert(undef==polygon_line_intersection(apply(tran,sq),apply(tran,[[11,11,-1],[11,11,1]])));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[5,0,-10], [5,0,10]])), apply(tran, [5,0,0]));
assert_equal(polygon_line_intersection(apply(tran,sq),apply(tran,[[5,0,1], [5,0,10]]),RAY), undef);
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[10,0,1],[10,0,10]])), apply(tran, [10,0,0]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[1,5,0],[9,6,0]])), apply(tran, [[[0,4.875,0],[10,6.125,0]]]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[1,5,0],[9,6,0]]),SEGMENT), apply(tran, [[[1,5,0],[9,6,0]]]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[-1,-1,0],[8,8,0]])), apply(tran, [[[0,0,0],[10,10,0]]]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[-1,-1,0],[8,8,0]]),SEGMENT), apply(tran, [[[0,0,0],[8,8,0]]]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[-1,-1,0],[8,8,0]]),RAY), apply(tran, [[[0,0,0],[10,10,0]]]));
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[-2,4,0], [12,11,0]]),RAY), apply(tran, [[[0,5,0],[10,10,0]]]));
assert_equal(polygon_line_intersection(apply(tran,sq),apply(tran,[[-20,0,0],[20,40,0]]),RAY), undef);
assert_approx(polygon_line_intersection(apply(tran,sq),apply(tran,[[-1,0,0],[11,0,0]])), apply(tran, [[[0,0,0],[10,0,0]]]));
}
assert_approx(polygon_line_intersection(path2d(sq),[[1,5],[9,6]],SEGMENT), [[[1,5],[9,6]]]);
assert_approx(polygon_line_intersection(path2d(sq),[[1,5],[9,6]],LINE), [[[0,4.875],[10,6.125]]]);
assert_approx(polygon_line_intersection(pentagram,[[50,10,-4],[54,12,4]], nonzero=true), [52,11,0]);
assert_equal(polygon_line_intersection(pentagram,[[50,10,-4],[54,12,4]], nonzero=false), undef);
assert_approx(polygon_line_intersection(pentagram,[[50,-10,-4],[54,-12,4]], nonzero=true), [52,-11,0]);
assert_approx(polygon_line_intersection(pentagram,[[50,-10,-4],[54,-12,4]], nonzero=false), [52,-11,0]);
assert_approx(polygon_line_intersection(star(8,step=3,od=10), [[-5,3], [5,3]]),
[[[-3.31370849898, 3], [-2.24264068712, 3]],
[[-0.828427124746, 3], [0.828427124746, 3]],
[[2.24264068712, 3], [3.31370849898, 3]]]);
tran = skew(sxy=1.2)*scale([.9,1,1.2])*yrot(14)*zrot(37)*xrot(9);
// assemble multiple edges into one edge
assert_approx(polygon_line_intersection(star(r=15,n=8,step=2), [[20,-5],[-5,20]]), [[[15,0],[0,15]]]);
assert_approx(polygon_line_intersection(apply(tran,path3d(star(r=15,n=8,step=2))), apply(tran,[[20,-5,0],[-5,20,0]])), apply(tran,[[[15,0,0],[0,15,0]]]));
// line going the other direction
assert_approx(polygon_line_intersection(star(r=15,n=8,step=2), [[-5,20],[20,-5]]), [[[0,15],[15,0]]]);
assert_approx(polygon_line_intersection(apply(tran,path3d(star(r=15,n=8,step=2))), apply(tran,[[-5,20,0],[20,-5,0]])),apply(tran, [[[0,15,0],[15,0,0]]]));
// single point
assert_approx(polygon_line_intersection(hexagon(r=15), [[15,-10],[15,13]], RAY), [[[15,0]]]);
assert_approx(polygon_line_intersection(apply(tran,path3d(hexagon(r=15))), apply(tran,[[15,-10,0],[15,13,0]]), RAY),
[[apply(tran,[15,0,0])]]);
// two points
assert_approx(polygon_line_intersection(star(r=15,n=8,step=3), rot(22.5,p=[[15,-10],[15,20]],cp=[15,0])),
[[[15,0]], [[10.6066017178, 10.6066017178]]]);
assert_approx(polygon_line_intersection(apply(tran,path3d(star(r=15,n=8,step=3))), apply(tran,rot(22.5,p=[[15,-10,0],[15,20,0]],cp=[15,0,0]))),
[[apply(tran,[15,0,0])], [apply(tran,[10.6066017178, 10.6066017178,0])]]);
// two segments and one point
star7 = star(r=25,ir=9,n=7);
assert_approx(polygon_line_intersection(star7, [left(10,p=star7[8]), right(50,p=star7[8])]),
[[[-22.5242216976, 10.8470934779]],
[[-5.60077322195, 10.8470934779], [0.997372374838, 10.8470934779]],
[[4.61675816681, 10.8470934779], [11.4280421589, 10.8470934779]]]);
assert_approx(polygon_line_intersection(apply(tran,path3d(star7)),
apply(tran, path3d([left(10,p=star7[8]), right(50,p=star7[8])]))),
[[apply(tran,[-22.5242216976, 10.8470934779,0])],
apply(tran,[[-5.60077322195, 10.8470934779,0], [0.997372374838, 10.8470934779,0]]),
apply(tran,[[4.61675816681, 10.8470934779,0], [11.4280421589, 10.8470934779,0]])]);
}
*test_polygon_line_intersection();
module test_is_coplanar() {
assert(is_coplanar([ [5,5,1],[0,0,1],[-1,-1,1] ]) == false);
assert(is_coplanar([ [5,5,1],[0,0,0],[-1,-1,1] ]) == true);
assert(is_coplanar([ [0,0,0],[1,0,1],[1,1,1], [0,1,2] ]) == false);
assert(is_coplanar([ [0,0,0],[1,0,1],[1,1,2], [0,1,1] ]) == true);
}
*test_is_coplanar();
module test__is_point_above_plane() {
plane = plane3pt([0,0,0], [0,10,10], [10,0,10]);
assert(_is_point_above_plane(plane, [5,5,10]) == false);
assert(_is_point_above_plane(plane, [-5,0,0]) == true);
assert(_is_point_above_plane(plane, [5,0,0]) == false);
assert(_is_point_above_plane(plane, [0,-5,0]) == true);
assert(_is_point_above_plane(plane, [0,5,0]) == false);
assert(_is_point_above_plane(plane, [0,0,5]) == true);
assert(_is_point_above_plane(plane, [0,0,-5]) == false);
}
*test__is_point_above_plane();
module test_polygon_area() {
assert(approx(polygon_area([[1,1],[-1,1],[-1,-1],[1,-1]]), 4));
assert(approx(polygon_area(circle(r=50,$fn=1000),signed=true), -PI*50*50, eps=0.1));
assert(approx(polygon_area(rot([13,27,75],
p=path3d(circle(r=50,$fn=1000),fill=23)),
signed=true), PI*50*50, eps=0.1));
assert(abs(polygon_area([[0,0], [0,10], [10,0]],signed=true) + 50) < EPSILON);
assert(abs(polygon_area([[0,0], [0,10], [0,15]],signed=true)) < EPSILON);
assert(abs(polygon_area([[0,0], [10,0], [0,10]],signed=true) - 50) < EPSILON);
}
*test_polygon_area();
module test_is_polygon_convex() {
assert(is_polygon_convex([[1,1],[-1,1],[-1,-1],[1,-1]]));
assert(is_polygon_convex(circle(r=50,$fn=1000)));
assert(is_polygon_convex(rot([50,120,30], p=path3d(circle(1,$fn=50)))));
assert(!is_polygon_convex([[1,1],[0,0],[-1,1],[-1,-1],[1,-1]]));
assert(!is_polygon_convex([for (i=[0:36]) let(a=-i*10) (10+i)*[cos(a),sin(a)]])); // spiral
}
*test_is_polygon_convex();
module test_reindex_polygon() {
pent = subdivide_path([for(i=[0:4])[sin(72*i),cos(72*i)]],5);
circ = circle($fn=5,r=2.2);
assert_approx(reindex_polygon(circ,pent), [[0.951056516295,0.309016994375],[0.587785252292,-0.809016994375],[-0.587785252292,-0.809016994375],[-0.951056516295,0.309016994375],[0,1]]);
poly = [[-1,1],[-1,-1],[1,-1],[1,1],[0,0]];
ref = [for(i=[0:4])[sin(72*i),cos(72*i)]];
assert_approx(reindex_polygon(ref,poly),[[0,0],[1,1],[1,-1],[-1,-1],[-1,1]]);
}
*test_reindex_polygon();
module test_align_polygon() {
// These tests fail because align_polygon displays output
/*
ellipse = yscale(3,circle(r=10, $fn=32));
tri = move([-50/3,-9],
subdivide_path([[0,0], [50,0], [0,27]], 32));
aligned = align_polygon(ellipse,tri, [0:5:180]);
assert_approx(aligned,
