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Merge remote-tracking branch 'upstream/master'

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Adrian Mariano
2021-10-20 23:39:52 -04:00
parent 76272d9d9a 6f1ac73d59
commit c98dc64d20
5 changed files with 339 additions and 305 deletions
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182
geometry.scad
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@@ -488,7 +488,7 @@ function _covariance_evec_eval(points) =
evals = _eigenvals_symm_3(M), // eigenvalues in decreasing order
evec = _eigenvec_symm_3(M,evals,i=2) )
[pm, evec, evals[0] ];
// Function: plane_from_points()
// Usage:
@@ -1638,17 +1638,26 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// Description:
// Given a simple polygon in 2D or 3D, triangulates it and returns a list
// of triples indexing into the polygon vertices. When the optional argument `ind` is
// given, the it is used as an index list into `poly` to define the polygon. In that case,
// `poly` may have a length greater than `ind`. Otherwise, all points in `poly`
// given, it is used as an index list into `poly` to define the polygon. In that case,
// `poly` may have a length greater than `ind`. When `ind` is undefined, all points in `poly`
// are considered as vertices of the polygon.
// .
// The function may issue an error if it finds that the polygon is not simple
// (self-intersecting) or its vertices are collinear. It can work for 3d non-planar polygons
// if they are close enough to planar but may otherwise issue an error for this case.
// .
// For 2d polygons, the output triangles will have the same winding (CW or CCW) of
// the input polygon. For 3d polygons, the triangle windings will induce a normal
// vector with the same direction of the polygon normal.
// .
// The function produce correct triangulations for some non-twisted non-simple polygons.
// A polygon is non-twisted iff it is simple or there is a partition of it in
// simple polygons with the same winding. These polygons may have "touching" vertices
// (two vertices having the same coordinates, but distinct adjacencies) and "contact" edges
// (edges whose vertex pairs have the same pairwise coordinates but are in reversed order) but has
// no self-crossing. See examples bellow. If all polygon edges are contact edges,
// it returns an empty list for 2d polygons and issues an error for 3d polygons.
// .
// Self-crossing polygons have no consistent winding and usually produce an error but
// when an error is not issued the outputs are not correct triangulations. The function
// can work for 3d non-planar polygons if they are close enough to planar but may otherwise
// issue an error for this case.
// Arguments:
// poly = Array of vertices for the polygon.
// ind = A list indexing the vertices of the polygon in `poly`.
@@ -1656,7 +1665,32 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// Example(2D,NoAxes):
// poly = star(id=10, od=15,n=11);
// tris = polygon_triangulate(poly);
// for(tri=tris) stroke(select(poly,tri), width=.2, closed=true);
// color("lightblue") for(tri=tris) polygon(select(poly,tri));
// color("blue") up(1) for(tri=tris) { stroke(select(poly,tri),.15,closed=true); }
// color("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with a hole and one "contact" edge
// poly = [ [-10,0], [10,0], [0,10], [-10,0], [-4,4], [4,4], [0,2], [-4,4] ];
// tris = polygon_triangulate(poly);
// color("lightblue") for(tri=tris) polygon(select(poly,tri));
// color("blue") up(1) for(tri=tris) { stroke(select(poly,tri),.15,closed=true); }
// color("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with "touching" vertices and no holes
// poly = [ [0,0], [5,5], [-5,5], [0,0], [-5,-5], [5,-5] ];
// tris = polygon_triangulate(poly);
// color("lightblue") for(tri=tris) polygon(select(poly,tri));
// color("blue") up(1) for(tri=tris) { stroke(select(poly,tri),.15,closed=true); }
// color("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with "contact" edges and no holes
// poly = [ [0,0], [10,0], [10,10], [0,10], [0,0], [3,3], [7,3],
// [7,7], [7,3], [3,3] ];
// tris = polygon_triangulate(poly); // see from the top
// color("lightblue") for(tri=tris) polygon(select(poly,tri));
// color("blue") up(1) for(tri=tris) { stroke(select(poly,tri),.15,closed=true); }
// color("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1);
// Example(3D):
// include <BOSL2/polyhedra.scad>
// vnf = regular_polyhedron_info(name="dodecahedron",side=5,info="vnf");
@@ -1665,82 +1699,42 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// color("blue")
// vnf_wireframe(vnf_tri, width=.15);
function polygon_triangulate(poly, ind, eps=EPSILON) =
assert(is_path(poly), "Polygon `poly` should be a list of 2d or 3d points")
assert(is_path(poly) && len(poly)>=3, "Polygon `poly` should be a list of at least three 2d or 3d points")
assert(is_undef(ind)
|| (is_vector(ind) && min(ind)>=0 && max(ind)<len(poly) ),
"Improper or out of bounds list of indices")
let( ind = deduplicate_indexed(poly,is_undef(ind) ? count(len(poly)) : ind) )
len(ind) == 3 ? [ind] :
len(ind) < 3 ? [] :
len(poly[ind[0]]) == 3
? // represents the polygon projection on its plane as a 2d polygon
let(
pts = select(poly,ind),
nrm = polygon_normal(pts)
)
// here, instead of an error, it might return [] or undef
assert( nrm!=undef,
"The polygon has self-intersections or its vertices are collinear or non coplanar.")
