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