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speed improvement for vnf_centroid

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Adrian Mariano 2020-06-14 09:52:27 -04:00
parent e9468f92e1
commit 408833d4ef
1 changed files with 14 additions and 19 deletions
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33
vnf.scad
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@ -358,7 +358,7 @@ module vnf_polyhedron(vnf, convexity=2) {
// no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume // no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume
// if face direction is counter-clockwise. // if face direction is counter-clockwise.
// Algorithm adapted/simplified from: https://wwwf.imperial.ac.uk/~rn/centroid.pdf // Divide the polyhedron into tetrahedra with the origin as one vertex and sum up the signed volume.
function vnf_volume(vnf) = function vnf_volume(vnf) =
let(verts = vnf[0]) let(verts = vnf[0])
sum([ sum([
@ -374,27 +374,22 @@ function vnf_volume(vnf) =
// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and // Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined. // no holes; otherwise the results are undefined.
// Algorithm from: https://wwwf.imperial.ac.uk/~rn/centroid.pdf // Divide the solid up into tetrahedra with the origin as one vertex. The centroid of a tetrahedron is the average of its vertices.
// The centroid of the total is the volume weighted average.
function vnf_centroid(vnf) = function vnf_centroid(vnf) =
let( let(
verts = vnf[0], verts = vnf[0],
val=sum([ val = sum([ for(face=vnf[1], j=[1:1:len(face)-2])
for(face=vnf[1], j=[1:1:len(face)-2]) let(
let( v0 = verts[face[0]],
v0 = verts[face[0]], v1 = verts[face[j]],
v1 = verts[face[j]], v2 = verts[face[j+1]],
v2 = verts[face[j+1]], vol = cross(v2,v1)*v0
n = cross(v2-v0,v1-v0) )
) [ [ vol, (v0+v1+v2)*vol ]
v0 * n, ])
vmul(n, )
sqr(v0 + v1) + val[1]/val[0]/4;
sqr(v0 + v2) +
sqr(v1 + v2)
)
]
])
) val[1]/val[0]/8;
function _triangulate_planar_convex_polygons(polys) = function _triangulate_planar_convex_polygons(polys) =