[[8.6933324366, 2.32937140592], [9.77174512453,
-1.69531953695], [10.8501578125, -5.72001047982],
[11.9285705004, -9.74470142269], [13.0069831883,
-13.7693923656], [9.28126928691, -14.7676943967],
[5.55555538551, -15.7659964278], [1.82984148411,
-16.7642984589], [-1.89587241729, -17.76260049],
[-5.62158631869, -18.7609025211], [-9.34730022009,
-19.7592045522], [-13.0730141215, -20.7575065833],
[-12.0623183481, -16.5048600039], [-11.0516225746,
-12.2522134245], [-10.0409268012, -7.99956684512],
[-9.03023102775, -3.74692026572], [-8.01953525431,
0.505726313678], [-7.00883948087, 4.75837289308],
[-5.99814370744, 9.01101947248], [-4.987447934,
13.2636660519], [-3.97675216056, 17.5163126313],
[-2.96605638713, 21.7689592107], [-1.95536061369,
26.0216057901], [-0.944664840253, 30.2742523695],
[0.0660309331843, 34.5268989489], [1.14444362111,
30.502208006], [2.22285630904, 26.4775170631],
[3.30126899697, 22.4528261203], [4.37968168489,
18.4281351774], [5.45809437282, 14.4034442345],
[6.53650706075, 10.3787532917], [7.61491974867,
6.35406234879]]);
ellipse2 = yscale(2,circle(r=10, $fn=32));
tri2 = subdivide_path([[0,0], [27,0], [-7,50]], 32);
T = [for(x=[-10:0], y=[-30:-15]) move([x,y])];
aligned2 = align_polygon(ellipse2,tri2, trans=T);
assert_approx(aligned2,
[[10.5384615385, -3.61538461538], [13.1538461538,
-7.46153846154], [15.7692307692, -11.3076923077],
[18.3846153846, -15.1538461538], [21, -19],
[17.1428571429, -19], [13.2857142857, -19],
[9.42857142857, -19], [5.57142857143, -19],
[1.71428571429, -19], [-2.14285714286, -19], [-6, -19],
[-6.58333333333, -14.8333333333], [-7.16666666667,
-10.6666666667], [-7.75, -6.5], [-8.33333333333,
-2.33333333333], [-8.91666666667, 1.83333333333], [-9.5,
6], [-10.0833333333, 10.1666666667], [-10.6666666667,
14.3333333333], [-11.25, 18.5], [-11.8333333333,
22.6666666667], [-12.4166666667, 26.8333333333], [-13,
31], [-10.3846153846, 27.1538461538], [-7.76923076923,
23.3076923077], [-5.15384615385, 19.4615384615],
[-2.53846153846, 15.6153846154], [0.0769230769231,
11.7692307692], [2.69230769231, 7.92307692308],
[5.30769230769, 4.07692307692], [7.92307692308,
0.230769230769]]);
*/
}
*test_align_polygon();
module test__noncollinear_triple() {
assert(_noncollinear_triple([[1,1],[2,2],[3,3],[4,4],[4,5],[5,6]]) == [0,5,3]);
assert(_noncollinear_triple([[1,1],[2,2],[8,3],[4,4],[4,5],[5,6]]) == [0,2,5]);
u = unit([5,3]);
assert_equal(_noncollinear_triple([for(i = [2,3,4,5,7,12,15]) i * u], error=false),[]);
}
*test__noncollinear_triple();
module test_centroid() {
// polygons
$fn = 24;
assert_approx(centroid(circle(d=100)), [0,0]);
assert_approx(centroid(rect([40,60],rounding=10,anchor=LEFT)), [20,0]);
assert_approx(centroid(rect([40,60],rounding=10,anchor=FWD)), [0,30]);
poly = move([1,2.5,3.1],p=rot([12,49,24], p=path3d(circle(10,$fn=33))));
assert_approx(centroid(poly), [1,2.5,3.1]);
// regions
R = [square(10), move([5,4],circle(r=3,$fn=32)), right(15,square(7)), move([18,3],circle(r=2,$fn=5))];
assert_approx(centroid(R), [9.82836532809, 4.76313546433]);
// VNFs
assert_approx(centroid(cube(100, center=false)), [50,50,50]);
assert_approx(centroid(cube(100, center=true)), [0,0,0]);
assert_approx(centroid(cube(100, anchor=[1,1,1])), [-50,-50,-50]);
assert_approx(centroid(cube(100, anchor=BOT)), [0,0,50]);
assert_approx(centroid(cube(100, anchor=TOP)), [0,0,-50]);
