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Speed improvement "icosa2" for spheroid

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Adrian Mariano 2022-01-30 11:24:53 -05:00
parent a268793cce
commit f9dd6e7235
1 changed files with 38 additions and 3 deletions
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shapes3d.scad
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@ -1617,8 +1617,8 @@ function sphere(r, d, circum=false, style="orig", anchor=CENTER, spin=0, orient=
// - `style="orig"` constructs a sphere the same way that the OpenSCAD `sphere()` built-in does.
// - `style="aligned"` constructs a sphere where, if `$fn` is a multiple of 4, it has vertices at all axis maxima and minima. ie: its bounding box is exactly the sphere diameter in length on all three axes. This is the default.
// - `style="stagger"` forms a sphere where all faces are triangular, but the top and bottom poles have thinner triangles.
// - `style="octa"` forms a sphere by subdividing an octahedron (8-sided platonic solid). This makes more uniform faces over the entirety of the sphere, and guarantees the bounding box is the sphere diameter in size on all axes. The effective `$fn` value is quantized to a multiple of 4, though. This is used in constructing rounded corners for various other shapes.
// - `style="icosa"` forms a sphere by subdividing an icosahedron (20-sided platonic solid). This makes even more uniform faces over the entirety of the sphere. The effective `$fn` value is quantized to a multiple of 5, though.
// - `style="octa"` forms a sphere by subdividing an octahedron (8-sided platonic solid). This makes more uniform faces over the entirety of the sphere, and guarantees the bounding box is the sphere diameter in size on all axes. The effective `$fn` value is quantized to a multiple of 4. This is used in constructing rounded corners for various other shapes.
// - `style="icosa"` forms a sphere by subdividing an icosahedron (20-sided platonic solid). This makes even more uniform faces over the entirety of the sphere. The effective `$fn` value is quantized to a multiple of 5.
// Arguments:
// r = Radius of the spheroid.
// style = The style of the spheroid's construction. One of "orig", "aligned", "stagger", "octa", or "icosa". Default: "aligned"
@ -1680,6 +1680,12 @@ module spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, orie
}
// p is a list of 3 points defining a triangle in any dimension. N is the number of extra points
// to add, so output triangle has N+2 points on each side.
function _subsample_triangle(p,N) =
[for(i=[0:N+1]) [for (j=[0:N+1-i]) unit(lerp(p[0],p[1],i/(N+1)) + (p[2]-p[0])*j/(N+1))]];
function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, orient=UP) =
let(
r = get_radius(r=r, d=d, dflt=1),
@ -1688,7 +1694,36 @@ function spheroid(r, style="aligned", d, circum=false, anchor=CENTER, spin=0, or
octa_steps = round(max(4,hsides)/4),
icosa_steps = round(max(5,hsides)/5),
rr = circum? (r / cos(90/vsides) / cos(180/hsides)) : r,
stagger = style=="stagger",
stagger = style=="stagger"
)
style=="icosa2" ? // subdivide faces of an icosahedron and project them onto a sphere
let(
N = icosa_steps-1,
// construct an icosahedron
icovert=[ for(i=[-1,1], j=[-1,1]) each [[0,i,j*PHI], [i,j*PHI,0], [j*PHI,0,i]]],
icoface = hull(icovert),
// Subsample face 0 of the icosahedron
face0 = select(icovert,icoface[0]),
sampled = rr * _subsample_triangle(face0,N),
dir0 = mean(face0),
point0 = face0[0]-dir0,
// Make a rotated copy of the subsampled triangle on each icosahedral face
tri_list = [sampled,
for(i=[1:1:len(icoface)-1])
let(face = select(icovert,icoface[i]))
apply(frame_map(z=mean(face),x=face[0]-mean(face))
*frame_map(z=dir0,x=point0,reverse=true),
sampled)],
// faces for the first triangle group
faces = vnf_tri_array(tri_list[0])[1],
size = repeat((N+2)*(N+3)/2,3),
// Expand to full face list
fullfaces = [for(i=idx(tri_list)) each [for(f=faces) f+i*size]],
fullvert = flatten(flatten(tri_list)) // eliminate triangle structure
)
[reorient(anchor,spin,orient, r=r, p=fullvert), fullfaces]
:
let(
verts = style=="orig"? [
for (i=[0:1:vsides-1]) let(phi = (i+0.5)*180/(vsides))
for (j=[0:1:hsides-1]) let(theta = j*360/hsides)