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Clarified triangulation code and added docs.

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Revar Desmera 2019-02-04 03:40:38 -08:00
parent 4762d72090
commit d52a0b7ab4
1 changed files with 55 additions and 30 deletions
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85
triangulation.scad
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@ -1,33 +1,44 @@
use <math.scad>
function winding_dir(points, face) =
// Given an array of vertices (`points`), and a list of indexes into the
// vertex array (`face`), returns the normal vector of the face.
// points = Array of vertices for the polyhedron.
// face = The face, given as a list of indices into the vertex array `points`.
function face_normal(points, face) =
let(count=len(face))
sum(
[
for(i=[0:count-1]) cross(
points[face[(i+1)%count]]-points[face[0]],
points[face[(i+2)%count]]-points[face[(i+1)%count]]
)
],
0
normalize(
sum(
[
for(i=[0:count-1]) cross(
points[face[(i+1)%count]]-points[face[0]],
points[face[(i+2)%count]]-points[face[(i+1)%count]]
)
]
)
)
;
function find_convex_vertex(dir, points, face, i=0) =
// Returns the index of a convex point on the given face.
// points = Array of vertices for the polyhedron.
// face = The face, given as a list of indices into the vertex array `points`.
// facenorm = The normal vector of the face.
function find_convex_vertex(points, face, facenorm, i=0) =
let(count=len(face),
p0=points[face[i]],
p1=points[face[(i+1)%count]],
p2=points[face[(i+2)%count]]
)
(len(face)>i)?
(cross(p1-p0, p2-p1)*dir>0)? (i+1)%count : find_convex_vertex(dir, points, face, i+1)
(cross(p1-p0, p2-p1)*facenorm>0)? (i+1)%count : find_convex_vertex(points, face, facenorm, i+1)
: //This should never happen since there is at least 1 convex vertex.
undef
;
// points = Array of vertices for the polyhedron.
// face = The face, given as a list of indices into the vertex array `points`.
function point_in_ear(points, face, tests, i=0) =
(i<len(face)-1)?
let(
@ -52,6 +63,8 @@ function check_point_in_ear(point, tests) =
;
// Removes the last item in an array if it is the same as the first item.
// v = The array to normalize.
function normalize_vertex_perimeter(v) =
(len(v) < 2)? v :
(v[len(v)-1] != v[0])? v :
@ -59,21 +72,15 @@ function normalize_vertex_perimeter(v) =
;
function triangulate_faces(points, faces) =
[
for (i=[0 : len(faces)-1])
let(facet = normalize_vertex_perimeter(faces[i]))
for (face = triangulate_face(points, facet))
if (face[0]!=face[1] && face[1]!=face[2] && face[2]!=face[0]) face
]
;
function is_last_off_a_line(points, facelist, vertex) =
// Given a face in a polyhedron, and a vertex in that face, returns true
// if that vertex is the only non-colinear vertex in the face.
// points = Array of vertices for the polyhedron.
// facelist = The face, given as a list of indices into the vertex array `points`.
// vertex = The index into `facelist`, of the vertex to test.
function is_only_noncolinear_vertex(points, facelist, vertex) =
let(
face=wrap_range(facelist, vertex+1, vertex-1),
count=len(face),
dir=winding_dir(points, face)
count=len(face)
)
0==sum(
[
@ -88,30 +95,34 @@ function is_last_off_a_line(points, facelist, vertex) =
;
// Given a face in a polyhedron, subdivides the face into triangular faces.
// Returns an array of faces, where each face is a list of vertex indices.
// points = Array of vertices for the polyhedron.
// face = The face, given as a list of indices into the vertex array `points`.
function triangulate_face(points, face) =
let(count=len(face))
(3==count)?
[face]
:
let(
dir=winding_dir(points, face),
cv=find_convex_vertex(dir, points, face),
facenorm=face_normal(points, face),
cv=find_convex_vertex(points, face, facenorm),
pv=(count+cv-1)%count,
nv=(cv+1)%count,
p0=points[face[pv]],
p1=points[face[cv]],
p2=points[face[nv]],
tests=[
[cross(dir, p0-p2), cross(dir, p0-p2)*p0],
[cross(dir, p1-p0), cross(dir, p1-p0)*p1],
[cross(dir, p2-p1), cross(dir, p2-p1)*p2]
[cross(facenorm, p0-p2), cross(facenorm, p0-p2)*p0],
[cross(facenorm, p1-p0), cross(facenorm, p1-p0)*p1],
[cross(facenorm, p2-p1), cross(facenorm, p2-p1)*p2]
],
ear_test=point_in_ear(points, face, tests),
clipable_ear=(ear_test[0]<0),
diagonal_point=ear_test[1]
)
(clipable_ear)? // There is no point inside the ear.
is_last_off_a_line(points, face, cv)?
is_only_noncolinear_vertex(points, face, cv)?
// In the point&line degeneracy clip to somewhere in the middle of the line.
flatten([
triangulate_face(points, wrap_range(face, cv, (cv+2)%count)),
@ -131,4 +142,18 @@ function triangulate_face(points, face) =
;
// Subdivides all faces for the given polyhedron that have more than 3 vertices.
// Returns an array of faces where each face is a list of 3 vertex array indices.
// points = Array of vertices for the polyhedron.
// faces = Array of faces for the polyhedron. Each face is a list of 3 or more indices into the `points` array.
function triangulate_faces(points, faces) =
[
for (i=[0 : len(faces)-1])
let(facet = normalize_vertex_perimeter(faces[i]))
for (face = triangulate_face(points, facet))
if (face[0]!=face[1] && face[1]!=face[2] && face[2]!=face[0]) face
]
;
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap