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Added code documentation to _make_octa_sphere()

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Revar Desmera
2025-08-24 15:44:45 -07:00
parent f6c9916727
commit 96c7623f86
1 changed files with 18 additions and 7 deletions
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shapes3d.scad
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@@ -3361,29 +3361,34 @@ function _dual_vertices(vnf) =
function _make_octa_sphere(r) =
let(
// Get number of triangles on each side of each octant.
subdivs = quantup(segs(r),4)/4,
// Get octant edge vertices, on sphere surface, for all three octant edges.
edge1 = [for (p = [0:1:subdivs]) spherical_to_xyz(r,0,p/subdivs*90)],
edge2 = zrot(90, p=edge1),
edge3 = xrot(-90, p=edge1),
// Given two edges, calculate interior vertices by rotating along greater circles.
get_pts = function(e1, e2) [
[ e1[0] ],
[ e1[0] ], // shared vertex where edges meet.
for (p = [1:1:subdivs])
let(
p1 = e1[p],
p1 = e1[p], // for each matching pair of edge vertices...
p2 = e2[p],
vec = vector_axis(p1, p2),
ang = vector_angle(p1, p2)
vec = vector_axis(p1, p2), // get rotation axis...
ang = vector_angle(p1, p2) // and angle between them, WRT the origin.
) [
for (t = [0:1:p])
for (t = [0:1:p]) // Subdivide this greater circle
let(
subang = lerp(0, ang, t/p),
pt = rot(a=subang, v=vec, p=p1)
) pt
]
],
// Calculate all the triangular vertex arrays for all three edge pairings.
pts1 = get_pts(edge1, edge2),
pts2 = get_pts(reverse(edge3), reverse(edge1)),
pts3 = get_pts(reverse(edge2), edge3),
// Rotate the calculated triangular arrays to match up.
rot_tri = function(tri)
let(
ll = len(last(tri)) - 1
@@ -3396,6 +3401,7 @@ function _make_octa_sphere(r) =
],
pts2b = rot_tri(rot_tri(pts2)),
pts3b = rot_tri(pts3),
// Average the respecive vertices from each triangular array, and normalize them to the radius.
pts = [
for (u = [0:1:subdivs]) [
for (v = [0:1:u])
@@ -3403,21 +3409,25 @@ function _make_octa_sphere(r) =
p1 = pts1[u][v],
p2 = pts2b[u][v],
p3 = pts3b[u][v],
mean = (p1 + p2 + p3) / 3
mean = p1 + p2 + p3
) unit(mean) * r
]
],
// Calculate the triangulations of the averaged octant vertices.
octant_vnf = vnf_tri_array(pts),
// Make 4 rotated copies of the octant to get the top of the sphere.
top_vnf = vnf_join([
for (a=[0:90:359])
zrot(a, p=octant_vnf)
]),
// Copy the top, flipped on the Z axis to get the bottom, and put them together into one VNF.
bot_vnf = zflip(p=top_vnf),
full_vnf = vnf_join([top_vnf, bot_vnf])
) full_vnf;
function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, orient=UP) =
assert(in_list(style, ["orig", "aligned", "stagger", "octa", "icosa"]))
let(
r = get_radius(r=r, d=d, dflt=1),
hsides = segs(r),
@@ -3547,7 +3557,7 @@ function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, or
]
)
]
: /*style=="orig"?*/
: style=="orig"?
[
[for (i=[0:1:hsides-1]) hsides-i-1],
[for (i=[0:1:hsides-1]) lv-hsides+i],
@@ -3556,6 +3566,7 @@ function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, or
[(i+1)*hsides+j, i*hsides+(j+1)%hsides, (i+1)*hsides+(j+1)%hsides],
]
]
: assert(in_list(style,["orig","aligned","stagger","octa","icosa"]))
) [reorient(anchor,spin,orient, r=r, p=verts), faces];