grey/BOSL2
1
0
Fork 0
mirror of https://github.com/BelfrySCAD/BOSL2.git synced 2025-01-01 09:49:45 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

Added point_segment_distance(), segment_distance(). Renamed distance_from_line() -> point_line_distance(). Renamed distance_from_plane() -> point_plane_distance()

Browse source
This commit is contained in:
Garth Minette 2021-06-10 15:49:44 -07:00
parent 9d9234513d
commit 5ee224f2d3
4 changed files with 135 additions and 47 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

74
geometry.scad
View file

@ -85,22 +85,80 @@ function collinear(a, b, c, eps=EPSILON) =
: noncollinear_triple(points,error=false,eps=eps)==[];
// Function: distance_from_line()
// Function: point_line_distance()
// Usage:
// distance_from_line(line, pt);
// point_line_distance(pt, line);
// Description:
// Finds the perpendicular distance of a point `pt` from the line `line`.
// Arguments:
// line = A list of two points, defining a line that both are on.
// pt = A point to find the distance of from the line.
// Example:
// distance_from_line([[-10,0], [10,0]], [3,8]); // Returns: 8
function distance_from_line(line, pt) =
// dist = point_line_distance([3,8], [[-10,0], [10,0]]); // Returns: 8
function point_line_distance(pt, line) =
assert( _valid_line(line) && is_vector(pt,len(line[0])),
"Invalid line, invalid point or incompatible dimensions." )
_dist2line(pt-line[0],unit(line[1]-line[0]));
// Function: point_segment_distance()
// Usage:
// dist = point_segment_distance(pt, seg);
// Description:
// Returns the closest distance of the given point to the given line segment.
// Arguments:
// pt = The point to check the distance of.
// seg = The two points representing the line segment to check the distance of.
// Example:
// dist = point_segment_distance([3,8], [[-10,0], [10,0]]); // Returns: 8
// dist2 = point_segment_distance([14,3], [[-10,0], [10,0]]); // Returns: 5
function point_segment_distance(pt, seg) =
norm(seg[0]-seg[1]) < EPSILON ? norm(pt-seg[0]) :
norm(pt-segment_closest_point(seg,pt));
// Function: segment_distance()
// Usage:
// dist = segment_distance(seg1, seg2);
// Description:
// Returns the closest distance of the two given line segments.
// Arguments:
// seg1 = The list of two points representing the first line segment to check the distance of.
// seg2 = The list of two points representing the second line segment to check the distance of.
// Example:
// dist = segment_distance([[-14,3], [-15,9]], [[-10,0], [10,0]]); // Returns: 5
// dist2 = segment_distance([[-5,5], [5,-5]], [[-10,3], [10,-3]]); // Returns: 0
function segment_distance(seg1, seg2) =
let(
dseg1 = seg1[1]-seg1[0],
dseg2 = seg2[1]-seg2[0],
A = [ [dseg1*dseg1, -dseg1*dseg2],
[-dseg2*dseg1, dseg2*dseg2] ],
b = -[ dseg1, -dseg2 ]*(seg1[0]-seg2[0]),
uv = linear_solve(A,b)
)
!uv ?
norm(dseg1)<EPSILON
? norm(dseg2)<EPSILON
? norm(seg1[0]-seg2[0])
: point_segment_distance(seg1[0],seg2)
: point_segment_distance(seg2[0],seg1) :
uv[0]>=0 && uv[0]<=1 ?
let( p1 = seg1[0] + uv[0]*dseg1 )
uv[1]>=0 && uv[1]<=1
? norm(p1 - (seg2[0] + uv[1]*dseg2) )
: min(norm(p1-seg2[0]), norm(p1-seg2[1])) :
uv[1]>=0 && uv[1]<=1
? let( p2 = seg2[0] + uv[1]*dseg2 )
min(norm(p2-seg1[0]), norm(p2-seg1[1]))
: min(
norm(seg1[0]-seg2[0]),
norm(seg1[0]-seg2[1]),
norm(seg1[1]-seg2[0]),
norm(seg1[1]-seg2[1])
);
// Function: line_normal()
// Usage:
// line_normal([P1,P2])
@ -1072,9 +1130,9 @@ function plane_point_nearest_origin(plane) =
point3d(plane) * plane[3];
// Function: distance_from_plane()
// Function: point_plane_distance()
// Usage:
// distance_from_plane(plane, point)
// point_plane_distance(plane, point)
// Description:
// Given a plane as [A,B,C,D] where the cartesian equation for that plane
// is Ax+By+Cz=D, determines how far from that plane the given point is.
@ -1085,7 +1143,7 @@ function plane_point_nearest_origin(plane) =
// Arguments:
// plane = The `[A,B,C,D]` plane definition where `Ax+By+Cz=D` is the formula of the plane.
// point = The distance evaluation point.
function distance_from_plane(plane, point) =
function point_plane_distance(plane, point) =
assert( _valid_plane(plane), "Invalid input plane." )
assert( is_vector(point,3), "The point should be a 3D point." )
let( plane = normalize_plane(plane) )
@ -1310,7 +1368,7 @@ function points_on_plane(points, plane, eps=EPSILON) =
// plane = The [A,B,C,D] coefficients for the first plane equation `Ax+By+Cz=D`.
