BOSL2/tests/test_geometry.scad

include <BOSL2/std.scad>


module test_point_on_segment2d() {
    assert(point_on_segment2d([-15,0], [[-10,0], [10,0]]) == false);
    assert(point_on_segment2d([-10,0], [[-10,0], [10,0]]) == true);
    assert(point_on_segment2d([-5,0], [[-10,0], [10,0]]) == true);
    assert(point_on_segment2d([0,0], [[-10,0], [10,0]]) == true);
    assert(point_on_segment2d([3,3], [[-10,0], [10,0]]) == false);
    assert(point_on_segment2d([5,0], [[-10,0], [10,0]]) == true);
    assert(point_on_segment2d([10,0], [[-10,0], [10,0]]) == true);
    assert(point_on_segment2d([15,0], [[-10,0], [10,0]]) == false);

    assert(point_on_segment2d([0,-15], [[0,-10], [0,10]]) == false);
    assert(point_on_segment2d([0,-10], [[0,-10], [0,10]]) == true);
    assert(point_on_segment2d([0, -5], [[0,-10], [0,10]]) == true);
    assert(point_on_segment2d([0,  0], [[0,-10], [0,10]]) == true);
    assert(point_on_segment2d([3,  3], [[0,-10], [0,10]]) == false);
    assert(point_on_segment2d([0,  5], [[0,-10], [0,10]]) == true);
    assert(point_on_segment2d([0, 10], [[0,-10], [0,10]]) == true);
    assert(point_on_segment2d([0, 15], [[0,-10], [0,10]]) == false);

    assert(point_on_segment2d([-15,-15], [[-10,-10], [10,10]]) == false);
    assert(point_on_segment2d([-10,-10], [[-10,-10], [10,10]]) == true);
    assert(point_on_segment2d([ -5, -5], [[-10,-10], [10,10]]) == true);
    assert(point_on_segment2d([  0,  0], [[-10,-10], [10,10]]) == true);
    assert(point_on_segment2d([  0,  3], [[-10,-10], [10,10]]) == false);
    assert(point_on_segment2d([  5,  5], [[-10,-10], [10,10]]) == true);
    assert(point_on_segment2d([ 10, 10], [[-10,-10], [10,10]]) == true);
    assert(point_on_segment2d([ 15, 15], [[-10,-10], [10,10]]) == false);
}
test_point_on_segment2d();


module test_point_left_of_segment() {
    assert(point_left_of_segment2d([ -3,  0], [[-10,-10], [10,10]]) > 0);
    assert(point_left_of_segment2d([  0,  0], [[-10,-10], [10,10]]) == 0);
    assert(point_left_of_segment2d([  3,  0], [[-10,-10], [10,10]]) < 0);
}
test_point_left_of_segment();


module test_collinear() {
    assert(collinear([-10,-10], [-15, -16], [10,10]) == false);
    assert(collinear([-10,-10], [-15, -15], [10,10]) == true);
    assert(collinear([-10,-10], [ -3,   0], [10,10]) == false);
    assert(collinear([-10,-10], [  0,   0], [10,10]) == true);
    assert(collinear([-10,-10], [  3,   0], [10,10]) == false);
    assert(collinear([-10,-10], [ 15,  15], [10,10]) == true);
    assert(collinear([-10,-10], [ 15,  16], [10,10]) == false);
}
test_collinear();


module test_collinear_indexed() {
    pts = [
        [-20,-20], [-10,-20], [0,-10], [10,0], [20,10], [20,20], [15,30]
    ];
    assert(collinear_indexed(pts, 0,1,2) == false);
    assert(collinear_indexed(pts, 1,2,3) == true);
    assert(collinear_indexed(pts, 2,3,4) == true);
    assert(collinear_indexed(pts, 3,4,5) == false);
    assert(collinear_indexed(pts, 4,5,6) == false);
    assert(collinear_indexed(pts, 4,3,2) == true);
    assert(collinear_indexed(pts, 0,5,6) == false);
}
test_collinear_indexed();


module test_distance_from_line() {
    assert(abs(distance_from_line([[-10,-10,-10], [10,10,10]], [1,1,1])) < EPSILON);
    assert(abs(distance_from_line([[-10,-10,-10], [10,10,10]], [-1,-1,-1])) < EPSILON);
    assert(abs(distance_from_line([[-10,-10,-10], [10,10,10]], [1,-1,0]) - sqrt(2)) < EPSILON);
    assert(abs(distance_from_line([[-10,-10,-10], [10,10,10]], [8,-8,0]) - 8*sqrt(2)) < EPSILON);
}
test_distance_from_line();


