diff --git a/common.scad b/common.scad index c72c77b..f0be6c1 100644 --- a/common.scad +++ b/common.scad @@ -129,6 +129,11 @@ function is_list_of(list,pattern) = is_list(list) && []==[for(entry=0*list) if (entry != pattern) entry]; +function _list_pattern(list) = + is_list(list) ? [for(entry=list) is_list(entry) ? _list_pattern(entry) : 0] + : 0; + + // Function: is_consistent() // Usage: diff --git a/geometry.scad b/geometry.scad index dd35ddc..443c026 100644 --- a/geometry.scad +++ b/geometry.scad @@ -1341,39 +1341,25 @@ function circle_circle_tangents(c1,r1,c2,r2,d1,d2) = // Section: Pointlists -// Function: first_noncollinear() -// Usage: -// first_noncollinear(i1, i2, points); -// Description: -// Returns index of the first point in `points` that is not collinear with the points indexed by `i1` and `i2`. -// Arguments: -// i1 = The first point. -// i2 = The second point. -// points = The list of points to find a non-collinear point from. -function first_noncollinear(i1, i2, points) = - [for (j = idx(points)) if (j!=i1 && j!=i2 && !collinear_indexed(points,i1,i2,j)) j][0]; - // Function: find_noncollinear_points() // Usage: // find_noncollinear_points(points); // Description: // Finds the indices of three good non-collinear points from the points list `points`. -function find_noncollinear_points(points) = +function find_noncollinear_points(points,error=true,eps=EPSILON) = let( - a = 0, - b = furthest_point(points[a], points), - pa = points[a], - pb = points[b], - c = max_index([ - for (p=points) - (approx(p,pa) || approx(p,pb))? 0 : - sin(vector_angle(points[a]-p,points[b]-p)) * - norm(p-points[a]) * norm(p-points[b]) - ]) + pa = points[0], + b = furthest_point(pa, points), + n = unit(points[b]-pa), + relpoints = [for(pt=points) pt-pa], + proj = relpoints * n, + distlist = [for(i=[0:len(points)-1]) norm(relpoints[i]-proj[i]*n)] ) - assert(c!=a && c!=b, "Cannot find three noncollinear points in pointlist.") - [a, b, c]; + max(distlist) -// include -// ``` -// Derived from Oskar Linde's Hull: -// - https://github.com/openscad/scad-utils -////////////////////////////////////////////////////////////////////// - - -// Section: Convex Hulls - - -// Function: hull() -// Usage: -// hull(points); -// Description: -// Takes a list of 2D or 3D points (but not both in the same list) and returns either the list of -// indexes into `points` that forms the 2D convex hull perimeter path, or the list of faces that -// form the 3d convex hull surface. Each face is a list of indexes into `points`. If the input -// points are co-linear, the result will be the indexes of the two extrema points. If the input -// points are co-planar, the results will be a simple list of vertex indices that will form a planar -// perimeter. Otherwise a list of faces will be returned, where each face is a simple list of -// vertex indices for the perimeter of the face. -// Arguments: -// points = The set of 2D or 3D points to find the hull of. -function hull(points) = let(two_d = len(points[0]) == 2) two_d? hull2d_path(points) : hull3d_faces(points); - - -// Module: hull_points() -// Usage: -// hull_points(points, [fast]); -// Description: -// If given a list of 2D points, creates a 2D convex hull polygon that encloses all those points. -// If given a list of 3D points, creates a 3D polyhedron that encloses all the points. This should -// handle about 4000 points in slow mode. If `fast` is set to true, this should be able to handle -// far more. -// Arguments: -// points = The list of points to form a hull around. -// fast = If true, uses a faster cheat that may handle more points, but also may emit warnings that can stop your script if you have "Halt on first warning" enabled. Default: false -// Example(2D): -// pts = [[-10,-10], [0,10], [10,10], [12,-10]]; -// hull_points(pts); -// Example: -// pts = [for (phi = [30:60:150], theta = [0:60:359]) spherical_to_xyz(10, theta, phi)]; -// hull_points(pts); -module hull_points(points, fast=false) { - assert(is_list(points)); - if (points) { - assert(is_list(points[0])); - if (fast) { - if (len(points[0]) == 2) { - hull() polygon(points=points); - } else { - extra = len(points)%3; - faces = concat( - [[for(i=[0:1:extra+2])i]], - [for(i=[extra+3:3:len(points)-3])[i,i+1,i+2]] - ); - hull() polyhedron(points=points, faces=faces); - } - } else { - perim = hull(points); - if (is_num(perim[0])) { - polygon(points=points, paths=[perim]); - } else { - polyhedron(points=points, faces=perim); - } - } - } -} - - -// Function: hull2d_path() -// Usage: -// hull2d_path(points) -// Description: -// Takes a list of arbitrary 2D points, and finds the minimal convex hull polygon to enclose them. -// Returns a path as a list of indices into `points`. -// Example(2D): -// pts = [[-10,-10], [0,10], [10,10], [12,-10]]; -// path = hull2d_path(pts); -// move_copies(pts) color("red") sphere(1); -// polygon(points=pts, paths=[path]); -function hull2d_path(points) = - (len(points) < 3)? [] : let( - a=0, b=1, - c = first_noncollinear(a, b, points) - ) (c == len(points))? _hull2d_collinear(points) : let( - remaining = [ for (i = [2:1:len(points)-1]) if (i != c) i ], - ccw = triangle_area(points[a], points[b], points[c]) > 0, - polygon = ccw? [a,b,c] : [a,c,b] - ) _hull2d_iterative(points, polygon, remaining); - - -// Adds the remaining points one by one to the convex hull -function _hull2d_iterative(points, polygon, remaining, _i=0) = - (_i >= len(remaining))? polygon : let ( - // pick a point - i = remaining[_i], - // find the segments that are in conflict with the point (point not inside) - conflicts = _find_conflicting_segments(points, polygon, points[i]) - // no conflicts, skip point and move on - ) (len(conflicts) == 0)? _hull2d_iterative(points, polygon, remaining, _i+1) : let( - // find the first conflicting segment and the first not conflicting - // conflict will be sorted, if not wrapping around, do it the easy way - polygon = _remove_conflicts_and_insert_point(polygon, conflicts, i) - ) _hull2d_iterative(points, polygon, remaining, _i+1); - - -function _hull2d_collinear(points) = - let( - a = points[0], - n = points[1] - a, - points1d = [ for(p = points) (p-a)*n ], - min_i = min_index(points1d), - max_i = max_index(points1d) - ) [min_i, max_i]; - - -function _find_conflicting_segments(points, polygon, point) = [ - for (i = [0:1:len(polygon)-1]) let( - j = (i+1) % len(polygon), - p1 = points[polygon[i]], - p2 = points[polygon[j]], - area = triangle_area(p1, p2, point) - ) if (area < 0) i -]; - - -// remove the conflicting segments from the polygon -function _remove_conflicts_and_insert_point(polygon, conflicts, point) = - (conflicts[0] == 0)? let( - nonconflicting = [ for(i = [0:1:len(polygon)-1]) if (!in_list(i, conflicts)) i ], - new_indices = concat(nonconflicting, (nonconflicting[len(nonconflicting)-1]+1) % len(polygon)), - polygon = concat([ for (i = new_indices) polygon[i] ], point) - ) polygon : let( - before_conflicts = [ for(i = [0:1:min(conflicts)]) polygon[i] ], - after_conflicts = (max(conflicts) >= (len(polygon)-1))? [] : [ for(i = [max(conflicts)+1:1:len(polygon)-1]) polygon[i] ], - polygon = concat(before_conflicts, point, after_conflicts) - ) polygon; - - - -// Function: hull3d_faces() -// Usage: -// hull3d_faces(points) -// Description: -// Takes a list of arbitrary 3D points, and finds the minimal convex hull polyhedron to enclose -// them. Returns a list of faces, where each face is a list of indexes into the given `points` -// list. If all points passed to it are coplanar, then the return is the list of indices of points -// forming the minimal convex hull polygon. -// Example(3D): -// pts = [[-20,-20,0], [20,-20,0], [0,20,5], [0,0,20]]; -// faces = hull3d_faces(pts); -// move_copies(pts) color("red") sphere(1); -// %polyhedron(points=pts, faces=faces); -function hull3d_faces(points) = - (len(points) < 3)? list_range(len(points)) : let ( - // start with a single non-collinear triangle - a = 0, - b = 1, - c = first_noncollinear(a, b, points) - ) (c == len(points))? _hull2d_collinear(points) : let( - plane = plane3pt_indexed(points, a, b, c), - d = _find_first_noncoplanar(plane, points, 3) - ) (d == len(points))? /* all coplanar*/ let ( - pts2d = [ for (p = points) project_plane(p, points[a], points[b], points[c]) ], - hull2d = hull2d_path(pts2d) - ) hull2d : let( - remaining = [for (i = [3:1:len(points)-1]) if (i != d) i], - // Build an initial tetrahedron. - // Swap b, c if d is in front of triangle t. - ifop = in_front_of_plane(plane, points[d]), - bc = ifop? [c,b] : [b,c], - b = bc[0], - c = bc[1], - triangles = [ - [a,b,c], - [d,b,a], - [c,d,a], - [b,d,c] - ], - // calculate the plane equations - planes = [ for (t = triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ] - ) _hull3d_iterative(points, triangles, planes, remaining); - - -// Adds the remaining points one by one to the convex hull -function _hull3d_iterative(points, triangles, planes, remaining, _i=0) = - _i >= len(remaining) ? triangles : - let ( - // pick a point - i = remaining[_i], - // find the triangles that are in conflict with the point (point not inside) - conflicts = _find_conflicts(points[i], planes), - // for all triangles that are in conflict, collect their halfedges - halfedges = [ - for(c = conflicts, i = [0:2]) let( - j = (i+1)%3 - ) [triangles[c][i], triangles[c][j]] - ], - // find the outer perimeter of the set of conflicting triangles - horizon = _remove_internal_edges(halfedges), - // generate a new triangle for each horizon halfedge together with the picked point i - new_triangles = [ for (h = horizon) concat(h,i) ], - // calculate the corresponding plane equations - new_planes = [ for (t = new_triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ] - ) _hull3d_iterative( - points, - // remove the conflicting triangles and add the new ones - concat(list_remove(triangles, conflicts), new_triangles), - concat(list_remove(planes, conflicts), new_planes), - remaining, - _i+1 - ); - - -function _remove_internal_edges(halfedges) = [ - for (h = halfedges) - if (!in_list(reverse(h), halfedges)) - h -]; - - -function _find_conflicts(point, planes) = [ - for (i = [0:1:len(planes)-1]) - if (in_front_of_plane(planes[i], point)) - i -]; - - -function _find_first_noncoplanar(plane, points, i) = - (i >= len(points) || !coplanar(plane, points[i]))? i : - _find_first_noncoplanar(plane, points, i+1); - - -// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap +////////////////////////////////////////////////////////////////////// +// LibFile: hull.scad +// Functions to create 2D and 3D convex hulls. +// To use, add the following line to the beginning of your file: +// ``` +// include +// include +// ``` +// Derived from Oskar Linde's Hull: +// - https://github.com/openscad/scad-utils +////////////////////////////////////////////////////////////////////// + + +// Section: Convex Hulls + + +// Function: hull() +// Usage: +// hull(points); +// Description: +// Takes a list of 2D or 3D points (but not both in the same list) and returns either the list of +// indexes into `points` that forms the 2D convex hull perimeter path, or the list of faces that +// form the 3d convex hull surface. Each face is a list of indexes into `points`. If the input +// points are co-linear, the result will be the indexes of the two extrema points. If the input +// points are co-planar, the results will be a simple list of vertex indices that will form a planar +// perimeter. Otherwise a list of faces will be returned, where each face is a simple list of +// vertex indices for the perimeter of the face. +// Arguments: +// points = The set of 2D or 3D points to find the hull of. +function hull(points) = + assert(is_path(points),"Invalid input to hull") + len(points[0]) == 2 + ? hull2d_path(points) + : hull3d_faces(points); + + +// Module: hull_points() +// Usage: +// hull_points(points, [fast]); +// Description: +// If given a list of 2D points, creates a 2D convex hull polygon that encloses all those points. +// If given a list of 3D points, creates a 3D polyhedron that encloses all the points. This should +// handle about 4000 points in slow mode. If `fast` is set to true, this should be able to handle +// far more. +// Arguments: +// points = The list of points to form a hull around. +// fast = If true, uses a faster cheat that may handle more points, but also may emit warnings that can stop your script if you have "Halt on first warning" enabled. Default: false +// Example(2D): +// pts = [[-10,-10], [0,10], [10,10], [12,-10]]; +// hull_points(pts); +// Example: +// pts = [for (phi = [30:60:150], theta = [0:60:359]) spherical_to_xyz(10, theta, phi)]; +// hull_points(pts); +module hull_points(points, fast=false) { + if (points) { + assert(is_list(points[0])); + if (fast) { + if (len(points[0]) == 2) { + hull() polygon(points=points); + } else { + extra = len(points)%3; + faces = concat( + [[for(i=[0:1:extra+2])i]], + [for(i=[extra+3:3:len(points)-3])[i,i+1,i+2]] + ); + hull() polyhedron(points=points, faces=faces); + } + } else { + perim = hull(points); + if (is_num(perim[0])) { + polygon(points=points, paths=[perim]); + } else { + polyhedron(points=points, faces=perim); + } + } + } +} + + +// Function: hull2d_path() +// Usage: +// hull2d_path(points) +// Description: +// Takes a list of arbitrary 2D points, and finds the convex hull polygon to enclose them. +// Returns a path as a list of indices into `points`. May return extra points, that are on edges of the hull. +// Example(2D): +// pts = [[-10,-10], [0,10], [10,10], [12,-10]]; +// path = hull2d_path(pts); +// move_copies(pts) color("red") sphere(1); +// polygon(points=pts, paths=[path]); +function hull2d_path(points) = + assert(is_path(points,2),"Invalid input to hull2d_path") + len(points) < 2 ? [] + : len(points) == 2 ? [0,1] + : let(tri=find_noncollinear_points(points, error=false)) + tri == [] ? _hull_collinear(points) + : let( + remaining = [ for (i = [0:1:len(points)-1]) if (i != tri[0] && i!=tri[1] && i!=tri[2]) i ], + ccw = triangle_area(points[tri[0]], points[tri[1]], points[tri[2]]) > 0, + polygon = ccw ? [tri[0],tri[1],tri[2]] : [tri[0],tri[2],tri[1]] + ) _hull2d_iterative(points, polygon, remaining); + + + +// Adds the remaining points one by one to the convex hull +function _hull2d_iterative(points, polygon, remaining, _i=0) = + (_i >= len(remaining))? polygon : let ( + // pick a point + i = remaining[_i], + // find the segments that are in conflict with the point (point not inside) + conflicts = _find_conflicting_segments(points, polygon, points[i]) + // no conflicts, skip point and move on + ) (len(conflicts) == 0)? _hull2d_iterative(points, polygon, remaining, _i+1) : let( + // find the first conflicting segment and the first not conflicting + // conflict will be sorted, if not wrapping around, do it the easy way + polygon = _remove_conflicts_and_insert_point(polygon, conflicts, i) + ) _hull2d_iterative(points, polygon, remaining, _i+1); + + +function _hull_collinear(points) = + let( + a = points[0], + n = points[1] - a, + points1d = [ for(p = points) (p-a)*n ], + min_i = min_index(points1d), + max_i = max_index(points1d) + ) [min_i, max_i]; + + +function _find_conflicting_segments(points, polygon, point) = [ + for (i = [0:1:len(polygon)-1]) let( + j = (i+1) % len(polygon), + p1 = points[polygon[i]], + p2 = points[polygon[j]], + area = triangle_area(p1, p2, point) + ) if (area < 0) i +]; + + +// remove the conflicting segments from the polygon +function _remove_conflicts_and_insert_point(polygon, conflicts, point) = + (conflicts[0] == 0)? let( + nonconflicting = [ for(i = [0:1:len(polygon)-1]) if (!in_list(i, conflicts)) i ], + new_indices = concat(nonconflicting, (nonconflicting[len(nonconflicting)-1]+1) % len(polygon)), + polygon = concat([ for (i = new_indices) polygon[i] ], point) + ) polygon : let( + before_conflicts = [ for(i = [0:1:min(conflicts)]) polygon[i] ], + after_conflicts = (max(conflicts) >= (len(polygon)-1))? [] : [ for(i = [max(conflicts)+1:1:len(polygon)-1]) polygon[i] ], + polygon = concat(before_conflicts, point, after_conflicts) + ) polygon; + + + +// Function: hull3d_faces() +// Usage: +// hull3d_faces(points) +// Description: +// Takes a list of arbitrary 3D points, and finds the convex hull polyhedron to enclose +// them. Returns a list of triangular faces, where each face is a list of indexes into the given `points` +// list. The output will be valid for use with the polyhedron command, but may include vertices that are in the interior of a face of the hull, so it is not +// necessarily the minimal representation of the hull. +// If all points passed to it are coplanar, then the return is the list of indices of points +// forming the convex hull polygon. +// Example(3D): +// pts = [[-20,-20,0], [20,-20,0], [0,20,5], [0,0,20]]; +// faces = hull3d_faces(pts); +// move_copies(pts) color("red") sphere(1); +// %polyhedron(points=pts, faces=faces); +function hull3d_faces(points) = + assert(is_path(points,3),"Invalid input to hull3d_faces") + len(points) < 3 ? list_range(len(points)) + : let ( // start with a single non-collinear triangle + tri = find_noncollinear_points(points, error=false) + ) + tri==[] ? _hull_collinear(points) + : let( + a = tri[0], + b = tri[1], + c = tri[2], + plane = plane3pt_indexed(points, a, b, c), + d = _find_first_noncoplanar(plane, points, 3) + ) + d == len(points) + ? /* all coplanar*/ + let ( + pts2d = [ for (p = points) project_plane(p, points[a], points[b], points[c]) ], + hull2d = hull2d_path(pts2d) + ) hull2d + : let( + remaining = [for (i = [0:1:len(points)-1]) if (i!