// point = The 3D point to test.
function in_front_of_plane(plane, point) =
distance_from_plane(plane, point) > EPSILON;
point_plane_distance(plane, point) > EPSILON;

36
skin.scad
View file

@ -812,24 +812,30 @@ function _skin_tangent_match(poly1, poly2) =
newbig = polygon_shift(big, shift),
repeat_counts = [for(i=[0:len(small)-1]) posmod(cutpts[i]-select(cutpts,i-1),len(big))],
newsmall = repeat_entries(small,repeat_counts)
)
assert(len(newsmall)==len(newbig), "Tangent alignment failed, probably because of insufficient points or a concave curve")
swap ? [newbig, newsmall] : [newsmall, newbig];
)
assert(len(newsmall)==len(newbig), "Tangent alignment failed, probably because of insufficient points or a concave curve")
swap ? [newbig, newsmall] : [newsmall, newbig];
function _find_one_tangent(curve, edge, curve_offset=[0,0,0], closed=true) =
let(
angles =
[for(i=[0:len(curve)-(closed?1:2)])
let(
plane = plane3pt( edge[0], edge[1], curve[i]),
tangent = [curve[i], select(curve,i+1)]
)
plane_line_angle(plane,tangent)],
zero_cross = [for(i=[0:len(curve)-(closed?1:2)]) if (sign(angles[i]) != sign(select(angles,i+1))) i],
d = [for(i=zero_cross) distance_from_line(edge, curve[i]+curve_offset)]
)
zero_cross[min_index(d)];
let(
angles = [
for (i = [0:len(curve)-(closed?1:2)])
let(
plane = plane3pt( edge[0], edge[1], curve[i]),
tangent = [curve[i], select(curve,i+1)]
) plane_line_angle(plane,tangent)
],
zero_cross = [
for (i = [0:len(curve)-(closed?1:2)])
if (sign(angles[i]) != sign(select(angles,i+1)))
i
],
d = [
for (i = zero_cross)
point_line_distance(curve[i]+curve_offset, edge)
]
) zero_cross[min_index(d)];
// Function: associate_vertices()

50
tests/test_geometry.scad
View file

@ -9,7 +9,9 @@ include <../std.scad>
test_point_on_segment2d();
test_point_left_of_line2d();
test_collinear();
test_distance_from_line();
test_point_line_distance();
test_point_segment_distance();
test_segment_distance();
test_line_normal();
test_line_intersection();
//test_line_ray_intersection();
@ -44,7 +46,7 @@ test_plane_normal();
test_plane_offset();
test_projection_on_plane();
test_plane_point_nearest_origin();
test_distance_from_plane();
test_point_plane_distance();
test__general_plane_line_intersection();
test_plane_line_angle();
@ -230,7 +232,7 @@ module test__general_plane_line_intersection() {
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
assert_approx(point_plane_distance(plane1, inters1[0]), 0, info1); // inters1[0] on the plane
}
// line parallel to the plane
@ -351,13 +353,35 @@ module test_collinear() {
*test_collinear();
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);
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));
}
*test_distance_from_line();
*test_point_line_distance();
module test_point_segment_distance() {
assert_approx(point_segment_distance([3,8], [[-10,0], [10,0]]), 8);
assert_approx(point_segment_distance([14,3], [[-10,0], [10,0]]), 5);
}
*test_point_segment_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() {
@ -713,12 +737,12 @@ module test_plane_normal() {
*test_plane_normal();
module test_distance_from_plane() {
module test_point_plane_distance() {
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);
assert(point_plane_distance(plane1, [0,0,5]) == 5);
assert(point_plane_distance(plane1, [5,5,8]) == 8);
}
*test_distance_from_plane();
*test_point_plane_distance();
module test_polygon_line_intersection() {

22
tests/test_shapes.scad
View file

@ -9,17 +9,17 @@ module test_prismoid() {
