From 75e5cd4979d6e660b88e66d742fbd24f908220b3 Mon Sep 17 00:00:00 2001 From: RonaldoCMP Date: Wed, 9 Sep 2020 09:37:31 +0100 Subject: [PATCH] Solving bugs in functions on planes --- geometry.scad | 95 +++++++------ regions.scad | 5 +- tests/test_geometry.scad | 283 ++++++++++++++++++++++++++++++++++----- 3 files changed, 301 insertions(+), 82 deletions(-) diff --git a/geometry.scad b/geometry.scad index 0ab9f73..e8132ee 100644 --- a/geometry.scad +++ b/geometry.scad @@ -762,8 +762,8 @@ function triangle_area(a,b,c) = // Usage: // plane3pt(p1, p2, p3); // Description: -// Generates the cartesian equation of a plane from three 3d points. -// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane. +// Generates the normalized cartesian equation of a plane from three 3d points. +// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane. // Returns [], if the points are collinear. // Arguments: // p1 = The first point on the plane. @@ -777,7 +777,7 @@ function plane3pt(p1, p2, p3) = nrm = norm(crx) ) approx(nrm,0) ? [] : - concat(crx/nrm, [crx*p1]/nrm); + concat(crx, crx*p1)/nrm; // Function: plane3pt_indexed() @@ -785,7 +785,7 @@ function plane3pt(p1, p2, p3) = // plane3pt_indexed(points, i1, i2, i3); // Description: // Given a list of 3d points, and the indices of three of those points, -// generates the cartesian equation of a plane that those points all +// generates the normalized cartesian equation of a plane that those points all // lie on. If the points are not collinear, returns [A,B,C,D] where Ax+By+Cz=D is the equation of a plane. // If they are collinear, returns []. // Arguments: @@ -816,15 +816,15 @@ function plane3pt_indexed(points, i1, i2, i3) = function plane_from_normal(normal, pt=[0,0,0]) = assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0), "Inputs `normal` and `pt` should 3d vectors/points and `normal` cannot be zero." ) - concat(normal, [normal*pt]); + concat(normal, normal*pt)/norm(normal); // Function: plane_from_points() // Usage: // plane_from_points(points, , ); // Description: -// Given a list of 3 or more coplanar 3D points, returns the coefficients of the cartesian equation of a plane, -// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane. +// Given a list of 3 or more coplanar 3D points, returns the coefficients of the normalized cartesian equation of a plane, +// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1. // If `fast` is false and the points in the list are collinear or not coplanar, then `undef` is returned. // if `fast` is true, then the coplanarity test is skipped and a plane passing through 3 non-collinear arbitrary points is returned. // Arguments: @@ -858,8 +858,8 @@ function plane_from_points(points, fast=false, eps=EPSILON) = // Usage: // plane_from_polygon(points, [fast], [eps]); // Description: -// Given a 3D planar polygon, returns the cartesian equation of its plane. -// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane. +// Given a 3D planar polygon, returns the normalized cartesian equation of its plane. +// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1. // If not all the points in the polygon are coplanar, then [] is returned. // If `fast` is true, the polygon coplanarity check is skipped and the plane may not contain all polygon points. // Arguments: @@ -897,8 +897,9 @@ function plane_normal(plane) = // Usage: // d = plane_offset(plane); // Description: -// Returns D, or the scalar offset of the plane from the origin. This can be a negative value. -// The absolute value of this is the distance of the plane from the origin at its closest approach. +// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin. +// This value may be negative. +// The absolute value of this coefficient is the distance of the plane from the origin. function plane_offset(plane) = assert( _valid_plane(plane), "Invalid input plane." ) plane[3]/norm([plane.x, plane.y, plane.z]); @@ -923,7 +924,8 @@ function plane_offset(plane) = // stroke(xypath,closed=true); function plane_transform(plane) = let( - n = plane_normal(plane), + plane = normalize_plane(plane), + n = point3d(plane), cp = n * plane[3] ) rot(from=n, to=UP) * move(-cp); @@ -949,8 +951,8 @@ function projection_on_plane(plane, points) = p = len(points[0])==2 ? [for(pi=points) point3d(pi) ] : points, - plane = plane/norm([plane.x,plane.y,plane.z]), - n = [plane.x,plane.y,plane.z] + plane = normalize_plane(plane), + n = point3d(plane) ) [for(pi=p) pi - (pi*n - plane[3])*n]; @@ -961,7 +963,8 @@ function projection_on_plane(plane, points) = // Description: // Returns the point on the plane that is closest to the origin. function plane_point_nearest_origin(plane) = - plane_normal(plane) * plane[3]; + let( plane = normalize_plane(plane) ) + point3d(plane) * plane[3]; // Function: distance_from_plane() @@ -980,8 +983,8 @@ function plane_point_nearest_origin(plane) = function distance_from_plane(plane, point) = assert( _valid_plane(plane), "Invalid input plane." ) assert( is_vector(point,3), "The point should be a 3D point." ) - let( nrml = [plane.x, plane.y, plane.z] ) - ( nrml* point - plane[3])/norm(nrml); + let( plane = normalize_plane(plane) ) + point3d(plane)* point - plane[3]; // Function: closest_point_on_plane() @@ -996,9 +999,9 @@ function distance_from_plane(plane, point) = function closest_point_on_plane(plane, point) = assert( _valid_plane(plane), "Invalid input plane." ) assert( is_vector(point,3), "Invalid point." ) - let( - n = unit([plane.x, plane.y, plane.z]), - d = distance_from_plane(plane, point) + let( plane = normalize_plane(plane), + n = point3d(plane), + d = n*point - plane[3] // distance from plane ) point - n*d; @@ -1008,19 +1011,23 @@ function closest_point_on_plane(plane, point) = // Returns undef if line is parallel to, but not on the given plane. function _general_plane_line_intersection(plane, line, eps=EPSILON) = let( - l0 = line[0], // Ray start point - u = line[1] - l0, // Ray direction vector - n = plane_normal(plane), - p0 = n * plane[3], // A point on the plane - w = l0 - p0 // Vector from plane point to ray start - ) approx(n*u, 0, eps=eps) ? ( - // Line is parallel to plane. - approx(n*w, 0, eps=eps) - ? [line, undef] // Line is on the plane. - : undef // Line never intersects the plane. - ) : let( - t = (-n * w) / (n * u) // Distance ratio along ray - ) [ l0 + u*t, t ]; + a = plane*[each line[0],-1], // evaluation of the plane expression at line[0] + b = plane*[each(line[1]-line[0]),0] // difference between the plane expression evaluation at line[1] and at line[0] + ) + approx(b,0,eps) // is (line[1]-line[0]) "parallel" to the plane ? + ? approx(a,0,eps) // is line[0] on the plane ? + ? [line,undef] // line is on the plane + : undef // line is parallel but not on the plane + : [ line[0]-a/b*(line[1]-line[0]), -a/b ]; + + +// Function: normalize_plane() +// Usage: normalize_plane(plane) +// Description: +// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one. +function normalize_plane(plane) = + assert( _valid_plane(plane), "Invalid plane." ) + plane/norm(point3d(plane)); // Function: plane_line_angle() @@ -1033,11 +1040,12 @@ function plane_line_angle(plane, line) = assert( _valid_plane(plane), "Invalid plane." ) assert( _valid_line(line), "Invalid line." ) let( - vect = line[1]-line[0], - zplane = plane_normal(plane), - sin_angle = vect*zplane/norm(zplane)/norm(vect) + linedir = unit(line[1]-line[0]), + normal = plane_normal(plane), + sin_angle = linedir*normal, + cos_angle = norm(cross(linedir,normal)) ) - asin(constrain(sin_angle,-1,1)); + atan2(sin_angle,cos_angle); // Function: plane_line_intersection() @@ -1085,7 +1093,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) = function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) = assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." ) assert(is_path(poly,dim=3), "Invalid polygon." ) - assert(is_bool(bounded) || (is_list(bounded) && len(bounded)==2), "Invalid bound condition(s).") + assert(!is_list(bounded) || len(bounded)==2, "Invalid bound condition(s).") assert(_valid_line(line,dim=3,eps=eps), "Invalid