assert_approx(centroid(sphere(d=100, anchor=CENTER, $fn=36)), [0,0,0]);
assert_approx(centroid(sphere(d=100, anchor=BOT, $fn=36)), [0,0,50]);
ellipse = xscale(2, p=circle($fn=24, r=3));
assert_approx(centroid(path_sweep(pentagon(r=1), path3d(ellipse), closed=true)),[0,0,0]);
}
*test_centroid();
module test_point_in_polygon() {
poly = [for (a=[0:30:359]) 10*[cos(a),sin(a)]];
poly2 = [ [-3,-3],[2,-3],[2,1],[-1,1],[-1,-1],[1,-1],[1,2],[-3,2] ];
assert(point_in_polygon([0,0], poly) == 1);
assert(point_in_polygon([20,0], poly) == -1);
assert(point_in_polygon([20,0], poly,nonzero=false) == -1);
assert(point_in_polygon([5,5], poly) == 1);
assert(point_in_polygon([-5,5], poly) == 1);
assert(point_in_polygon([-5,-5], poly) == 1);
assert(point_in_polygon([5,-5], poly) == 1);
assert(point_in_polygon([5,-5], poly,nonzero=false,eps=EPSILON) == 1);
assert(point_in_polygon([-10,-10], poly) == -1);
assert(point_in_polygon([10,0], poly) == 0);
assert(point_in_polygon([0,10], poly) == 0);
assert(point_in_polygon([0,-10], poly) == 0);
assert(point_in_polygon([0,-10], poly,nonzero=false) == 0);
assert(point_in_polygon([0,0], poly2,nonzero=true) == 1);
assert(point_in_polygon([0,1], poly2,nonzero=true) == 0);
assert(point_in_polygon([0,1], poly2,nonzero=false) == 0);
assert(point_in_polygon([1,0], poly2,nonzero=false) == 0);
assert(point_in_polygon([0,0], poly2,nonzero=false,eps=EPSILON) == -1);
}
*test_point_in_polygon();
module test_is_polygon_clockwise() {
assert(is_polygon_clockwise([[-1,1],[1,1],[1,-1],[-1,-1]]));
assert(!is_polygon_clockwise([[1,1],[-1,1],[-1,-1],[1,-1]]));
assert(is_polygon_clockwise(circle(d=100)));
assert(is_polygon_clockwise(square(100)));
}
*test_is_polygon_clockwise();
module test_clockwise_polygon() {
path = circle(d=100);
rpath = concat([path[0]], reverse(select(path,1,-1)));
assert(clockwise_polygon(path) == path);
assert(clockwise_polygon(rpath) == path);
}
*test_clockwise_polygon();
module test_ccw_polygon() {
path = circle(d=100);
rpath = concat([path[0]], reverse(select(path,1,-1)));
assert(ccw_polygon(path) == rpath);
assert(ccw_polygon(rpath) == rpath);
}
*test_ccw_polygon();
module test_reverse_polygon() {
path = circle(d=100);
rpath = concat([path[0]], reverse(select(path,1,-1)));
assert(reverse_polygon(path) == rpath);
assert(reverse_polygon(rpath) == path);
}
*test_reverse_polygon();
module test_convex_distance() {
// 2D
c1 = circle(10,$fn=24);
c2 = move([15,0], p=c1);
assert(convex_distance(c1, c2)==0);
c3 = move([22,0],c1);
assert_approx(convex_distance(c1, c3),2);
// 3D
s1 = sphere(10,$fn=4);
s2 = move([15,0], p=s1);
assert_approx(convex_distance(s1[0], s2[0]), 0.857864376269);
s3 = move([25.3,0],s1);
assert_approx(convex_distance(s1[0], s3[0]), 11.1578643763);
s4 = move([30,25],s1);
assert_approx(convex_distance(s1[0], s4[0]), 28.8908729653);
s5 = move([10*sqrt(2),0],s1);
assert_approx(convex_distance(s1[0], s5[0]), 0);
}
*test_convex_distance();
module test_convex_collision() {
// 2D
c1 = circle(10,$fn=24);
c2 = move([15,0], p=c1);
assert(convex_collision(c1, c2));
c3 = move([22,0],c1);
assert(!convex_collision(c1, c3));
// 3D
s1 = sphere(10,$fn=4);
s2 = move([15,0], p=s1);
assert(!convex_collision(s1[0], s2[0]));
s3 = move([25.3,0],s1);
assert(!convex_collision(s1[0], s3[0]));
s4 = move([5,0],s1);
assert(convex_collision(s1[0], s4[0]));
s5 = move([10*sqrt(2),0],s1);