assert_approx(prismoid([100,80],[40,50],h=50,anchor=BOT), [[[20,25,50],[20,-25,50],[-20,-25,50],[-20,25,50],[50,40,0],[50,-40,0],[-50,-40,0],[-50,40,0]],[[0,1,2],[0,2,3],[0,4,5],[0,5,1],[1,5,6],[1,6,2],[2,6,7],[2,7,3],[3,7,4],[3,4,0],[4,7,6],[4,6,5]]]);
assert_approx(prismoid([100,80],[40,50],h=50,anchor=TOP+RIGHT), [[[0,25,0],[0,-25,0],[-40,-25,0],[-40,25,0],[30,40,-50],[30,-40,-50],[-70,-40,-50],[-70,40,-50]],[[0,1,2],[0,2,3],[0,4,5],[0,5,1],[1,5,6],[1,6,2],[2,6,7],[2,7,3],[3,7,4],[3,4,0],[4,7,6],[4,6,5]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5]), [[[30,30,50],[30,-20,50],[-10,-20,50],[-10,30,50],[50,40,0],[50,-40,0],[-50,-40,0],[-50,40,0]],[[0,1,2],[0,2,3],[0,4,5],[0,5,1],[1,5,6],[1,6,2],[2,6,7],[2,7,3],[3,7,4],[3,4,0],[4,7,6],[4,6,5]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer=5), [[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-15,50],[25,-20,50],[-5,-20,50],[-10,-15,50],[-10,25,50],[-5,30,50],[25,30,50],[30,25,50]],[[4,1,0],[1,4,2],[2,4,3],[4,0,5],[14,5,6],[5,0,6],[14,6,7],[6,0,7],[0,1,8],[7,0,8],[1,2,9],[8,1,9],[14,8,9],[2,3,10],[9,2,10],[14,9,10],[14,10,11],[3,4,11],[10,3,11],[4,5,12],[14,11,12],[11,4,12],[5,14,13],[14,12,13],[12,5,13],[14,7,15],[7,8,15],[8,14,15]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=5),[[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-20,50],[-10,-20,50],[-10,30,50],[30,30,50]],[[4,1,0],[1,4,2],[2,4,3],[4,0,5],[11,5,6],[5,0,6],[0,11,7],[11,6,7],[6,0,7],[11,0,8],[0,1,8],[1,2,8],[3,4,9],[2,3,9],[8,2,9],[11,8,9],[4,5,10],[5,11,10],[11,9,10],[9,4,10]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer2=5), [[[50,-40,0],[-50,-40,0],[-50,40,0],[50,40,0],[30,-15,50],[25,-20,50],[-5,-20,50],[-10,-15,50],[-10,25,50],[-5,30,50],[25,30,50],[30,25,50]],[[2,1,0],[10,2,3],[2,0,3],[3,0,4],[10,4,5],[0,1,5],[4,0,5],[10,5,6],[5,1,6],[1,2,7],[6,1,7],[10,6,7],[10,7,8],[7,2,8],[2,10,9],[10,8,9],[8,2,9],[10,3,11],[3,4,11],[4,10,11]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=5,chamfer2=10), [[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-10,50],[20,-20,50],[0,-20,50],[-10,-10,50],[-10,20,50],[0,30,50],[20,30,50],[30,20,50]],[[4,1,0],[1,4,2],[2,4,3],[4,0,5],[14,5,6],[5,0,6],[14,6,7],[6,0,7],[0,1,8],[7,0,8],[1,2,9],[8,1,9],[14,8,9],[2,3,10],[9,2,10],[14,9,10],[14,10,11],[3,4,11],[10,3,11],[4,5,12],[14,11,12],[11,4,12],[5,14,13],[14,12,13],[12,5,13],[14,7,15],[7,8,15],[8,14,15]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding=5), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-15,50],[29.8296291314,-16.2940952255,50],[29.3301270189,-17.5,50],[28.5355339059,-18.5355339059,50],[27.5,-19.3301270189,50],[26.2940952255,-19.8296291314,50],[25,-20,50],[-5,-20,50],[-6.29409522551,-19.8296291314,50],[-7.5,-19.3301270189,50],[-8.53553390593,-18.5355339059,50],[-9.33012701892,-17.5,50],[-9.82962913145,-16.2940952255,50],[-10,-15,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[25,30,50],[26.2940952255,29.8296291314,50],[27.5,29.3301270189,50],[28.5355339059,28.5355339059,50],[29.3301270189,27.5,50],[29.8296291314,26.2940952255,50],[30,25,50]],[[16,1,0],[1,16,2],[2,16,3],[3,16,4],[4,16,5],[5,16,6],[6,16,7],[7,16,8],[8,16,9],[9,16,10],[10,16,11],[11,16,12],[12,16,13],[13,16,14],[14,16,15],[16,0,17],[17,0,18],[18,0,19],[19,0,20],[20,0,21],[21,0,22],[51,22,23],[22,0,23],[51,23,24],[23,0,24],[24,0,25],[25,0,26],[26,0,27],[0,1,28],[27,0,28],[1,2,29],[28,1,29],[51,28,29],[2,3,30],[29,2,30],[51,29,30],[3,4,31],[30,3,31],[51,30,31],[4,5,32],[31,4,32],[51,31,32],[5,6,33],[32,5,33],[51,32,33],[51,33,34],[6,7,34],[33,6,34],[51,34,35],[7,8,