let(
imax = max_index([for(p=pts) norm(p-pts[0]) ]),
v1 = unit( pts[imax] - pts[0] ),
v2 = cross(v1,nrm),
prpts = pts*transpose([v1,v2])
)
[for(tri=_triangulate(prpts, count(len(ind)), eps)) select(ind,tri) ]
: let( cw = is_polygon_clockwise(select(poly, ind)) )
cw
? [for(tri=_triangulate( poly, reverse(ind), eps )) reverse(tri) ]
: _triangulate( poly, ind, eps );
let( ind = is_undef(ind) ? count(len(poly)) : ind )
len(ind) == 3
? _is_degenerate([poly[ind[0]], poly[ind[1]], poly[ind[2]]], eps) ? [] :
// non zero area
assert( norm(scalar_vec3(cross(poly[ind[1]]-poly[ind[0]], poly[ind[2]]-poly[ind[0]]))) > 2*eps,
"The polygon vertices are collinear.")
[ind]
: len(poly[ind[0]]) == 3
? // represents the polygon projection on its plane as a 2d polygon
let(
ind = deduplicate_indexed(poly, ind, eps)
)
len(ind)<3 ? [] :
let(
pts = select(poly,ind),
nrm = polygon_normal(pts)
)
assert( nrm!=undef,
"The polygon has self-intersections or its vertices are collinear or non coplanar.")
let(
imax = max_index([for(p=pts) norm(p-pts[0]) ]),
v1 = unit( pts[imax] - pts[0] ),
v2 = cross(v1,nrm),
prpts = pts*transpose([v1,v2])
)
[for(tri=_triangulate(prpts, count(len(ind)), eps)) select(ind,tri) ]
: let( cw = is_polygon_clockwise(select(poly, ind)) )
cw
? [for(tri=_triangulate( poly, reverse(ind), eps )) reverse(tri) ]
: _triangulate( poly, ind, eps );
// requires ccw 2d polygons
// returns ccw triangles
function _old_triangulate(poly, ind, eps=EPSILON, tris=[]) =
len(ind)==3 ? concat(tris,[ind]) :
let( ear = _get_ear(poly,ind,eps) )
assert( ear!=undef,
"The polygon has self-intersections or its vertices are collinear or non coplanar.")
