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Fixed octa spheroid() symmetry.

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Revar Desmera
2025-08-22 18:24:50 -07:00
parent 7204e03240
commit 3bc59ceeb1
1 changed files with 71 additions and 60 deletions
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131
shapes3d.scad
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@@ -3359,12 +3359,69 @@ function _dual_vertices(vnf) =
]; ];
function _make_octa_sphere(r) =
let(
subdivs = quantup(segs(r),4)/4,
edge1 = [for (p = [0:1:subdivs]) spherical_to_xyz(r,0,p/subdivs*90)],
edge2 = zrot(90, p=edge1),
edge3 = xrot(-90, p=edge1),
get_pts = function(e1, e2) [
[ e1[0] ],
for (p = [1:1:subdivs])
let(
p1 = e1[p],
p2 = e2[p],
vec = vector_axis(p1, p2),
ang = vector_angle(p1, p2)
) [
for (t = [0:1:p])
let(
subang = lerp(0, ang, t/p),
pt = rot(a=subang, v=vec, p=p1)
) pt
]
],
pts1 = get_pts(edge1, edge2),
pts2 = get_pts(reverse(edge3), reverse(edge1)),
pts3 = get_pts(reverse(edge2), edge3),
rot_tri = function(tri)
let(
ll = len(last(tri)) - 1
) [
for (u = [0:1:ll]) [
for (v = [0:1:u])
let(c = u-v, r = ll-v)
tri[r][c]
]
],
pts2b = rot_tri(rot_tri(pts2)),
pts3b = rot_tri(pts3),
pts = [
for (u = [0:1:subdivs]) [
for (v = [0:1:u])
let(
p1 = pts1[u][v],
p2 = pts2b[u][v],
p3 = pts3b[u][v],
mean = (p1 + p2 + p3) / 3
) mean
]
],
octant_vnf = vnf_tri_array(pts),
top_vnf = vnf_join([
for (a=[0:90:359])
zrot(a, p=octant_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) = function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, orient=UP) =
let( let(
r = get_radius(r=r, d=d, dflt=1), r = get_radius(r=r, d=d, dflt=1),
hsides = segs(r), hsides = segs(r),
vsides = max(2,ceil(hsides/2)), vsides = max(2,ceil(hsides/2)),
octa_steps = round(max(4,hsides)/4),
icosa_steps = round(max(5,hsides)/5), icosa_steps = round(max(5,hsides)/5),
stagger = style=="stagger" stagger = style=="stagger"
) )
@@ -3390,6 +3447,10 @@ function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, or
) )
[reorient(anchor,spin,orient, r=r, p=dualvert), faces] [reorient(anchor,spin,orient, r=r, p=dualvert), faces]
: :
style=="octa" ?
let( vnf = _make_octa_sphere(r) )
reorient(anchor,spin,orient, r=r, p=vnf)
:
style=="icosa" ? // subdivide faces of an icosahedron and project them onto a sphere style=="icosa" ? // subdivide faces of an icosahedron and project them onto a sphere
let( let(
N = icosa_steps-1, N = icosa_steps-1,
@@ -3445,19 +3506,6 @@ function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, or
spherical_to_xyz(r, theta, phi), spherical_to_xyz(r, theta, phi),
spherical_to_xyz(r, 0, 180) spherical_to_xyz(r, 0, 180)
] ]
: style=="octa"?
let(
meridians = [
1,
for (i = [1:1:octa_steps]) i*4,
for (i = [octa_steps-1:-1:1]) i*4,
1,
]
)
[
for (i=idx(meridians), j=[0:1:meridians[i]-1])
spherical_to_xyz(r, j*360/meridians[i], i*180/(len(meridians)-1))
]
: assert(in_list(style,["orig","aligned","stagger","octa","icosa"])), : assert(in_list(style,["orig","aligned","stagger","octa","icosa"])),
lv = len(verts), lv = len(verts),
faces = circum && style=="stagger" ? faces = circum && style=="stagger" ?
@@ -3499,52 +3547,15 @@ 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], [for (i=[0:1:hsides-1]) hsides-i-1],
for (i=[0:1:vsides-2], j=[0:1:hsides-1]) [for (i=[0:1:hsides-1]) lv-hsides+i],
each [ for (i=[0:1:vsides-2], j=[0:1:hsides-1]) each [
[(i+1)*hsides+j, i*hsides+j, i*hsides+(j+1)%hsides], [(i+1)*hsides+j, i*hsides+j, i*hsides+(j+1)%hsides],
[(i+1)*hsides+j, i*hsides+(j+1)%hsides, (i+1)*hsides+(j+1)%hsides], [(i+1)*hsides+j, i*hsides+(j+1)%hsides, (i+1)*hsides+(j+1)%hsides],
] ]
] ]
: /*style=="octa"?*/
let(
meridians = [
0, 1,
for (i = [1:1:octa_steps]) i*4,
for (i = [octa_steps-1:-1:1]) i*4,
1,
],
offs = cumsum(meridians),
pc = last(offs)-1,
os = octa_steps * 2
)
[
for (i=[0:1:3]) [0, 1+(i+1)%4, 1+i],
for (i=[0:1:3]) [pc-0, pc-(1+(i+1)%4), pc-(1+i)],
for (i=[1:1:octa_steps-1])
let(m = meridians[i+2]/4)
for (j=[0:1:3], k=[0:1:m-1])
let(
m1 = meridians[i+1],
m2 = meridians[i+2],
p1 = offs[i+0] + (j*m1/4 + k+0) % m1,
p2 = offs[i+0] + (j*m1/4 + k+1) % m1,
p3 = offs[i+1] + (j*m2/4 + k+0) % m2,
p4 = offs[i+1] + (j*m2/4 + k+1) % m2,
p5 = offs[os-i+0] + (j*m1/4 + k+0) % m1,
p6 = offs[os-i+0] + (j*m1/4 + k+1) % m1,
p7 = offs[os-i-1] + (j*m2/4 + k+0) % m2,
p8 = offs[os-i-1] + (j*m2/4 + k+1) % m2
)
each [
[p1, p4, p3],
if (k<m-1) [p1, p2, p4],
[p5, p7, p8],
if (k<m-1) [p5, p8, p6],
],
]
) [reorient(anchor,spin,orient, r=r, p=verts), faces]; ) [reorient(anchor,spin,orient, r=r, p=verts), faces];