35],[34,7,35],[51,35,36],[8,9,36],[35,8,36],[51,36,37],[9,10,37],[36,9,37],[51,37,38],[10,11,38],[37,10,38],[51,38,39],[11,12,39],[38,11,39],[51,39,40],[12,13,40],[39,12,40],[51,40,41],[13,14,41],[40,13,41],[51,41,42],[14,15,42],[41,14,42],[51,42,43],[15,16,43],[42,15,43],[51,43,44],[16,17,44],[43,16,44],[17,18,45],[44,17,45],[51,44,45],[18,19,46],[45,18,46],[51,45,46],[19,20,47],[46,19,47],[51,46,47],[20,21,48],[47,20,48],[51,47,48],[21,22,49],[51,48,49],[48,21,49],[22,51,50],[51,49,50],[49,22,50],[51,24,52],[24,25,52],[28,51,52],[25,26,53],[52,25,53],[28,52,53],[26,27,54],[53,26,54],[28,53,54],[27,28,55],[28,54,55],[54,27,55]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-20,50],[-10,-20,50],[-10,30,50],[30,30,50]],[[16,1,0],[1,16,2],[2,16,3],[3,16,4],[4,16,5],[5,16,6],[6,16,7],[7,16,8],[8,16,9],[9,16,10],[10,16,11],[11,16,12],[12,16,13],[13,16,14],[14,16,15],[16,0,17],[17,0,18],[18,0,19],[19,0,20],[31,20,21],[20,0,21],[31,21,22],[21,0,22],[31,22,23],[22,0,23],[31,23,24],[23,0,24],[31,24,25],[24,0,25],[31,25,26],[25,0,26],[0,31,27],[31,26,27],[26,0,27],[31,0,28],[0,1,28],[1,2,28],[2,3,28],[3,4,28],[4,5,28],[5,6,28],[6,7,28],[13,14,29],[7,8,29],[28,7,29],[8,9,29],[9,10,29],[10,11,29],[11,12,29],[12,13,29],[31,28,29],[17,18,30],[18,19,30],[19,20,30],[20,31,30],[15,16,30],[14,15,30],[29,14,30],[16,17,30],[31,29,30]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding2=5), [[[50,-40,0],[-50,-40,0],[-50,40,0],[50,40,0],[30,-15,50],[29.8296291314,-16.2940952255,50],[29.3301270189,-17.5,50],[28.5355339059,-18.5355339059,50],[27.5,-19.3301270189,50],[26.2940952255,-19.8296291314,50],[25,-20,50],[-5,-20,50],[-6.29409522551,-19.8296291314,50],[-7.5,-19.3301270189,50],[-8.53553390593,-18.5355339059,50],[-9.33012701892,-17.5,50],[-9.82962913145,-16.2940952255,50],[-10,-15,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[25,30,50],[26.2940952255,29.8296291314,50],[27.5,29.3301270189,50],[28.5355339059,28.5355339059,50],[29.3301270189,27.5,50],[29.8296291314,26.2940952255,50],[30,25,50]],[[2,1,0],[2,0,3],[3,0,4],[28,4,5],[4,0,5],[28,5,6],[5,0,6],[28,6,7],[6,0,7],[28,7,8],[7,0,8],[28,8,9],[8,0,9],[28,9,10],[0,1,10],[9,0,10],[10,1,11],[28,10,11],[11,1,12],[28,11,12],[12,1,13],[28,12,13],[13,1,14],[28,13,14],[14,1,15],[28,14,15],[15,1,16],[28,15,16],[1,2,17],[16,1,17],[28,16,17],[28,17,18],[17,2,18],[28,18,19],[18,2,19],[28,19,20],[19,2,20],[28,20,21],[20,2,21],[28,21,22],[21,2,22],[22,2,23],[28,22,23],[2,3,24],[23,2,24],[28,23,24],[28,24,25],[24,3,25],[28,25,26],[25,3,26],[3,28,27],[28,26,27],[26,3,27],[28,3,29],[4,28,29],[4,29,30],[29,3,30],[3,4,31],[4,30,31],[30,3,31]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5,rounding2=10), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-10,50],[29.6592582629,-12.588190451,50],[28.6602540378,-15,50],[27.0710678119,-17.0710678119,50],[25,-18.6602540378,50],[22.588190451,-19.6592582629,50],[20,-20,50],[0,-20,50],[-2.58819045103,-19.6592582629,50],[-5,-18.6602540378,50],[-7.07106781187,-17.0710678119,50],[-8.66025403784,-15,50],[-9.65925826289,-12.588190451,50],[-10,-10,50],[-10,20,50],[-9.65925826289,22.588190451,50],[-8.66025403784,25,50],[-7.07106781187,27.0710678119,50],[-5,28.6602540378,50],[-2.58819045103,29.6592582629,50],[0,30,50],[20,30,50],[22.588190451,29.6592582629,50],[25,28.6602540378,50],[27.0710678119,27.0710678119,50],[28.6602540378,25,50],[29.6592582629,22.588190451,50],[30,20,50]],[[16,1,0],[1,16,2],[2,16,3],[3,16,4],[4,16,5],[5,16,6],[6,16,7],[7,16,8],[8,16,9],[9,16,10],[10,16,11],[11,16,12],