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Quadrupled bezier patch speed.

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Revar Desmera
2019-03-30 15:44:36 -07:00
parent b8239d2dde
commit d0595fb132
2 changed files with 177 additions and 39 deletions
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beziers.scad
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@@ -241,9 +241,9 @@ function bezier_triangle_point(patch, u, v) =
len(patch) == 1 ? patch[0][0] :
let(
n = len(patch)-1,
Pu = [for(i=[0:n-1]) select(patch[i],1,-1)],
Pv = [for(i=[0:n-1]) select(patch[i],0,-2)],
Pw = select(patch,1,-1)
Pu = [for(i=[0:n-1]) [for (j=[1:len(patch[i])-1]) patch[i][j]]],
Pv = [for(i=[0:n-1]) [for (j=[0:len(patch[i])-2]) patch[i][j]]],
Pw = [for(i=[1:len(patch)-1]) patch[i]]
)
bezier_triangle_point(u*Pu + v*Pv + (1-u-v)*Pw, u, v);
@@ -254,9 +254,9 @@ function _vertex_list_merge(v1, v2) = concat(v1, [for (v=v2) if (!in_list(v,v1))
function _vertex_list_face(v, face) = [for (pt = face) search([pt], v, num_returns_per_match=1)[0]];
// Function: bezier_patch_vertices_and_faces()
// Function: bezier_patch()
// Usage:
// bezier_patch_vertices_and_faces(patch, [splinesteps], [vertices], [faces]);
// bezier_patch(patch, [splinesteps], [vertices], [faces]);
// Description:
// Calculate vertices and faces for forming a partial polyhedron
// from the given bezier rectangular patch. Returns a list containing
@@ -270,30 +270,33 @@ function _vertex_list_face(v, face) = [for (pt = face) search([pt], v, num_retur
// splinesteps = Number of steps to divide each bezier segment into. Default: 16
// vertices = Vertex list to add new points to. Default: []
// faces = Face list to add new faces to. Default: []
function bezier_patch_vertices_and_faces(patch, splinesteps=16, vertices=[], faces=[]) =
function bezier_patch(patch, splinesteps=16, vertices=[], faces=[]) =
let(
base = len(vertices),
pts = [for (v=[0:splinesteps], u=[0:splinesteps]) bezier_patch_point(patch, u/splinesteps, v/splinesteps)],
new_vertices = _vertex_list_merge(vertices, pts),
new_vertices = concat(vertices, pts),
new_faces = [
for (
v=[0:splinesteps-1],
u=[0:splinesteps-1],
i=[0,1]
) let (
v1 = u+v*(splinesteps+1),
v1 = u+v*(splinesteps+1) + base,
v2 = v1 + 1,
v3 = v1 + splinesteps + 1,
v4 = v3 + 1,
face = i? [v1,v3,v2] : [v2,v3,v4],
facepts = [for (idx = face) pts[idx]]
) _vertex_list_face(new_vertices, facepts)
face = i? [v1,v3,v2] : [v2,v3,v4]
) face
]
) [new_vertices, concat(faces, new_faces)];
// Function: bezier_triangle_vertices_and_faces()
function _tri_count(n) = (n*(1+n))/2;
// Function: bezier_triangle()
// Usage:
// bezier_triangle_vertices_and_faces(patch, [splinesteps], [vertices], [faces]);
// bezier_triangle(patch, [splinesteps], [vertices], [faces]);
// Description:
// Calculate vertices and faces for forming a partial polyhedron
// from the given bezier triangular patch. Returns a list containing
@@ -307,24 +310,40 @@ function bezier_patch_vertices_and_faces(patch, splinesteps=16, vertices=[], fac
// splinesteps = Number of steps to divide each bezier segment into. Default: 16
// vertices = Vertex list to add new points to. Default: []
// faces = Face list to add new faces to. Default: []
function bezier_triangle_vertices_and_faces(patch, splinesteps=16, vertices=[], faces=[]) =
// Example(3D):
// tri = [
// [[-50,-33,0], [-25,16,-50], [0,66,0]],
// [[0,-33,-50], [25,16,-50]],