=a && i!=b && i!=c && i!=d) i], + // Build an initial tetrahedron. + // Swap b, c if d is in front of triangle t. + ifop = in_front_of_plane(plane, points[d]), + bc = ifop? [c,b] : [b,c], + b = bc[0], + c = bc[1], + triangles = [ + [a,b,c], + [d,b,a], + [c,d,a], + [b,d,c] + ], + // calculate the plane equations + planes = [ for (t = triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ] + ) _hull3d_iterative(points, triangles, planes, remaining); + + +// Adds the remaining points one by one to the convex hull +function _hull3d_iterative(points, triangles, planes, remaining, _i=0) = + _i >= len(remaining) ? triangles : + let ( + // pick a point + i = remaining[_i], + // find the triangles that are in conflict with the point (point not inside) + conflicts = _find_conflicts(points[i], planes), + // for all triangles that are in conflict, collect their halfedges + halfedges = [ + for(c = conflicts, i = [0:2]) let( + j = (i+1)%3 + ) [triangles[c][i], triangles[c][j]] + ], + // find the outer perimeter of the set of conflicting triangles + horizon = _remove_internal_edges(halfedges), + // generate a new triangle for each horizon halfedge together with the picked point i + new_triangles = [ for (h = horizon) concat(h,i) ], + // calculate the corresponding plane equations + new_planes = [ for (t = new_triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ] + ) _hull3d_iterative( + points, + // remove the conflicting triangles and add the new ones + concat(list_remove(triangles, conflicts), new_triangles), + concat(list_remove(planes, conflicts), new_planes), + remaining, + _i+1 + ); + + +function _remove_internal_edges(halfedges) = [ + for (h = halfedges) + if (!in_list(reverse(h), halfedges)) + h +]; + + +function _find_conflicts(point, planes) = [ + for (i = [0:1:len(planes)-1]) + if (in_front_of_plane(planes[i], point)) + i +]; + + +function _find_first_noncoplanar(plane, points, i) = + (i >= len(points) || !coplanar(plane, points[i]))? i : + _find_first_noncoplanar(plane, points, i+1); + + +// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap diff --git a/tests/test_geometry.scad b/tests/test_geometry.scad index 78c3e57..8f780f4 100644 --- a/tests/test_geometry.scad +++ b/tests/test_geometry.scad @@ -519,6 +519,7 @@ module test_polygon_shift_to_closest_point() { test_polygon_shift_to_closest_point(); +/* module test_first_noncollinear(){ pts = [ [1,1], [2,2], [3,3], [4,4], [4,5], [5,6] @@ -555,11 +556,14 @@ module test_first_noncollinear(){ assert(first_noncollinear(5,4,pts) == 0); } test_first_noncollinear(); +*/ module test_find_noncollinear_points() { assert(find_noncollinear_points([[1,1],[2,2],[3,3],[4,4],[4,5],[5,6]]) == [0,5,3]); assert(find_noncollinear_points([[1,1],[2,2],[8,3],[4,4],[4,5],[5,6]]) == [0,2,5]); + u = unit([5,3]); + assert_equal(find_noncollinear_points([for(i = [2,3,4,5,7,12,15]) i * u], error=false),[]); } test_find_noncollinear_points(); diff --git a/tests/test_hull.scad b/tests/test_hull.scad new file mode 100644 index 0000000..616971d --- /dev/null +++ b/tests/test_hull.scad @@ -0,0 +1,100 @@ +include <../std.scad> +include <../hull.scad> + +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(hull(test_collinear_2d), [7,1]); + test_collinear_3d = let(u = unit([5,3,2])) [ for(i = [9,2,3,4,5,7,12,15,13]) i * u ]; + assert_equal(hull(test_collinear_3d), [7,1]); + + /* // 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(hull(testpoints_on_sphere), [[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(hull(rand10_3d),[[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(hull(rand25_3d),[[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();