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_wrap(pts)) {
        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]);
}
test_line_intersection();


module test_segment_intersection() {
    assert(segment_intersection([[-10,-10], [ -1, -1]], [[ 10,-10], [  1, -1]]) == undef);
    assert(segment_intersection([[-10,-10], [ -1,-10]], [[ 10,-10], [  1,-10]]) == undef);
    assert(segment_intersection([[-10,  0], [ -1,  0]], [[ 10,  0], [  1,  0]]) == undef);
    assert(segment_intersection([[-10,  0], [ -1,  0]], [[  1,  0], [ 10,  0]]) == undef);
    assert(segment_intersection([[-10, 10], [ -1,  1]], [[ 10, 10], [  1,  1]]) == undef);
    assert(segment_intersection([[-10,  0], [ 10,  0]], [[-10,  0], [ 10,  0]]) == undef);
    assert(segment_intersection([[-10, 10], [ 10, 10]], [[-10,-10], [ 10,-10]]) == undef);
    assert(segment_intersection([[-10,  0], [  0, 10]], [[  0, 10], [ 10,  0]]) == [0,10]);
    assert(segment_intersection([[-10,  0], [  0, 10]], [[-10, 20], [ 10,  0]]) == [0,10]);
    assert(segment_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [-10, 10]]) == [0,0]);
    assert(segment_intersection([[ -8,  0], [ 12,  4]], [[ 12,  0], [ -8,  4]]) == [2,2]);
}
test_segment_intersection();


module test_line_segment_intersection() {
    assert(line_segment_intersection([[-10,-10], [ -1,-10]], [[ 10,-10], [  1,-10]]) == undef);
    assert(line_segment_intersection([[-10,  0], [ -1,  0]], [[ 10,  0], [  1,  0]]) == undef);
    assert(line_segment_intersection([[-10,  0], [ -1,  0]], [[  1,  0], [ 10,  0]]) == undef);
    assert(line_segment_intersection([[-10,  0], [ 10,  0]], [[-10,  0], [ 10,  0]]) == undef);
    assert(line_segment_intersection([[-10, 10], [ 10, 10]], [[-10,-10], [ 10,-10]]) == undef);
    assert(line_segment_intersection([[-10,-10], [ -1, -1]], [[ 10,-10], [  1, -1]]) == undef);
    assert(line_segment_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [-10, 10]]) == [0,0]);
    assert(line_segment_intersection([[ -8,  0], [ 12,  4]], [[ 12,  0], [ -8,  4]]) == [2,2]);
    assert(line_segment_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [  1, -1]]) == undef);
    assert(line_segment_intersection([[-10,-10], [ 10, 10]], [[ 10,-10], [ -1,  1]]) == [0,0]);
}
test_line_segment_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]));
}
test_line_closest_point();


module test_segment_closest_point() {
    assert(approx(segment_closest_point([[-10,-10], [10,10]], [1,-1]), [0,0]));
    assert(approx(segment_closest_point([[-10,-10], [10,10]], [-1,1]), [0,0]));
    assert(approx(segment_closest_point([[-10,-20], [10,20]], [1,2]+[-2,1]), [1,2]));
    assert(approx(segment_closest_point([[-10,-20], [10,20]], [1,2]+[2,-1]), [1,2]));
    assert(approx(segment_closest_point([[-10,-20], [10,20]], [13,31]), [10,20]));
    assert(approx(segment_closest_point([[-10,-20], [10,20]], [15,25]), [10,20]));
}
test_segment_closest_point();