// [[50,-33,0]]
// ];
// vnf = bezier_triangle(tri, splinesteps=16);
// polyhedron(points=vnf[0], faces=vnf[1]);
function bezier_triangle(patch, splinesteps=16, vertices=[], faces=[]) =
let(
pts = [for (u=[0:splinesteps], v=[0:splinesteps-u]) bezier_triangle_point(patch, u/splinesteps, v/splinesteps)],
new_vertices = _vertex_list_merge(vertices, pts),
base = len(vertices),
pts = [
for (
u=[0:splinesteps],
v=[0:splinesteps-u]
) bezier_triangle_point(patch, u/splinesteps, v/splinesteps)
],
new_vertices = concat(vertices, pts),
patchlen = len(patch),
tricnt = _tri_count(splinesteps+1),
new_faces = [
for (
u=[0:splinesteps-1],
v=[0:splinesteps-u-1]
) let (
v1 = bezier_triangle_point(patch, u/splinesteps, v/splinesteps),
v2 = bezier_triangle_point(patch, (u+1)/splinesteps, v/splinesteps),
v3 = bezier_triangle_point(patch, u/splinesteps, (v+1)/splinesteps),
v4 = bezier_triangle_point(patch, (u+1)/splinesteps, (v+1)/splinesteps),
v1 = v + (tricnt - _tri_count(splinesteps+1-u)) + base,
v2 = v1 + 1,
v3 = v + (tricnt - _tri_count(splinesteps-u)) + base,
v4 = v3 + 1,
allfaces = concat(
[[v1,v2,v3]],
((u<splinesteps-1 && v<splinesteps-u-1)? [[v2,v4,v3]] : [])
)
) for (facepts=allfaces) _vertex_list_face(new_vertices, facepts)
) for (face=allfaces) face
]
) [new_vertices, concat(faces, new_faces)];
@@ -436,7 +455,7 @@ function patches_rotate(patches, a=undef, v=undef, cp=[0,0,0]) = [for (patch=pat
// polyhedron.
// Arguments:
// patches = A list of rectangular bezier patches.
// tripatches = A list of triangular bezier patches.
// tris = A list of triangular bezier patches.
// splinesteps = Number of steps to divide each bezier segment into. Default: 16
// vertices = Vertex list to add new points to. Default: []
// faces = Face list to add new faces to. Default: []
@@ -455,14 +474,14 @@ function patches_rotate(patches, a=undef, v=undef, cp=[0,0,0]) = [for (patch=pat
// ];
// vnf = bezier_surface_vertices_and_faces(patches=[patch1, patch2], splinesteps=16);
// polyhedron(points=vnf[0], faces=vnf[1]);
function bezier_surface_vertices_and_faces(patches=[], tripatches=[], splinesteps=16, i=0, vertices=[], faces=[]) =
function bezier_surface_vertices_and_faces(patches=[], tris=[], splinesteps=16, i=0, vertices=[], faces=[]) =
let(
vnf = (i >= len(patches))? [vertices, faces] :
bezier_patch_vertices_and_faces(patches[i], splinesteps=splinesteps, vertices=vertices, faces=faces),
vnf2 = (i >= len(tripatches))? vnf :
bezier_triangle_vertices_and_faces(tripatches[i], splinesteps=splinesteps, vertices=vnf[0], faces=vnf[1])
) (i >= len(patches) && i >= len(tripatches))? vnf2 :
bezier_surface_vertices_and_faces(patches=patches, tripatches=tripatches, splinesteps=splinesteps, i=i+1, vertices=vnf2[0], faces=vnf2[1]);
bezier_patch(patches[i], splinesteps=splinesteps, vertices=vertices, faces=faces),
vnf2 = (i >= len(tris))? vnf :
bezier_triangle(tris[i], splinesteps=splinesteps, vertices=vnf[0], faces=vnf[1])
) (i >= len(patches) && i >= len(tris))? vnf2 :
bezier_surface_vertices_and_faces(patches=patches, tris=tris, splinesteps=splinesteps, i=i+1, vertices=vnf2[0], faces=vnf2[1]);
@@ -926,7 +945,7 @@ module trace_bezier(bez, N=3, size=1) {
// Takes a list of two or more bezier patches and attempts to make a complete polyhedron from them.
// Arguments:
// patches = A list of rectangular bezier patches.
// tripatches = A list of triangular bezier patches.