assert(convex_collision(s1[0], s5[0]));
}
*test_convex_distance();
module test_rot_decode() {
Tlist = [
rot(37),
xrot(49),
yrot(88),
rot(37,v=[1,3,3]),
rot(41,v=[2,-3,4]),
rot(180),
xrot(180),
yrot(180),
rot(180, v=[3,2,-5], cp=[3,5,18]),
rot(0.1, v=[1,2,3]),
rot(-47,v=[3,4,5],cp=[9,3,4]),
rot(197,v=[13,4,5],cp=[9,-3,4]),
move([3,4,5]),
move([3,4,5]) * rot(a=56, v=[5,3,-3], cp=[2,3,4]),
ident(4)
];
errlist = [for(T = Tlist)
let(
parm = rot_decode(T),
restore = move(parm[3])*rot(a=parm[0],v=parm[1],cp=parm[2])
)
norm_fro(restore-T)];
assert(max(errlist)<1e-13);
}
*test_rot_decode();
function standard_faces(faces) =
sort([for(face=faces)
list_rotate(face, min_index(face))]);
module test_hull() {
assert_equal(hull([[3,4],[5,5]]), [0,1]);
assert_equal(hull([[3,4,1],[5,5,3]]), [0,1]);
test_collinear_2d = let(u = unit([5,3])) [ for(i = [9,2,3,4,5,7,12,15,13]) i * u ];
assert_equal(sort(hull(test_collinear_2d)), [1,7]);
test_collinear_3d = let(u = unit([5,3,2])) [ for(i = [9,2,3,4,5,7,12,15,13]) i * u ];
assert_equal(sort(hull(test_collinear_3d)), [1,7]);
/* // produces some extra points along edges
test_square_2d = [for(x=[1:5], y=[2:6]) [x,y]];
echo(test_square_2d);
move_copies(test_square_2d) circle(r=.1,$fn=16);
color("red")move_copies(select(test_square_2d,hull(test_square_2d))) circle(r=.1,$fn=16);
*/
/* // also produces extra points along edges
test_square_2d = rot(22,p=[for(x=[1:5], y=[2:6]) [x,y]]);
echo(test_square_2d);
move_copies(test_square_2d) circle(r=.1,$fn=16);
color("red")move_copies(select(test_square_2d,hull(test_square_2d))) circle(r=.1,$fn=16);
*/
rand10_2d = [[1.55356, -1.98965], [4.23157, -0.947788], [-4.06193, -1.55463],
[1.23889, -3.73133], [-1.02637, -4.0155], [4.26806, -4.61909],
[3.59556, -3.1574], [-2.77776, -4.21857], [-3.66253,-4.34458], [1.82324, 0.102025]];
assert_equal(sort(hull(rand10_2d)), [1,2,5,8,9]);
rand75_2d = [[-3.14743, -3.28139], [0.15343, -0.370249], [0.082565, 3.95939], [-2.56925, -3.16262], [-1.59463, 4.20893],
[-4.90744, -1.21374], [-1.0819, -1.93703], [-3.72723, -3.0744], [-3.34339, 1.53535], [3.15803, -0.307388], [4.23289,
4.46259], [1.73624, 1.38918], [3.72087, -1.55028], [1.2604, 2.30502], [-0.966431, 1.673], [-3.26866, -0.531443], [1.52605,
0.991804], [-1.26305, 1.0737], [-4.31943, 4.11932], [0.488101, 0.0425981], [1.0233, -0.723037], [-4.73406, 2.14568],
[-4.75915, 3.83262], [4.90999, -2.76668], [1.91971, -3.8604], [4.38594, -0.761767], [-0.352984, 1.55291], [2.02714,
-0.340099], [1.76052, 2.09196], [-1.27485, -4.39477], [4.36364, 3.84964], [0.593612, -4.00028], [3.06833, -3.67117],
[4.26834, -4.21213], [4.60226, -0.120432], [-2.45646, 2.60327], [-4.79461, 3.83724], [-3.29755, 0.760159], [0.218423,
4.1687], [-0.115829, -2.06242], [-3.96188, 3.21568], [4.3018, -2.5299], [-4.41694, 4.75173], [-3.8393, 2.82212], [-1.14268,
1.80751], [2.05805, 1.68593], [-3.0159, -2.91139], [-1.44828, -1.93564], [-0.265887, 0.519893], [-0.457361, -0.610096],
[-0.426359, -2.37315], [-3.1018, 2.31141], [0.179141, -3.56242], [-0.491786, 0.813055], [-3.28502, -1.18933], [0.0914813,
2.16122], [4.5777, 4.83972], [-1.07096, 2.74992], [-0.698689, 3.9032], [-1.21809, -1.54434], [3.14457, 4.92302], [-4.63176,
2.81952], [4.84414, 4.63699], [2.4259, -0.747268], [-1.52088, -4.58305], [1.6961, -3.73678], [-0.483003, -3.67283],