module test_find_circle_2tangents() {
    assert(approx(find_circle_2tangents([10,10],[0,0],[10,-10],r=10/sqrt(2))[0],[10,0]));
    assert(approx(find_circle_2tangents([-10,10],[0,0],[-10,-10],r=10/sqrt(2))[0],[-10,0]));
    assert(approx(find_circle_2tangents([-10,10],[0,0],[10,10],r=10/sqrt(2))[0],[0,10]));
    assert(approx(find_circle_2tangents([-10,-10],[0,0],[10,-10],r=10/sqrt(2))[0],[0,-10]));
    assert(approx(find_circle_2tangents([0,10],[0,0],[10,0],r=10)[0],[10,10]));
    assert(approx(find_circle_2tangents([10,0],[0,0],[0,-10],r=10)[0],[10,-10]));
    assert(approx(find_circle_2tangents([0,-10],[0,0],[-10,0],r=10)[0],[-10,-10]));
    assert(approx(find_circle_2tangents([-10,0],[0,0],[0,10],r=10)[0],[-10,10]));
    assert(approx(find_circle_2tangents(polar_to_xy(10,60),[0,0],[10,0],r=10)[0],polar_to_xy(20,30)));
}
test_find_circle_2tangents();


module test_find_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 = list_range(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 = find_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 = list_range(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 = find_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 = list_range(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 = find_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 = list_range(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 = find_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_find_circle_3points();


module test_circle_point_tangents() {
    tangs = circle_point_tangents(r=50,cp=[0,0],pt=[50*sqrt(2),0]);
    assert(approx(subindex(tangs,0), [45,-45]));
    expected = [for (ang=subindex(tangs,0)) polar_to_xy(50,ang)];
    got = subindex(tangs,1);
    if (!approx(flatten(got), flatten(expected))) {
        echo("TAN_PTS:", got=got, expected=expected, delta=got-expected);
        assert(approx(flatten(got), flatten(expected)));
    }
}
test_circle_point_tangents();


module test_tri_calc() {
    sides = rands(1,100,100,seed_value=8888);
    for (p=pair_wrap(sides)) {
        opp = p[0];
        adj = p[1];
        hyp = norm([opp,adj]);
        ang = acos(adj/hyp);
        ang2 = 90-ang;
        expected = [adj, opp, hyp, ang, ang2];
        assert(approx(tri_calc(adj=adj, hyp=hyp), expected));
        assert(approx(tri_calc(opp=opp, hyp=hyp), expected));
        assert(approx(tri_calc(adj=adj, opp=opp), expected));
        assert(approx(tri_calc(adj=adj, ang=ang), expected));
        assert(approx(tri_calc(opp=opp, ang=ang), expected, eps=1e-8));
        assert(approx(tri_calc(hyp=hyp, ang=ang), expected));
        assert(approx(tri_calc(adj=adj, ang2=ang2), expected));
        assert(approx(tri_calc(opp=opp, ang2=ang2), expected, eps=1e-8));
        assert(approx(tri_calc(hyp=hyp, ang2=ang2), expected));
    }
}
test_tri_calc();


// Dummy modules to show up in coverage check script.
module test_hyp_opp_to_adj();
module test_hyp_ang_to_adj();
module test_opp_ang_to_adj();
module test_hyp_adj_to_opp();
module test_hyp_ang_to_opp();
module test_adj_ang_to_opp();
module test_adj_opp_to_hyp();
module test_adj_ang_to_hyp();
module test_opp_ang_to_hyp();
module test_hyp_adj_to_ang();
module test_hyp_opp_to_ang();
module test_adj_opp_to_ang();

module test_tri_functions() {
    sides = rands(1,100,100,seed_value=8181);
    for (p = pair_wrap(sides)) {
        adj = p.x;
        opp = p.y;
        hyp = norm([opp,adj]);
        ang = atan2(opp,adj);
        assert_approx(hyp_opp_to_adj(hyp,opp), adj);
        assert_approx(hyp_ang_to_adj(hyp,ang), adj);
        assert_approx(opp_ang_to_adj(opp,ang), adj);
        assert_approx(hyp_adj_to_opp(hyp,adj), opp);
        assert_approx(hyp_ang_to_opp(hyp,ang), opp);
        assert_approx(adj_ang_to_opp(adj,ang), opp);
        assert_approx(adj_opp_to_hyp(adj,opp), hyp);
        assert_approx(adj_ang_to_hyp(adj,ang), hyp);
        assert_approx(opp_ang_to_hyp(opp,ang), hyp);
        assert_approx(hyp_adj_to_ang(hyp,adj), ang);
        assert_approx(hyp_opp_to_ang(hyp,opp), ang);
        assert_approx(adj_opp_to_ang(adj,opp), ang);
    }
}
test_tri_functions();