line." ) let( bounded = is_list(bounded)? bounded : [bounded, bounded], @@ -1094,7 +1102,6 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) = ) indices==[] ? undef : let( - indices = sort(indices), p1 = poly[indices[0]], p2 = poly[indices[1]], p3 = poly[indices[2]], @@ -1120,8 +1127,8 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) = ) isegs ) - : bounded[0]&&res[1]<0? [] : - bounded[1]&&res[1]>1? [] : + : bounded[0] && res[1]<0? undef : + bounded[1] && res[1]>1? undef : let( proj = clockwise_polygon(project_plane(poly, p1, p2, p3)), pt = project_plane(res[0], p1, p2, p3) @@ -1142,15 +1149,15 @@ function plane_intersection(plane1,plane2,plane3) = "The input must be 2 or 3 planes." ) is_def(plane3) ? let( - matrix = [for(p=[plane1,plane2,plane3]) select(p,0,2)], + matrix = [for(p=[plane1,plane2,plane3]) point3d(p)], rhs = [for(p=[plane1,plane2,plane3]) p[3]] ) linear_solve(matrix,rhs) : let( normal = cross(plane_normal(plane1), plane_normal(plane2)) ) approx(norm(normal),0) ? undef : let( - matrix = [for(p=[plane1,plane2]) select(p,0,2)], - rhs = [for(p=[plane1,plane2]) p[3]], + matrix = [for(p=[plane1,plane2]) point3d(p)], + rhs = [plane1[3], plane2[3]], point = linear_solve(matrix,rhs) ) point==[]? undef: [point, point+normal]; diff --git a/regions.scad b/regions.scad index fa761f0..fb72723 100644 --- a/regions.scad +++ b/regions.scad @@ -180,8 +180,9 @@ function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON) ), subpaths = [ for (p = pair(crossings)) - deduplicate(eps=eps, - path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1], closed=closed) + deduplicate( + path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1], closed=closed), + eps=eps ) ] ) diff --git a/tests/test_geometry.scad b/tests/test_geometry.scad index e69a8ac..3fd0512 100644 --- a/tests/test_geometry.scad +++ b/tests/test_geometry.scad @@ -4,6 +4,8 @@ include <../std.scad> //the commented lines are for tests to be written //the tests are ordered as they appear in geometry.scad + + test_point_on_segment2d(); test_point_left_of_line2d(); test_collinear(); @@ -35,33 +37,30 @@ test_tri_calc(); test_triangle_area(); test_plane3pt(); test_plane3pt_indexed(); -//test_plane_from_normal(); +test_plane_from_normal(); test_plane_from_points(); -//test_plane_from_polygon(); +test_plane_from_polygon(); test_plane_normal(); -//test_plane_offset(); -//test_plane_transform(); +test_plane_offset(); +test_plane_transform(); test_projection_on_plane(); -//test_plane_point_nearest_origin(); +test_plane_point_nearest_origin(); test_distance_from_plane(); -test_find_circle_2tangents(); -test_find_circle_3points(); -test_circle_point_tangents(); -test_tri_functions(); -//test_closest_point_on_plane(); -//test__general_plane_line_intersection(); -//test_plane_line_angle(); -//test_plane_line_intersection(); +test_closest_point_on_plane(); +test__general_plane_line_intersection(); +test_plane_line_angle(); +test_normalize_plane(); +test_plane_line_intersection(); test_polygon_line_intersection(); -//test_plane_intersection(); +test_plane_intersection(); test_coplanar(); test_points_on_plane(); test_in_front_of_plane(); -//test_find_circle_2tangents(); -//test_find_circle_3points(); -//test_circle_point_tangents(); -//test_circle_circle_tangents(); +test_find_circle_2tangents(); +test_find_circle_3points(); +test_circle_point_tangents(); + test_noncollinear_triple(); test_pointlist_bounds(); test_closest_point(); @@ -92,24 +91,204 @@ test_simplify_path(); test_simplify_path_indexed(); test_is_region(); + // to be used when there are two alternative symmetrical outcomes -// from a function like a plane output. +// from a function like a plane output; v must be a vector function standardize(v) = v==[]? [] : - sign([for(vi=v) if( ! approx(vi,0)) vi,0 ][0])*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_closest_point_on_plane(){ + plane = rands(-5,5,4)+[10,0,0,0]; + point = rands(-1,1,3); + point2 = closest_point_on_plane(plane,point); + assert_approx(norm(point-point2), abs(distance_from_plane(plane,point))); +} +*test_closest_point_on_plane(); + + +module