[-3.72746, -0.284265], [2.07629, 1.99902], [-3.12698, -0.96353], [4.02254, 3.41521], [-0.963391, -3.2143], [0.315255,
0.593049], [1.57006, 1.80436], [4.60957, -2.86325]];
assert_equal(sort(hull(rand75_2d)),[5,7,23,33,36,42,56,60,62,64]);
rand10_2d_rot = rot([22,44,12], p=path3d(rand10_2d));
assert_equal(sort(hull(rand10_2d_rot)), [1,2,5,8,9]);
rand75_2d_rot = rot([122,-44,32], p=path3d(rand75_2d));
assert_equal(sort(hull(rand75_2d_rot)), [5,7,23,33,36,42,56,60,62,64]);
testpoints_on_sphere = [ for(p =
[
[1,PHI,0], [-1,PHI,0], [1,-PHI,0], [-1,-PHI,0],
[0,1,PHI], [0,-1,PHI], [0,1,-PHI], [0,-1,-PHI],
[PHI,0,1], [-PHI,0,1], [PHI,0,-1], [-PHI,0,-1]
])
unit(p)
];
assert_equal(standard_faces(hull(testpoints_on_sphere)),
standard_faces([[8, 4, 0], [0, 4, 1], [4, 8, 5], [8, 2, 5], [2, 3, 5], [0, 1, 6], [3, 2, 7], [1, 4, 9], [4, 5, 9],
[5, 3, 9], [8, 0, 10], [2, 8, 10], [0, 6, 10], [6, 7, 10], [7, 2, 10], [6, 1, 11], [3, 7, 11], [7, 6, 11], [1, 9, 11], [9, 3, 11]]));
rand10_3d = [[14.0893, -15.2751, 21.0843], [-14.1564, 17.5751, 3.32094], [17.4966, 12.1717, 18.0607], [24.5489, 9.64591, 10.4738], [-12.0233, -24.4368, 13.1614],
[6.24019, -18.4135, 24.9554], [11.9438, -15.9724, -22.6454], [11.6147, 7.56059, 7.5667], [-19.7491, 9.42769, 15.3419], [-10.3726, 16.3559, 3.38503]];
assert_equal(standard_faces(hull(rand10_3d)),
standard_faces([[3, 6, 0], [1, 3, 2], [3, 0, 2], [6, 1, 4], [0, 6, 5], [6, 4, 5], [2, 0, 5], [1, 2, 8], [2, 5, 8], [4, 1, 8], [5, 4, 8], [6, 3, 9], [3, 1, 9], [1, 6, 9]]));
rand25_3d = [[-20.5261, 14.5058, -11.6349], [16.4625, 20.1316, 12.9816], [-14.0268, 5.58802, 17.686], [-5.47944, 16.2501,
5.3086], [20.2168, -11.8466, 12.4598], [14.4633, -15.1479, 4.82151], [12.7897, 5.25704, 19.6205], [11.2456,
18.2794, -3.47074], [-1.87665, 22.9852, 1.99367], [-15.6052, -2.11009, 14.0096], [-10.7389, -14.569,
5.6121], [24.5965, 17.9039, 20.8313], [-13.7054, 13.3362, 1.50374], [10.1111, -23.1494, 19.9305], [14.154,
19.6682, -0.170182], [-22.6438, 22.7429, -0.776773], [-9.75056, 17.8896, -8.04152], [23.1746, 20.5475,
22.6957], [-10.5356, -4.32407, -7.0911], [2.20779, -8.30749, 6.87185], [23.2643, 2.64462, -19.0087],
[24.4055, 24.4504, 23.4777], [-3.84086, -6.98473, -10.2889], [0.178043, -16.07, 16.8081], [-8.86482,
-12.8256, 14.7418], [11.1759, -11.5614, -11.643], [7.16751, 13.9344, -19.1675], [2.26602, -10.5374,
0.125718], [-13.9053, 11.1143, -21.9289], [24.9018, -23.5307, -21.4684], [-13.6609, -19.6495, -8.91583],
[-16.5393, -22.4105, -6.91617], [-4.11378, -3.14362, -5.6881], [7.50883, -17.5284, -0.0615319], [-7.41739,
0.0721313, -7.47111], [22.6975, -7.99655, 14.0555], [-13.3644, 9.26993, 20.858], [-13.6889, 16.7462,
-14.5836], [16.5137, 3.90703, -5.49396], [-6.75614, -11.1444, -24.5309], [22.9868, 10.0028, 12.2866],
[-4.81079, -0.967785, -10.4726], [-0.949023, 23.1441, -2.08208], [16.1256, -8.2295, -24.0113], [6.45274,
-7.21416, 23.1409], [22.8274, 1.07038, 19.1756], [-10.6256, -10.0112, -6.12274], [6.29254, -7.81875,
-24.4037], [22.8538, 8.78163, -6.82567], [-1.96142, 19.1728, -1.726]];
assert_equal(sort(hull(rand25_3d)),sort([[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
31], [15, 9, 31], [9, 24, 31], [24, 13, 31], [28, 0, 31], [11, 29, 35], [29, 13, 35], [15,
21, 36], [9, 15, 36], [24, 9, 36], [13, 24, 36], [15, 28, 37], [28, 26, 37], [28, 31, 39],
[31, 29, 39], [14, 21, 42], [21, 15, 42], [26, 14, 42], [15, 37, 42], [37, 26, 42], [29, 20,