// tris = A list of triangular bezier patches.
// vertices = Vertex list for additional non-bezier faces. Default: []
// faces = Additional non-bezier faces. Default: []
// splinesteps = Number of steps to divide each bezier segment into. Default: 16
@@ -944,9 +963,9 @@ module trace_bezier(bez, N=3, size=1) {
// [[18,82,0], [33,100, 0], [ 67,100, 0], [ 82, 82,0]],
// ];
// bezier_polyhedron([patch1, patch2], splinesteps=8);
module bezier_polyhedron(patches=[], tripatches=[], splinesteps=16, vertices=[], faces=[])
module bezier_polyhedron(patches=[], tris=[], splinesteps=16, vertices=[], faces=[])
{
sfc = bezier_surface_vertices_and_faces(patches=patches, tripatches=tripatches, splinesteps=splinesteps, vertices=vertices, faces=faces);
sfc = bezier_surface_vertices_and_faces(patches=patches, tris=tris, splinesteps=splinesteps, vertices=vertices, faces=faces);
polyhedron(points=sfc[0], faces=sfc[1]);
}
@@ -955,13 +974,13 @@ module bezier_polyhedron(patches=[], tripatches=[], splinesteps=16, vertices=[],
// Module: trace_bezier_patches()
// Usage:
// trace_bezier_patches(patches, [size], [showcps], [splinesteps]);
// trace_bezier_patches(tripatches, [size], [showcps], [splinesteps]);
// trace_bezier_patches(patches, tripatches, [size], [showcps], [splinesteps]);
// trace_bezier_patches(tris, [size], [showcps], [splinesteps]);
// trace_bezier_patches(patches, tris, [size], [showcps], [splinesteps]);
// Description:
// Shows the surface, and optionally, control points of a list of bezier patches.
// Arguments:
// patches = A list of rectangular bezier patches.
// tripatches = A list of triangular bezier patches.
// tris = A list of triangular bezier patches.
// splinesteps = Number of steps to divide each bezier segment into. default=16
// showcps = If true, show the controlpoints as well as the surface.
// size = Size to show control points and lines.
@@ -979,7 +998,7 @@ module bezier_polyhedron(patches=[], tripatches=[], splinesteps=16, vertices=[],
// [[15,85,0], [33,100, 0], [ 67,100, 0], [ 85, 85,0]],
// ];
// trace_bezier_patches(patches=[patch1, patch2], splinesteps=8, showcps=true);
module trace_bezier_patches(patches=[], tripatches=[], size=1, showcps=false, splinesteps=16)
module trace_bezier_patches(patches=[], tris=[], size=1, showcps=false, splinesteps=16)
{
if (showcps) {
for (patch = patches) {
@@ -989,9 +1008,10 @@ module trace_bezier_patches(patches=[], tripatches=[], size=1, showcps=false, sp
if (i<len(patch)-1) extrude_from_to(patch[i][j], patch[i+1][j]) circle(d=size);
if (j<len(patch[i])-1) extrude_from_to(patch[i][j], patch[i][j+1]) circle(d=size);
}
vnf = bezier_patch_vertices_and_faces(patch, splinesteps=splinesteps);
vnf = bezier_patch(patch, splinesteps=splinesteps);
color("blue") place_copies(vnf[0]) sphere(d=size);
}
for (patch = tripatches) {
for (patch = tris) {
place_copies(flatten(patch)) color("red") sphere(d=size*2);
color("cyan")
for (i=[0:len(patch)-2], j=[0:len(patch[i])-2]) {
@@ -999,10 +1019,11 @@ module trace_bezier_patches(patches=[], tripatches=[], size=1, showcps=false, sp
extrude_from_to(patch[i][j], patch[i][j+1]) circle(d=size);
extrude_from_to(patch[i+1][j], patch[i][j+1]) circle(d=size);
}
vnf = bezier_triangle_vertices_and_faces(patch, splinesteps=splinesteps);
vnf = bezier_triangle(patch, splinesteps=splinesteps);
color("blue") place_copies(vnf[0]) sphere(d=size);
}
}
bezier_polyhedron(patches=patches, tripatches=tripatches, splinesteps=splinesteps);
bezier_polyhedron(patches=patches, tris=tris, splinesteps=splinesteps);
}