let(
ear_tri = select(ind,ear,ear+2),
indr = select(ind,ear+2, ear) // indices of the remaining points
)
_triangulate(poly, indr, eps, concat(tris,[ear_tri]));
// search a valid ear from the remaining polygon
function _old_get_ear(poly, ind, eps, _i=0) =
_i>=len(ind) ? undef : // poly has no ears
let( // the _i-th ear candidate
p0 = poly[ind[_i]],
p1 = poly[ind[(_i+1)%len(ind)]],
p2 = poly[ind[(_i+2)%len(ind)]]
)
// if it is not a convex vertex, try the next one
_is_cw2(p0,p1,p2,eps) ? _get_ear(poly,ind,eps, _i=_i+1) :
let( // vertex p1 is convex; check if the triangle contains any other point
to_tst = select(ind,_i+3, _i-1),
pt2tst = select(poly,to_tst), // points other than p0, p1 and p2
q = [(p0-p2).y, (p2-p0).x], // orthogonal to ray [p0,p2] pointing right
q0 = q*p0,
atleft = [for(p=pt2tst) if(p*q<=q0) p ]
)
atleft==[] ? _i : // no point inside -> an ear
let(
q = [(p2-p1).y, (p1-p2).x], // orthogonal to ray [p1,p2] pointing right
q0 = q*p2,
atleft = [for(p=atleft) if(p*q<=q0) p ]
)
atleft==[] ? _i : // no point inside -> an ear
let(
q = [(p1-p0).y, (p0-p1).x], // orthogonal to ray [p1,p0] pointing right
q0 = q*p1,
atleft = [for(p=atleft) if(p*q<=q0) p ]
)
atleft==[] ? _i : // no point inside -> an ear
// check the next ear candidate
_get_ear(poly, ind, eps, _i=_i+1);
function _triangulate(poly, ind, eps=EPSILON, tris=[]) =
len(ind)==3
? _is_degenerate(select(poly,ind),eps)
@@ -1749,18 +1743,18 @@ function _triangulate(poly, ind, eps=EPSILON, tris=[]) =
: let( ear = _get_ear(poly,ind,eps) )
assert( ear!=undef,
"The polygon has self-intersections or its vertices are collinear or non coplanar.")
ear<0 // degenerate ear
? let( indr = select(ind,-ear+1, -ear-1) ) // discard it
_triangulate(poly, indr, eps, tris)
is_list(ear) // degenerate ear
? _triangulate(poly, select(ind,ear[0]+2, ear[0]), eps, tris) // discard it
: let(
ear_tri = select(ind,ear,ear+2),
indr = select(ind,ear+2, ear) // indices of the remaining points
indr = select(ind,ear+2, ear) // remaining point indices
)
_triangulate(poly, indr, eps, concat(tris,[ear_tri]));
// a returned ear will be:
// 1. a CCW triangle without points inside except possibly at its vertices
// 1. a CCW (non-degenerate) triangle, made of subsequent vertices, without other
// points inside except possibly at its vertices
// 2. or a degenerate triangle where two vertices are coincident
// the returned ear is specified by the index of `ind` of its first vertex
function _get_ear(poly, ind, eps, _i=0) =
@@ -1770,29 +1764,25 @@ function _get_ear(poly, ind, eps, _i=0) =
p1 = poly[ind[(_i+1)%len(ind)]],
p2 = poly[ind[(_i+2)%len(ind)]]
)
// if it is a degenerate triangle, return it (codified)
_is_degenerate([p0,p1,p2],eps) ? -(_i+1) :
// if it is not a convex vertex, try the next one
// degenerate triangles are returned codified
_is_degenerate([p0,p1,p2],eps) ? [_i] :
// if it is not a convex vertex, check the next one
_is_cw2(p0,p1,p2,eps) ? _get_ear(poly,ind,eps, _i=_i+1) :
let( // vertex p1 is convex
// check if the triangle contains any other point
// except possibly its own vertices
to_tst = select(ind,_i+3, _i-1),
pt2tst = select(poly,to_tst), // points other than p0, p1 and p2
q = [(p0-p2).y, (p2-p0).x], // orthogonal to ray [p0,p2] pointing right
q0 = q*p0,
r = [(p2-p1).y, (p1-p2).x], // orthogonal to ray [p2,p1] pointing right
r0 = r*p2,
s = [(p1-p0).y, (p0-p1).x], // orthogonal to ray [p1,p0] pointing right
s0 = s*p1,
inside = [for(p=pt2tst)
if( p*q<=q0 && p*r<=r0 && p*s<=s0 ) // p is in the triangle
if( norm(p-p0)>eps // and doesn't coincide with
&& norm(p-p1)>eps // any of its vertices
inside = [for(p=select(poly,to_tst)) // for vertices other than p0, p1 and p2
if( (p-p0)*q<=0 && (p-p2)*r<=0 && (p-p1)*s<=0 // p is on the triangle
&& norm(p-p0)>eps // but not on any vertex of it
&& norm(p-p1)>eps
&& norm(p-p2)>eps )
p ]
)
inside==[] ? _i : // no point inside -> an ear
inside==[] ? _i : // found an ear
// check the next ear candidate
_get_ear(poly, ind, eps, _i=_i+1);