[12,16,13],[13,16,14],[14,16,15],[16,0,17],[17,0,18],[18,0,19],[19,0,20],[20,0,21],[21,0,22],[51,22,23],[22,0,23],[51,23,24],[23,0,24],[24,0,25],[25,0,26],[26,0,27],[0,1,28],[27,0,28],[1,2,29],[28,1,29],[51,28,29],[2,3,30],[29,2,30],[51,29,30],[3,4,31],[30,3,31],[51,30,31],[4,5,32],[31,4,32],[51,31,32],[5,6,33],[32,5,33],[51,32,33],[51,33,34],[6,7,34],[33,6,34],[51,34,35],[7,8,35],[34,7,35],[51,35,36],[8,9,36],[35,8,36],[51,36,37],[9,10,37],[36,9,37],[51,37,38],[10,11,38],[37,10,38],[51,38,39],[11,12,39],[38,11,39],[51,39,40],[12,13,40],[39,12,40],[51,40,41],[13,14,41],[40,13,41],[51,41,42],[14,15,42],[41,14,42],[51,42,43],[15,16,43],[42,15,43],[51,43,44],[16,17,44],[43,16,44],[51,44,45],[17,18,45],[44,17,45],[51,45,46],[18,19,46],[45,18,46],[19,20,47],[46,19,47],[51,46,47],[20,21,48],[47,20,48],[51,47,48],[21,22,49],[51,48,49],[48,21,49],[22,51,50],[51,49,50],[49,22,50],[51,24,52],[24,25,52],[28,51,52],[25,26,53],[52,25,53],[28,52,53],[26,27,54],[53,26,54],[28,53,54],[27,28,55],[28,54,55],[54,27,55]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5,chamfer2=10), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-10,50],[20,-20,50],[0,-20,50],[-10,-10,50],[-10,20,50],[0,30,50],[20,30,50],[30,20,50]],[[0,16,9],[28,0,1],[0,9,1],[28,1,2],[1,9,2],[28,2,3],[2,9,3],[3,9,4],[4,9,5],[5,9,6],[6,9,7],[7,9,8],[9,16,10],[10,16,11],[11,16,12],[12,16,13],[13,16,14],[14,16,15],[16,0,17],[17,0,18],[18,0,19],[19,0,20],[20,0,21],[21,0,22],[22,0,23],[23,0,24],[24,0,25],[25,0,26],[0,28,27],[26,0,27],[28,3,29],[3,4,29],[4,5,29],[5,6,29],[6,7,29],[8,9,30],[7,8,30],[29,7,30],[9,10,30],[28,29,30],[28,30,31],[10,11,31],[30,10,31],[11,12,31],[12,13,31],[13,14,31],[28,31,32],[15,16,32],[14,15,32],[31,14,32],[16,17,32],[20,21,33],[28,32,33],[19,20,33],[17,18,33],[32,17,33],[18,19,33],[23,24,34],[28,33,34],[21,22,34],[33,21,34],[22,23,34],[26,27,35],[27,28,35],[25,26,35],[28,34,35],[24,25,35],[34,24,35]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer=[0,5,10,15]), [[[50,-25,0],[35,-40,0],[-40,-40,0],[-50,-30,0],[-50,35,0],[-45,40,0],[50,40,0],[30,-5,50],[15,-20,50],[0,-20,50],[-10,-10,50],[-10,25,50],[-5,30,50],[30,30,50]],[[4,1,0],[1,4,2],[2,4,3],[4,0,5],[0,13,6],[13,5,6],[5,0,6],[13,0,7],[0,1,7],[1,2,8],[7,1,8],[13,7,8],[13,8,9],[2,3,9],[8,2,9],[13,9,10],[3,4,10],[9,3,10],[4,5,11],[13,10,11],[10,4,11],[5,13,12],[13,11,12],[11,5,12]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=[15,10,5,0], rounding2=[0,5,10,15]), [[[50,-40,0],[-45,-40,0],[-50,-35,0],[-50,30,0],[-40,40,0],[35,40,0],[50,25,0],[30,-5,50],[29.4888873943,-8.88228567654,50],[27.9903810568,-12.5,50],[25.6066017178,-15.6066017178,50],[22.5,-17.9903810568,50],[18.8822856765,-19.4888873943,50],[15,-20,50],[0,-20,50],[-2.58819045103,-19.6592582629,50],[-5,-18.6602540378,50],[-7.07106781187,-17.0710678119,50],[-8.66025403784,-15,50],[-9.65925826289,-12.588190451,50],[-10,-10,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[30,30,50]],[[3,1,0],[1,3,2],[3,0,4],[28,4,5],[4,0,5],[0,28,6],[28,5,6],[5,0,6],[28,0,7],[7,0,8],[28,7,8],[28,8,9],[8,0,9],[28,9,10],[9,0,10],[28,10,11],[10,0,11],[28,11,12],[11,0,12],[28,12,13],[0,1,13],[12,0,13],[28,13,14],[13,1,14],[28,14,15],[14,1,15],[28,15,16],[15,1,16],[28,16,17],[1,2,17],[16,1,17],[28,17,18],[17,2,18],[28,18,19],[18,2,19],[28,19,20],[2,3,20],[19,2,20],[28,20,21],[20,3,21],[21,3,22],[28,21,22],[22,3,23],[28,22,23],[3,4,24],[23,3,24],[28,23,24],[28,24,25],[24,4,25],[28,25,26],[25,4,26],[4,28,27],[28,26,27],[26,4,27]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer=5), [[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-15,50],[25,-20,50],[-5,-20,50],[-10,-15,50],[-10,25,50],[-5,30,50],[25,30,50],[30,25,50]],[[14,7,15],[7,8,15],[8,14,15],[5,14,13],[14,12,13],[12,5,13],[14,11,12],[11,4,12],[4,5,12],[14,10,11],[3,4,11],[10,3,11],[2,3,10],[9,2,10],[14,9,10],[14,8,9],[1,2,9],[8,1,9],[7,0,8],[0,1,8],[14,6,7],[6,0,7],[14,5,6],[5,0,6],[4,0,5],[2,4,3],[1,4,2],[4,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=5), [[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-20,50],[-10,-20,50],[-10,30,50],[30,30,50]],[[11,9,10],[9,4,10],[4,5,10],[5,11,10],[2,3,9],[8,2,9],[11,8,9],[3,4,9],[1,2,8],[11,0,8],[0,1,8],[0,11,7],[11,6,7],[6,0,7],[11,5,6],[5,0,6],[4,0,5],[2,4,3],[1,4,2],[4,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer2=5), [[[50,-40,0],[-50,-40,0],[-50,40,0],[50,40,0],[30,-15,50],[25,-20,50],[-5,-20,50],[-10,-15,50],[-10,25,50],[-5,30,50],[25,30,50],[30,25,50]],[[10,3,11],[3,4,11],[4,10,11],[2,10,9],[10,8,9],[8,2,9],[10,7,8],[7,2,8],[1,2,7],[6,1,7],[10,6,7],[10,5,6],[5,1,6],[10,4,5],[0,1,5],[4,0,5],[3,0,4],[10,2,3],[2,0,3],[2,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=5,chamfer2=10), [[[50,-35,0],[45,-40,0],[-45,-40,0],[-50,-35,0],[-50,35,0],[-45,40,0],[45,40,0],[50,35,0],[30,-10,50],[20,-20,50],[0,-20,50],[-10,-10,50],[-10,20,50],[0,30,50],[20,30,50],[30,20,50]],[[14,7,15],[7,8,15],[8,14,15],[5,14,13],[14,12,13],[12,5,13],[14,11,12],[11,4,12],[4,5,12],[14,10,11],[3,4,11],[10,3,11],[2,3,10],[9,2,10],[14,9,10],[14,8,9],[1,2,9],[8,1,9],[7,0,8],[0,1,8],[14,6,7],[6,0,7],[14,5,6],[5,0,6],[4,0,5],[2,4,3],[1,4,2],[4,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding=5), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-15,50],[29.8296291314,-16.2940952255,50],[29.3301270189,-17.5,50],[28.5355339059,-18.5355339059,50],[27.5,-19.3301270189,50],[26.2940952255,-19.8296291314,50],[25,-20,50],[-5,-20,50],[-6.29409522551,-19.8296291314,50],[-7.5,-19.3301270189,50],[-8.53553390593,-18.5355339059,50],[-9.33012701892,-17.5,50],[-9.82962913145,-16.2940952255,50],[-10,-15,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[25,30,50],[26.2940952255,29.8296291314,50],[27.5,29.3301270189,50],[28.5355339059,28.5355339059,50],[29.3301270189,27.5,50],[29.8296291314,26.2940952255,50],[30,25,50]],[[27,28,55],[28,54,55],[54,27,55],[28,53,54],[26,27,54],[53,26,54],[28,52,53],[25,26,53],[52,25,53],[28,51,52],[51,24,52],[24,25,52],[22,51,50],[51,49,50],[49,22,50],[51,48,49],[48,21,49],[21,22,49],[20,21,48],[47,20,48],[51,47,48],[19,20,47],[46,19,47],[51,46,47],[51,45,46],[18,19,46],[45,18,46],[51,44,45],[17,18,45],[44,17,45],[16,17,44],[43,16,44],[51,43,44],[15,16,43],[42,15,43],[51,42,43],[14,15,42],[41,14,42],[51,41,42],[13,14,41],[40,13,41],[51,40,41],[12,13,40],[39,12,40],[51,39,40],[11,12,39],[38,11,39],[51,38,39],[10,11,38],[37,10,38],[51,37,38],[9,10,37],[36,9,37],[51,36,37],[8,9,36],[35,8,36],[51,35,36],[7,8,35],[34,7,35],[51,34,35],[6,7,34],[33,6,34],[51,33,34],[51,32,33],[5,6,33],[32,5,33],[51,31,32],[4,5,32],[31,4,32],[51,30,31],[3,4,31],[30,3,31],[51,29,30],[2,3,30],[29,2,30],[51,28,29],[1,2,29],[28,1,29],[27,0,28],[0,1,28],[26,0,27],[25,0,26],[24,0,25],[51,23,24],[23,0,24],[51,22,23],[22,0,23],[21,0,22],[20,0,21],[19,0,20],[18,0,19],[17,0,18],[16,0,17],[14,16,15],[13,16,14],[12,16,13],[11,16,12],[10,16,11],[9,16,10],[8,16,9],[7,16,8],[6,16,7],[5,16,6],[4,16,5],[3,16,4],[2,16,3],[1,16,2],[16,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-20,50],[-10,-20,50],[-10,30,50],[30,30,50]],[[16,17,30],