module test_triangle_area() {
    assert(abs(triangle_area([0,0], [0,10], [10,0]) + 50) < EPSILON);
    assert(abs(triangle_area([0,0], [0,10], [0,15])) < EPSILON);
    assert(abs(triangle_area([0,0], [10,0], [0,10]) - 50) < EPSILON);
}
test_triangle_area();


module test_plane3pt() {
    assert(plane3pt([0,0,20], [0,10,10], [0,0,0]) == [1,0,0,0]);
    assert(plane3pt([2,0,20], [2,10,10], [2,0,0]) == [1,0,0,2]);
    assert(plane3pt([0,0,0], [10,0,10], [0,0,20]) == [0,1,0,0]);
    assert(plane3pt([0,2,0], [10,2,10], [0,2,20]) == [0,1,0,2]);
    assert(plane3pt([0,0,0], [10,10,0], [20,0,0]) == [0,0,1,0]);
    assert(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(plane3pt_indexed(pts, 0,3,2) == [1,0,0,0]);
    assert(plane3pt_indexed(pts, 0,2,3) == [-1,0,0,0]);
    assert(plane3pt_indexed(pts, 0,1,3) == [0,1,0,0]);
    assert(plane3pt_indexed(pts, 0,3,1) == [0,-1,0,0]);
    assert(plane3pt_indexed(pts, 0,2,1) == [0,0,1,0]);
    assert(plane3pt_indexed(pts, 0,1,2) == [0,0,-1,0]);
    assert(plane3pt_indexed(pts, 3,2,1) == [s13,s13,s13,10*s13]);
    assert(plane3pt_indexed(pts, 1,2,3) == [-s13,-s13,-s13,-10*s13]);
}
test_plane3pt_indexed();


module test_plane_from_points() {
    assert(plane_from_points([[0,0,20], [0,10,10], [0,0,0], [0,5,3]]) == [1,0,0,0]);
    assert(plane_from_points([[2,0,20], [2,10,10], [2,0,0], [2,3,4]]) == [1,0,0,2]);
    assert(plane_from_points([[0,0,0], [10,0,10], [0,0,20], [5,0,7]]) == [0,1,0,0]);
    assert(plane_from_points([[0,2,0], [10,2,10], [0,2,20], [4,2,3]]) == [0,1,0,2]);
    assert(plane_from_points([[0,0,0], [10,10,0], [20,0,0], [8,3,0]]) == [0,0,1,0]);
    assert(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_plane_normal() {
    assert(plane_normal(plane3pt([0,0,20], [0,10,10], [0,0,0])) == [1,0,0]);
    assert(plane_normal(plane3pt([2,0,20], [2,10,10], [2,0,0])) == [1,0,0]);
    assert(plane_normal(plane3pt([0,0,0], [10,0,10], [0,0,20])) == [0,1,0]);
    assert(plane_normal(plane3pt([0,2,0], [10,2,10], [0,2,20])) == [0,1,0]);
    assert(plane_normal(plane3pt([0,0,0], [10,10,0], [20,0,0])) == [0,0,1]);
    assert(plane_normal(plane3pt([0,0,2], [10,10,2], [20,0,2])) == [0,0,1]);
}
test_plane_normal();


module test_distance_from_plane() {
    plane1 = plane3pt([-10,0,0], [0,10,0], [10,0,0]);
    assert(distance_from_plane(plane1, [0,0,5]) == 5);
    assert(distance_from_plane(plane1, [5,5,8]) == 8);
}
test_distance_from_plane();


