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add geom_dodecahedron

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This commit is contained in:
Justin Lin 2021-09-22 16:07:34 +08:00
parent 66d02d02e2
commit 9340f73f1a
3 changed files with 102 additions and 0 deletions
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1
src/experimental/_impl/_geom_prj2sphere.scad Normal file
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function _geom_prj2sphere(t, r) = [for(p = t) p / norm(p) * r];

34
src/experimental/_impl/_geom_pts_faces.scad Normal file
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use <__comm__/_pt3_hash.scad>;
use <util/map/hashmap.scad>;
use <util/map/hashmap_put.scad>;
use <util/map/hashmap_get.scad>;
function _pimap_pts(radius, points, leng, hash, m, deduped_pts = [], n = -1, i = 0) =
i == leng ? [m, deduped_pts] :
let(v = hashmap_get(m, points[i], hash = hash))
is_undef(v) ?
_pimap_pts(radius, points, leng, hash, hashmap_put(m, points[i], n + 1, hash = hash), concat(deduped_pts, [points[i] / norm(points[i]) * radius]), n + 1, i + 1) :
_pimap_pts(radius, points, leng, hash, m, deduped_pts, n, i + 1);
function _geom_pts_faces(points, radius) =
let(
number_of_buckets = ceil(sqrt(len(points)) * 1.5),
hash = function(p) _pt3_hash(p),
leng = len(points),
m_pts = _pimap_pts(
radius,
points,
leng,
hash,
hashmap(number_of_buckets = number_of_buckets)
),
faces = [
for(i = [0:3:leng - 3])
[
hashmap_get(m_pts[0], points[i], hash = hash),
hashmap_get(m_pts[0], points[i + 1], hash = hash),
hashmap_get(m_pts[0], points[i + 2], hash = hash)
]
]
)
[m_pts[1], faces];

67
src/experimental/geom_dodecahedron.scad Normal file
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use <experimental/tri_subdivide.scad>;
use <experimental/_impl/_geom_prj2sphere.scad>;
use <experimental/_impl/_geom_pts_faces.scad>;
function _geom_dodecahedron(dodecahedron_points, tris, radius, detail) =
let(
points = detail == 0 ? [for(tri = tris) each tri] : [
for(tri = tris)
each [for(t = tri_subdivide(tri, detail)) each t]
]
)
_geom_pts_faces(points, radius);
function _geom_dodecahedron_quick(dodecahedron_points, tris, radius, detail) =
let(
points = detail == 0 ? [for(tri = tris) each _geom_prj2sphere(tri, radius)] : [
for(tri = tris)
each [for(t = tri_subdivide(tri, detail)) each _geom_prj2sphere(t, radius)]
],
faces = [for(i = [0:3:len(points) - 3]) [i, i + 1, i + 2]]
)
[points, faces];
function geom_dodecahedron(radius, detail = 0, quick_mode = true) =
let(
t = (1 + sqrt(5)) / 2,
r = 1 / t,
dodecahedron_points = [
// (±1, ±1, ±1)
[-1, -1, -1], [-1, -1, 1],
[-1, 1, -1], [-1, 1, 1],
[1, -1, -1], [1, -1, 1],
[1, 1, -1], [1, 1, 1],
// (0, ±1/φ, ±φ)
[0, -r, -t], [0, -r, t],
[0, r, -t], [0, r, t],
// (±1/φ, ±φ, 0)
[-r, -t, 0], [-r, t, 0],
[r, -t, 0], [r, t, 0],
// (±φ, 0, ±1/φ)
[-t, 0, -r], [t, 0, -r],
[-t, 0, r], [t, 0, r]
],
dodecahedron_faces = [
[7, 11, 3], [15, 7, 3], [13, 15, 3],
[17, 19, 7], [6, 17, 7], [15, 6, 7],
[8, 4, 17], [10, 8, 17], [6, 10, 17],
[16, 0, 8], [2, 16, 8], [10, 2, 8],
[1, 12, 0], [18, 1, 0], [16, 18, 0],
[2, 10, 6], [13, 2, 6], [15, 13, 6],
[18, 16, 2], [3, 18, 2], [13, 3, 2],
[9, 1, 18], [11, 9, 18], [3, 11, 18],
[12, 14, 4], [0, 12, 4], [8, 0, 4],
[5, 9, 11], [19, 5, 11], [7, 19, 11],
[14, 5, 19], [4, 14, 19], [17, 4, 19],
[14, 12, 1], [5, 14, 1], [9, 5, 1]
],
tris = [
for(face = dodecahedron_faces)
[for(i = face) dodecahedron_points[i]]
]
)
quick_mode ? _geom_dodecahedron_quick(dodecahedron_points, tris, radius, detail) :
_geom_dodecahedron(dodecahedron_points, tris, radius, detail);