[31,29,30],[15,16,30],[14,15,30],[29,14,30],[19,20,30],[20,31,30],[18,19,30],[17,18,30],[12,13,29],[31,28,29],[11,12,29],[10,11,29],[9,10,29],[8,9,29],[7,8,29],[28,7,29],[13,14,29],[6,7,28],[5,6,28],[4,5,28],[3,4,28],[2,3,28],[1,2,28],[31,0,28],[0,1,28],[0,31,27],[31,26,27],[26,0,27],[31,25,26],[25,0,26],[31,24,25],[24,0,25],[31,23,24],[23,0,24],[31,22,23],[22,0,23],[31,21,22],[21,0,22],[31,20,21],[20,0,21],[19,0,20],[18,0,19],[17,0,18],[16,0,17],[14,16,15],[13,16,14],[12,16,13],[11,16,12],[10,16,11],[9,16,10],[8,16,9],[7,16,8],[6,16,7],[5,16,6],[4,16,5],[3,16,4],[2,16,3],[1,16,2],[16,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding2=5), [[[50,-40,0],[-50,-40,0],[-50,40,0],[50,40,0],[30,-15,50],[29.8296291314,-16.2940952255,50],[29.3301270189,-17.5,50],[28.5355339059,-18.5355339059,50],[27.5,-19.3301270189,50],[26.2940952255,-19.8296291314,50],[25,-20,50],[-5,-20,50],[-6.29409522551,-19.8296291314,50],[-7.5,-19.3301270189,50],[-8.53553390593,-18.5355339059,50],[-9.33012701892,-17.5,50],[-9.82962913145,-16.2940952255,50],[-10,-15,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[25,30,50],[26.2940952255,29.8296291314,50],[27.5,29.3301270189,50],[28.5355339059,28.5355339059,50],[29.3301270189,27.5,50],[29.8296291314,26.2940952255,50],[30,25,50]],[[3,4,31],[4,30,31],[30,3,31],[4,29,30],[29,3,30],[28,3,29],[4,28,29],[3,28,27],[28,26,27],[26,3,27],[28,25,26],[25,3,26],[28,24,25],[24,3,25],[2,3,24],[23,2,24],[28,23,24],[22,2,23],[28,22,23],[28,21,22],[21,2,22],[28,20,21],[20,2,21],[28,19,20],[19,2,20],[28,18,19],[18,2,19],[28,17,18],[17,2,18],[1,2,17],[16,1,17],[28,16,17],[15,1,16],[28,15,16],[14,1,15],[28,14,15],[13,1,14],[28,13,14],[12,1,13],[28,12,13],[11,1,12],[28,11,12],[10,1,11],[28,10,11],[0,1,10],[9,0,10],[28,9,10],[8,0,9],[28,8,9],[28,7,8],[7,0,8],[28,6,7],[6,0,7],[28,5,6],[5,0,6],[28,4,5],[4,0,5],[3,0,4],[2,0,3],[2,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5,rounding2=10), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-10,50],[29.6592582629,-12.588190451,50],[28.6602540378,-15,50],[27.0710678119,-17.0710678119,50],[25,-18.6602540378,50],[22.588190451,-19.6592582629,50],[20,-20,50],[0,-20,50],[-2.58819045103,-19.6592582629,50],[-5,-18.6602540378,50],[-7.07106781187,-17.0710678119,50],[-8.66025403784,-15,50],[-9.65925826289,-12.588190451,50],[-10,-10,50],[-10,20,50],[-9.65925826289,22.588190451,50],[-8.66025403784,25,50],[-7.07106781187,27.0710678119,50],[-5,28.6602540378,50],[-2.58819045103,29.6592582629,50],[0,30,50],[20,30,50],[22.588190451,29.6592582629,50],[25,28.6602540378,50],[27.0710678119,27.0710678119,50],[28.6602540378,25,50],[29.6592582629,22.588190451,50],[30,20,50]],[[27,28,55],[28,54,55],[54,27,55],[28,53,54],[26,27,54],[53,26,54],[28,52,53],[25,26,53],[52,25,53],[28,51,52],[51,24,52],[24,25,52],[22,51,50],[51,49,50],[49,22,50],[51,48,49],[48,21,49],[21,22,49],[20,21,48],[47,20,48],[51,47,48],[19,20,47],[46,19,47],[51,46,47],[18,19,46],[45,18,46],[51,45,46],[17,18,45],[44,17,45],[51,44,45],[16,17,44],[43,16,44],[51,43,44],[15,16,43],[42,15,43],[51,42,43],[14,15,42],[41,14,42],[51,41,42],[13,14,41],[40,13,41],[51,40,41],[12,13,40],[39,12,40],[51,39,40],[11,12,39],[38,11,39],[51,38,39],[10,11,38],[37,10,38],[51,37,38],[9,10,37],[36,9,37],[51,36,37],[8,9,36],[35,8,36],[51,35,36],[7,8,35],[34,7,35],[51,34,35],[6,7,34],[33,6,34],[51,33,34],[51,32,33],[5,6,33],[32,5,33],[51,31,32],[4,5,32],[31,4,32],[51,30,31],[3,4,31],[30,3,31],[51,29,30],[2,3,30],[29,2,30],[51,28,29],[1,2,29],[28,1,29],[27,0,28],[0,1,28],[26,0,27],[25