43], [39, 29, 43], [20, 26, 43], [26, 28, 43], [21, 13, 44], [13, 36, 44], [36, 21, 44],
[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]));
/* // Inconsistently treats coplanar faces: sometimes face center vertex is included in output, sometimes not
test_cube_3d = [for(x=[1:3], y=[1:3], z=[1:3]) [x,y,z]];
assert_equal(hull(test_cube_3d), [[3, 2, 0], [2, 3, 4], [26, 2, 5], [2, 4, 5], [4, 3, 6], [5, 4, 6], [5, 6, 7], [6, 26, 7], [26, 5, 8],
[5, 7, 8], [7, 26, 8], [0, 2, 9], [3, 0, 9], [6, 3, 9], [9, 2, 10], [2, 26, 11], [10, 2, 11], [6, 9, 12],
[26, 6, 15], [6, 12, 15], [9, 10, 18], [10, 11, 18], [12, 9, 18], [15, 12, 18], [26, 18, 19], [18, 11, 19],
[11, 26, 20], [26, 19, 20], [19, 11, 20], [15, 18, 21], [18, 26, 21], [26, 15, 24], [15, 21, 24], [21, 26, 24]]);
echo(len=len(hull(test_cube_3d)));
*/
}
test_hull();
module test_hull2d_path() {
assert_equal(hull([[3,4],[5,5]]), [0,1]);
assert_equal(hull([[3,4,1],[5,5,3]]), [0,1]);
test_collinear_2d = let(u = unit([5,3])) [ for(i = [9,2,3,4,5,7,12,15,13]) i * u ];
assert_equal(sort(hull(test_collinear_2d)), [1,7]);
test_collinear_3d = let(u = unit([5,3,2])) [ for(i = [9,2,3,4,5,7,12,15,13]) i * u ];
assert_equal(sort(hull(test_collinear_3d)), [1,7]);
rand10_2d = [[1.55356, -1.98965], [4.23157, -0.947788], [-4.06193, -1.55463],
[1.23889, -3.73133], [-1.02637, -4.0155], [4.26806, -4.61909],
[3.59556, -3.1574], [-2.77776, -4.21857], [-3.66253,-4.34458], [1.82324, 0.102025]];
assert_equal(sort(hull(rand10_2d)), [1,2,5,8,9]);
rand75_2d = [[-3.14743, -3.28139], [0.15343, -0.370249], [0.082565, 3.95939], [-2.56925, -3.16262], [-1.59463, 4.20893],
[-4.90744, -1.21374], [-1.0819, -1.93703], [-3.72723, -3.0744], [-3.34339, 1.53535], [3.15803, -0.307388], [4.23289,
4.46259], [1.73624, 1.38918], [3.72087, -1.55028], [1.2604, 2.30502], [-0.966431, 1.673], [-3.26866, -0.531443], [1.52605,
0.991804], [-1.26305, 1.0737], [-4.31943, 4.11932], [0.488101, 0.0425981], [1.0233, -0.723037], [-4.73406, 2.14568],
[-4.75915, 3.83262], [4.90999, -2.76668], [1.91971, -3.8604], [4.38594, -0.761767], [-0.352984, 1.55291], [2.02714,
-0.340099], [1.76052, 2.09196], [-1.27485, -4.39477], [4.36364, 3.84964], [0.593612, -4.00028], [3.06833, -3.67117],
[4.26834, -4.21213], [4.60226, -0.120432], [-2.45646, 2.60327], [-4.79461, 3.83724], [-3.29755, 0.760159], [0.218423,
4.1687], [-0.115829, -2.06242], [-3.96188, 3.21568], [4.3018, -2.5299], [-4.41694, 4.75173], [-3.8393, 2.82212], [-1.14268,
1.80751], [2.05805, 1.68593], [-3.0159, -2.91139], [-1.44828, -1.93564], [-0.265887, 0.519893], [-0.457361, -0.610096],
[-0.426359, -2.37315], [-3.1018, 2.31141], [0.179141, -3.56242], [-0.491786, 0.813055], [-3.28502, -1.18933], [0.0914813,
2.16122], [4.5777, 4.83972], [-1.07096, 2.74992], [-0.698689, 3.9032], [-1.21809, -1.54434], [3.14457, 4.92302], [-4.63176,
2.81952], [4.84414, 4.63699], [2.4259, -0.747268], [-1.52088, -4.58305], [1.6961, -3.73678], [-0.483003, -3.67283],
[-3.72746, -0.284265], [2.07629, 1.99902], [-3.12698, -0.96353], [4.02254, 3.41521], [-0.963391, -3.2143], [0.315255,
0.593049], [1.57006, 1.80436], [4.60957, -2.86325]];
assert_equal(sort(hull(rand75_2d)),[5,7,23,33,36,42,56,60,62,64]);
rand10_2d_rot = rot([22,44,12], p=path3d(rand10_2d));
assert_equal(sort(hull(rand10_2d_rot)), [1,2,5,8,9]);
rand75_2d_rot = rot([122,-44,32], p=path3d(rand75_2d));