module test_coplanar() {
    plane = plane3pt([0,0,0], [0,10,10], [10,0,10]);
    assert(coplanar(plane, [5,5,10]) == true);
    assert(coplanar(plane, [10/3,10/3,20/3]) == true);
    assert(coplanar(plane, [0,0,0]) == true);
    assert(coplanar(plane, [1,1,0]) == false);
    assert(coplanar(plane, [-1,1,0]) == true);
    assert(coplanar(plane, [1,-1,0]) == true);
    assert(coplanar(plane, [5,5,5]) == false);
}
test_coplanar();


module test_in_front_of_plane() {
    plane = plane3pt([0,0,0], [0,10,10], [10,0,10]);
    assert(in_front_of_plane(plane, [5,5,10]) == false);
    assert(in_front_of_plane(plane, [-5,0,0]) == true);
    assert(in_front_of_plane(plane, [5,0,0]) == false);
    assert(in_front_of_plane(plane, [0,-5,0]) == true);
    assert(in_front_of_plane(plane, [0,5,0]) == false);
    assert(in_front_of_plane(plane, [0,0,5]) == true);
    assert(in_front_of_plane(plane, [0,0,-5]) == false);
}
test_in_front_of_plane();


module test_is_path() {
    assert(!is_path(123));
    assert(!is_path("foo"));
    assert(!is_path(true));
    assert(!is_path([]));
    assert(!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();


module test_is_closed_path() {
    assert(!is_closed_path([[1,2,3],[4,5,6],[1,8,9]]));
    assert(is_closed_path([[1,2,3],[4,5,6],[1,8,9],[1,2,3]]));
}
test_is_closed_path();


module test_close_path() {
    assert(close_path([[1,2,3],[4,5,6],[1,8,9]]) == [[1,2,3],[4,5,6],[1,8,9],[1,2,3]]);
    assert(close_path([[1,2,3],[4,5,6],[1,8,9],[1,2,3]]) == [[1,2,3],[4,5,6],[1,8,9],[1,2,3]]);
}
test_close_path();


module test_cleanup_path() {
    assert(cleanup_path([[1,2,3],[4,5,6],[1,8,9]]) == [[1,2,3],[4,5,6],[1,8,9]]);
    assert(cleanup_path([[1,2,3],[4,5,6],[1,8,9],[1,2,3]]) == [[1,2,3],[4,5,6],[1,8,9]]);
}
test_cleanup_path();


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)), -PI*50*50, eps=0.1));
}
test_polygon_area();


module test_polygon_shift() {
    path = [[1,1],[-1,1],[-1,-1],[1,-1]];
    assert(polygon_shift(path,1) == [[-1,1],[-1,-1],[1,-1],[1,1]]);
    assert(polygon_shift(path,2) == [[-1,-1],[1,-1],[1,1],[-1,1]]);
}
test_polygon_shift();


module test_polygon_shift_to_closest_point() {
    path = [[1,1],[-1,1],[-1,-1],[1,-1]];
    assert(polygon_shift_to_closest_point(path,[1.1,1.1]) == [[1,1],[-1,1],[-1,-1],[1,-1]]);
    assert(polygon_shift_to_closest_point(path,[-1.1,1.1]) == [[-1,1],[-1,-1],[1,-1],[1,1]]);
    assert(polygon_shift_to_closest_point(path,[-1.1,-1.1]) == [[-1,-1],[1,-1],[1,1],[-1,1]]);
    assert(polygon_shift_to_closest_point(path,[1.1,-1.1]) == [[1,-1],[1,1],[-1,1],[-1,-1]]);
}
test_polygon_shift_to_closest_point();