,0,26],[24,0,25],[51,23,24],[23,0,24],[51,22,23],[22,0,23],[21,0,22],[20,0,21],[19,0,20],[18,0,19],[17,0,18],[16,0,17],[14,16,15],[13,16,14],[12,16,13],[11,16,12],[10,16,11],[9,16,10],[8,16,9],[7,16,8],[6,16,7],[5,16,6],[4,16,5],[3,16,4],[2,16,3],[1,16,2],[16,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],rounding1=5,chamfer2=10), [[[50,-35,0],[49.8296291314,-36.2940952255,0],[49.3301270189,-37.5,0],[48.5355339059,-38.5355339059,0],[47.5,-39.3301270189,0],[46.2940952255,-39.8296291314,0],[45,-40,0],[-45,-40,0],[-46.2940952255,-39.8296291314,0],[-47.5,-39.3301270189,0],[-48.5355339059,-38.5355339059,0],[-49.3301270189,-37.5,0],[-49.8296291314,-36.2940952255,0],[-50,-35,0],[-50,35,0],[-49.8296291314,36.2940952255,0],[-49.3301270189,37.5,0],[-48.5355339059,38.5355339059,0],[-47.5,39.3301270189,0],[-46.2940952255,39.8296291314,0],[-45,40,0],[45,40,0],[46.2940952255,39.8296291314,0],[47.5,39.3301270189,0],[48.5355339059,38.5355339059,0],[49.3301270189,37.5,0],[49.8296291314,36.2940952255,0],[50,35,0],[30,-10,50],[20,-20,50],[0,-20,50],[-10,-10,50],[-10,20,50],[0,30,50],[20,30,50],[30,20,50]],[[24,25,35],[34,24,35],[25,26,35],[28,34,35],[26,27,35],[27,28,35],[22,23,34],[21,22,34],[33,21,34],[28,33,34],[23,24,34],[18,19,33],[17,18,33],[32,17,33],[19,20,33],[28,32,33],[20,21,33],[16,17,32],[15,16,32],[14,15,32],[31,14,32],[28,31,32],[13,14,31],[12,13,31],[11,12,31],[10,11,31],[30,10,31],[28,30,31],[28,29,30],[9,10,30],[8,9,30],[7,8,30],[29,7,30],[6,7,29],[5,6,29],[4,5,29],[28,3,29],[3,4,29],[0,28,27],[26,0,27],[25,0,26],[24,0,25],[23,0,24],[22,0,23],[21,0,22],[20,0,21],[19,0,20],[18,0,19],[17,0,18],[16,0,17],[14,16,15],[13,16,14],[12,16,13],[11,16,12],[10,16,11],[9,16,10],[7,9,8],[6,9,7],[5,9,6],[4,9,5],[3,9,4],[28,2,3],[2,9,3],[28,1,2],[1,9,2],[28,0,1],[0,9,1],[0,16,9]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer=[0,5,10,15]), [[[50,-25,0],[35,-40,0],[-40,-40,0],[-50,-30,0],[-50,35,0],[-45,40,0],[50,40,0],[30,-5,50],[15,-20,50],[0,-20,50],[-10,-10,50],[-10,25,50],[-5,30,50],[30,30,50]],[[5,13,12],[13,11,12],[11,5,12],[13,10,11],[10,4,11],[4,5,11],[13,9,10],[3,4,10],[9,3,10],[2,3,9],[8,2,9],[13,8,9],[13,7,8],[1,2,8],[7,1,8],[13,0,7],[0,1,7],[0,13,6],[13,5,6],[5,0,6],[4,0,5],[2,4,3],[1,4,2],[4,1,0]]]);
assert_approx(prismoid([100,80],[40,50],h=50,shift=[10,5],chamfer1=[15,10,5,0], rounding2=[0,5,10,15]), [[[50,-40,0],[-45,-40,0],[-50,-35,0],[-50,30,0],[-40,40,0],[35,40,0],[50,25,0],[30,-5,50],[29.4888873943,-8.88228567654,50],[27.9903810568,-12.5,50],[25.6066017178,-15.6066017178,50],[22.5,-17.9903810568,50],[18.8822856765,-19.4888873943,50],[15,-20,50],[0,-20,50],[-2.58819045103,-19.6592582629,50],[-5,-18.6602540378,50],[-7.07106781187,-17.0710678119,50],[-8.66025403784,-15,50],[-9.65925826289,-12.588190451,50],[-10,-10,50],[-10,25,50],[-9.82962913145,26.2940952255,50],[-9.33012701892,27.5,50],[-8.53553390593,28.5355339059,50],[-7.5,29.3301270189,50],[-6.29409522551,29.8296291314,50],[-5,30,50],[30,30,50]],[[4,28,27],[28,26,27],[26,4,27],[28,25,26],[25,4,26],[28,24,25],[24,4,25],[3,4,24],[23,3,24],[28,23,24],[22,3,23],[28,22,23],[21,3,22],[28,21,22],[28,20,21],[20,3,21],[28,19,20],[2,3,20],[19,2,20],[28,18,19],[18,2,19],[28,17,18],[17,2,18],[1,2,17],[16,1,17],[28,16,17],[15,1,16],[28,15,16],[14,1,15],[28,14,15],[13,1,14],[28,13,14],[0,1,13],[12,0,13],[28,12,13],[11,0,12],[28,11,12],[10,0,11],[28,10,11],[9,0,10],[28,9,10],[8,0,9],[28,8,9],[28,7,8],[7,0,8],[28,0,7],[0,28,6],[28,5,6],[5,0,6],[28,4,5],[4,0,5],[3,0,4],[1,3,2],[3,1,0]]]);
}
test_prismoid();