test_normalize_plane(){ + plane = rands(-5,5,4)+[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),rands(-1,1,3)+[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_point_nearest_origin(){ + point = rands(-1,1,3)+[2,0,0]; // a non zero vector + plane = [ each point, point*point]; // a plane containing `point` + info = info_str([["point = ",point],["plane = ",plane]]); + assert_approx(plane_point_nearest_origin(plane),point,info); + assert_approx(plane_point_nearest_origin([each point,5]),5*unit(point)/norm(point),info); +} +test_plane_point_nearest_origin(); + + +module test_plane_transform(){ + normal = rands(-1,1,3)+[2,0,0]; + offset = rands(-1,1,1)[0]; + info = info_str([["normal = ",normal],["offset = ",offset]]); + assert_approx(plane_transform([0,0,1,offset]),move([0,0,-offset]),info ); + assert_approx(plane_transform([0,1,0,offset]),xrot(90)*move([0,-offset,0]),info ); +} +*test_plane_transform(); + + +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_std(plane_from_polygon(poly1),plane3pt(poly1[0],poly1[1],poly1[2]),info); + assert_std(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_std(plane_from_normal(normal,point),normalize_plane([each normal,displ]),info); + assert_std(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(distance_from_plane(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 assert_std(vc,ve) { assert(standardize(vc)==standardize(ve)); } module test_points_on_plane() { pts = [for(i=[0:40]) rands(-1,1,3) ]; dir = rands(-10,10,3); - normal0 = unit([1,2,3]); + normal0 = [1,2,3]; ang = rands(0,360,1)[0]; normal = rot(a=ang,p=normal0); plane = [each normal, normal*dir]; prj_pts = projection_on_plane(plane,pts); - assert(points_on_plane(prj_pts,plane)); - assert(!points_on_plane(concat(pts,[normal-dir]),plane)); + info = info_str([["pts = ",pts],["dir = ",dir],["ang = ",ang]]); + assert(points_on_plane(prj_pts,plane),info); + assert(!points_on_plane(concat(pts,[normal-dir]),plane),info); } *test_points_on_plane(); @@ -122,14 +301,15 @@ module test_projection_on_plane(){ 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( projection_on_plane(plane,pts), - projection_on_plane(plane,projection_on_plane(plane,pts))); + projection_on_plane(plane,projection_on_plane(plane,pts)),info); assert_approx( projection_on_plane(plane,pts), - rot(a=ang,p=projection_on_plane(plane0,rot(a=-ang,p=pts)))); + rot(a=ang,p=projection_on_plane(plane0,rot(a=-ang,p=pts))),info); assert_approx( move((-normal*dir)*normal,p=projection_on_plane(planem,pts)), - projection_on_plane(plane,pts)); + projection_on_plane(plane,pts),info); assert_approx( move((normal*dir)*normal,p=projection_on_plane(plane,pts)), - projection_on_plane(planem,pts)); + projection_on_plane(planem,pts),info); } *test_projection_on_plane(); @@ -543,12 +723,43 @@ module test_distance_from_plane() { module test_polygon_line_intersection() { - poly1 = [[50,50,50], [50,-50,50], [-50,-50,50]]; - assert_approx(polygon_line_intersection(poly1, [CENTER, UP]), [0,0,50]); - assert_approx(polygon_line_intersection(poly1, [CENTER, UP+RIGHT]), [50,0,50]); - assert_approx(polygon_line_intersection(poly1, [CENTER, UP+BACK+RIGHT]), [50,50,50]); - assert_approx(polygon_line_intersection(poly1, [[0,0,50], [1,0,50]]), [[[0,0,50], [50,0,50]]]); - assert_approx(polygon_line_intersection(poly1, [[0,0,0], [1,0,0]]), undef); + 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); } *test_polygon_line_intersection(); @@ -576,6 +787,8 @@ module test_in_front_of_plane() { module test_is_path() { + assert(is_path([[1,2,3],[4,5,6]])); + assert(is_path([[1,2,3],[4,5,6],[7,8,9]])); assert(!is_path(123)); assert(!is_path("foo")); assert(!is_path(true)); @@ -584,8 +797,6 @@ module test_is_path() { assert(!is_path([["foo","bar","baz"]])); assert(!is_path([[1,2,3]])); assert(!is_path([["foo","bar","baz"],["qux","quux","quuux"]])); - assert(is_path([[1,2,3],[4,5,6]])); - assert(is_path([[1,2,3],[4,5,6],[7,8,9]])); } *test_is_path();