assert_equal(sort(hull(rand75_2d_rot)), [5,7,23,33,36,42,56,60,62,64]);
}
test_hull2d_path();
module test_hull3d_faces() {
testpoints_on_sphere = [ for(p =
[
[1,PHI,0], [-1,PHI,0], [1,-PHI,0], [-1,-PHI,0],
[0,1,PHI], [0,-1,PHI], [0,1,-PHI], [0,-1,-PHI],
[PHI,0,1], [-PHI,0,1], [PHI,0,-1], [-PHI,0,-1]
])
unit(p)
];
assert_equal(standard_faces(hull(testpoints_on_sphere)),
standard_faces([[8, 4, 0], [0, 4, 1], [4, 8, 5], [8, 2, 5], [2, 3, 5], [0, 1, 6], [3, 2, 7], [1, 4, 9], [4, 5, 9],
[5, 3, 9], [8, 0, 10], [2, 8, 10], [0, 6, 10], [6, 7, 10], [7, 2, 10], [6, 1, 11], [3, 7, 11], [7, 6, 11], [1, 9, 11], [9, 3, 11]]));
rand10_3d = [[14.0893, -15.2751, 21.0843], [-14.1564, 17.5751, 3.32094], [17.4966, 12.1717, 18.0607], [24.5489, 9.64591, 10.4738], [-12.0233, -24.4368, 13.1614],
[6.24019, -18.4135, 24.9554], [11.9438, -15.9724, -22.6454], [11.6147, 7.56059, 7.5667], [-19.7491, 9.42769, 15.3419], [-10.3726, 16.3559, 3.38503]];
assert_equal(standard_faces(hull(rand10_3d)),
standard_faces([[3, 6, 0], [1, 3, 2], [3, 0, 2], [6, 1, 4], [0, 6, 5], [6, 4, 5], [2, 0, 5], [1, 2, 8], [2, 5, 8], [4, 1, 8], [5, 4, 8], [6, 3, 9], [3, 1, 9], [1, 6, 9]]));
rand25_3d = [[-20.5261, 14.5058, -11.6349], [16.4625, 20.1316, 12.9816], [-14.0268, 5.58802, 17.686], [-5.47944, 16.2501,
5.3086], [20.2168, -11.8466, 12.4598], [14.4633, -15.1479, 4.82151], [12.7897, 5.25704, 19.6205], [11.2456,
18.2794, -3.47074], [-1.87665, 22.9852, 1.99367], [-15.6052, -2.11009, 14.0096], [-10.7389, -14.569,
5.6121], [24.5965, 17.9039, 20.8313], [-13.7054, 13.3362, 1.50374], [10.1111, -23.1494, 19.9305], [14.154,
19.6682, -0.170182], [-22.6438, 22.7429, -0.776773], [-9.75056, 17.8896, -8.04152], [23.1746, 20.5475,
22.6957], [-10.5356, -4.32407, -7.0911], [2.20779, -8.30749, 6.87185], [23.2643, 2.64462, -19.0087],
[24.4055, 24.4504, 23.4777], [-3.84086, -6.98473, -10.2889], [0.178043, -16.07, 16.8081], [-8.86482,
-12.8256, 14.7418], [11.1759, -11.5614, -11.643], [7.16751, 13.9344, -19.1675], [2.26602, -10.5374,
0.125718], [-13.9053, 11.1143, -21.9289], [24.9018, -23.5307, -21.4684], [-13.6609, -19.6495, -8.91583],
[-16.5393, -22.4105, -6.91617], [-4.11378, -3.14362, -5.6881], [7.50883, -17.5284, -0.0615319], [-7.41739,
0.0721313, -7.47111], [22.6975, -7.99655, 14.0555], [-13.3644, 9.26993, 20.858], [-13.6889, 16.7462,
-14.5836], [16.5137, 3.90703, -5.49396], [-6.75614, -11.1444, -24.5309], [22.9868, 10.0028, 12.2866],
[-4.81079, -0.967785, -10.4726], [-0.949023, 23.1441, -2.08208], [16.1256, -8.2295, -24.0113], [6.45274,
-7.21416, 23.1409], [22.8274, 1.07038, 19.1756], [-10.6256, -10.0112, -6.12274], [6.29254, -7.81875,
-24.4037], [22.8538, 8.78163, -6.82567], [-1.96142, 19.1728, -1.726]];
assert_equal(sort(hull(rand25_3d)), sort([[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
31], [15, 9, 31], [9, 24, 31], [24, 13, 31], [28, 0, 31], [11, 29, 35], [29, 13, 35], [15,
21, 36], [9, 15, 36], [24, 9, 36], [13, 24, 36], [15, 28, 37], [28, 26, 37], [28, 31, 39],
[31, 29, 39], [14, 21, 42], [21, 15, 42], [26, 14, 42], [15, 37, 42], [37, 26, 42], [29, 20,
43], [39, 29, 43], [20, 26, 43], [26, 28, 43], [21, 13, 44], [13, 36, 44], [36, 21, 44],
[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]));
}
test_hull3d_faces();
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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