module test_first_noncollinear(){
    pts = [
        [1,1], [2,2], [3,3], [4,4], [4,5], [5,6]
    ];
    assert(first_noncollinear(0,1,pts) == 4);
    assert(first_noncollinear(1,0,pts) == 4);
    assert(first_noncollinear(0,2,pts) == 4);
    assert(first_noncollinear(2,0,pts) == 4);
    assert(first_noncollinear(1,2,pts) == 4);
    assert(first_noncollinear(2,1,pts) == 4);
    assert(first_noncollinear(0,3,pts) == 4);
    assert(first_noncollinear(3,0,pts) == 4);
    assert(first_noncollinear(1,3,pts) == 4);
    assert(first_noncollinear(3,1,pts) == 4);
    assert(first_noncollinear(2,3,pts) == 4);
    assert(first_noncollinear(3,2,pts) == 4);
    assert(first_noncollinear(0,4,pts) == 1);
    assert(first_noncollinear(4,0,pts) == 1);
    assert(first_noncollinear(1,4,pts) == 0);
    assert(first_noncollinear(4,1,pts) == 0);
    assert(first_noncollinear(2,4,pts) == 0);
    assert(first_noncollinear(4,2,pts) == 0);
    assert(first_noncollinear(3,4,pts) == 0);
    assert(first_noncollinear(4,3,pts) == 0);
    assert(first_noncollinear(0,5,pts) == 1);
    assert(first_noncollinear(5,0,pts) == 1);
    assert(first_noncollinear(1,5,pts) == 0);
    assert(first_noncollinear(5,1,pts) == 0);
    assert(first_noncollinear(2,5,pts) == 0);
    assert(first_noncollinear(5,2,pts) == 0);
    assert(first_noncollinear(3,5,pts) == 0);
    assert(first_noncollinear(5,3,pts) == 0);
    assert(first_noncollinear(4,5,pts) == 0);
    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]);
}
test_find_noncollinear_points();


module test_centroid() {
    $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]);
}
test_centroid();


module test_simplify_path() {
    path = [[-20,-20], [-10,-20], [0,-10], [10,0], [20,10], [20,20], [15,30]];
    assert(simplify_path(path) == [[-20,-20], [-10,-20], [20,10], [20,20], [15,30]]);
}
test_simplify_path();


module test_simplify_path_indexed() {
    pts = [[10,0], [0,-10], [20,20], [20,10], [-20,-20], [15,30], [-10,-20]];
    path = [4,6,1,0,3,2,5];
    assert(simplify_path_indexed(pts, path) == [4,6,3,2,5]);
}
test_simplify_path_indexed();


module test_point_in_polygon() {
    poly = [for (a=[0:30:359]) 10*[cos(a),sin(a)]];
    assert(point_in_polygon([0,0], poly) == 1);
    assert(point_in_polygon([20,0], 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) == 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);
}
test_point_in_polygon();


module test_pointlist_bounds() {
    pts = [
        [-53,27,12],
        [-63,97,36],
        [84,-32,-5],
        [63,-24,42],
        [23,57,-42]
    ];
    assert(pointlist_bounds(pts) == [[-63,-32,-42], [84,97,42]]);
}
test_pointlist_bounds();


module test_closest_point() {
    ptlist = [for (i=list_range(100)) rands(-100,100,2,seed_value=8463)];
    testpts = [for (i=list_range(100)) rands(-100,100,2,seed_value=6834)];
    for (pt = testpts) {
        pidx = closest_point(pt,ptlist);
        dists = [for (p=ptlist) norm(pt-p)];
        mindist = min(dists);
        assert(mindist == dists[pidx]);
    }
}
test_closest_point();


module test_furthest_point() {
    ptlist = [for (i=list_range(100)) rands(-100,100,2,seed_value=8463)];
    testpts = [for (i=list_range(100)) rands(-100,100,2,seed_value=6834)];
    for (pt = testpts) {
        pidx = furthest_point(pt,ptlist);
        dists = [for (p=ptlist) norm(pt-p)];
        mindist = max(dists);
        assert(mindist == dists[pidx]);
    }
}
test_furthest_point();


module test_polygon_is_clockwise() {
    assert(polygon_is_clockwise([[-1,1],[1,1],[1,-1],[-1,-1]]));
    assert(!polygon_is_clockwise([[1,1],[-1,1],[-1,-1],[1,-1]]));
    assert(polygon_is_clockwise(circle(d=100)));
    assert(polygon_is_clockwise(square(100)));
}
test_polygon_is_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_is_region() {
    assert(is_region([circle(d=10),square(10)]));
    assert(is_region([circle(d=10),square(10),circle(d=50)]));
    assert(is_region([square(10)]));
    assert(!is_region([]));
    assert(!is_region(23));
    assert(!is_region(true));
    assert(!is_region("foo"));
}
test_is_region();



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