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