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Correction in _cleave_connected_region and polygon_triangulate and some few tweaks

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RonaldoCMP
2021-11-04 12:09:29 +00:00
parent 10604cd20b
commit 6bd1dd918f
6 changed files with 105 additions and 98 deletions
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88
geometry.scad
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@@ -104,15 +104,16 @@ function _tri_class(tri, eps=EPSILON) =
/// class = _pt_in_tri(point, tri);
/// Topics: Geometry, Points, Triangles
/// Description:
/// Return 1 if point is inside the triangle interion.
/// Return =0 if point is on the triangle border.
/// Return -1 if point is outside the triangle.
// For CW triangles `tri` :
/// return 1 if point is inside the triangle interior.
/// return =0 if point is on the triangle border.
/// return -1 if point is outside the triangle.
/// Arguments:
/// point = The point to check position of.
/// tri = A list of the three 2d vertices of a triangle.
/// eps = Tolerance in the geometrical tests.
function _pt_in_tri(point, tri, eps=EPSILON) =
min( _tri_class([tri[0],tri[1],point],eps),
min( _tri_class([tri[0],tri[1],point],eps),
_tri_class([tri[1],tri[2],point],eps),
_tri_class([tri[2],tri[0],point],eps) );
@@ -1701,7 +1702,7 @@ 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, it is used as an index list into `poly` to define the polygon. In that case,
// given, it is used as an index list into `poly` to define the polygon vertices. 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.
// .
@@ -1710,47 +1711,49 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// 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
// A polygon is non-twisted iff it is simple or it has a partition in
// simple polygons with the same winding such that the intersection of any two partitions is
// made of full edges of both partitions. These polygons may have "touching" vertices
// made of full edges and/or vertices of both partitions. 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 (polygons with
// zero area), it returns an empty list for 2d polygons and issues an error for 3d polygons.
// zero area), it returns an empty list for 2d polygons and reports an error for 3d polygons.
// Triangulation errors are reported either by an assert error (when `error=true`) or by returning
// `undef` (when `error=false`). Invalid arguments always produce an assert error.
// .
// Twisted polygons have no consistent winding and when input to this function usually produce
// an error but when an error is not issued the outputs are not correct triangulations. The function
// Twisted polygons have no consistent winding and when input to this function usually reports
// an error but when an error is not reported 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.
// report an error for this case.
// Arguments:
// poly = Array of the polygon vertices.
// ind = A list indexing the vertices of the polygon in `poly`.
// eps = A maximum tolerance in geometrical tests. Default: EPSILON
// Example(2D,NoAxes):
// Example(2D,NoAxes): a simple polygon; see from above
// poly = star(id=10, od=15,n=11);
// 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([path3d(poly),[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with a hole and one "contact" edge
// Example(2D,NoAxes): a polygon with a hole and one "contact" edge; see from above
// 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([path3d(poly),[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with "touching" vertices and no holes
// Example(2D,NoAxes): a polygon with "touching" vertices and no holes; see from above
// 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([path3d(poly),[]],faces=false,size=1);
// Example(2D,NoAxes): a polygon with "contact" edges and no holes
// Example(2D,NoAxes): a polygon with "contact" edges and no holes; see from above
// 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 above
// 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);
@@ -1762,19 +1765,18 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// vnf_tri = [vnf[0], [for(face=vnf[1]) each polygon_triangulate(vnf[0], face) ] ];
// color("blue")
// vnf_wireframe(vnf_tri, width=.15);
function polygon_triangulate(poly, ind, eps=EPSILON) =
function polygon_triangulate(poly, ind, error=true, eps=EPSILON) =
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) ),
assert(is_undef(ind) || (is_vector(ind) && min(ind)>=0 && max(ind)<len(poly) ),
"Improper or out of bounds list of indices")
(! is_undef(ind) ) && len(ind) == 0 ? [] :
let( ind = is_undef(ind) ? count(len(poly)) : ind )
len(ind) <=2 ? [] :
len(ind) == 3
? _degenerate_tri([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]
let( degen = norm(scalar_vec3(cross(poly[ind[1]]-poly[ind[0]], poly[ind[2]]-poly[ind[0]]))) < 2*eps )
assert( ! error || ! degen, "The polygon vertices are collinear.")
degen ? undef : [ind]
: len(poly[ind[0]]) == 3
? // find a representation of the polygon as a 2d polygon by projecting it on its own plane
let(
@@ -1785,44 +1787,46 @@ function polygon_triangulate(poly, ind, eps=EPSILON) =
pts = select(poly,ind),
nrm = -polygon_normal(pts)
)
assert( nrm!=undef,
assert( ! error || (nrm != undef),
"The polygon has self-intersections or zero area or its vertices are collinear or non coplanar.")
nrm == undef ? undef :
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]) // the 2d projection of pts on the polygon plane
)
[for(tri=_triangulate(prpts, count(len(ind)), eps)) select(ind,tri) ]
let( tris = _triangulate(prpts, count(len(ind)), error, eps) )
tris == undef ? undef :
[for(tri=tris) select(ind,tri) ]
: is_polygon_clockwise(select(poly, ind))
? _triangulate( poly, ind, eps )
: [for(tri=_triangulate( poly, reverse(ind), eps )) reverse(tri) ];
? _triangulate( poly, ind, error, eps )
: let( tris = _triangulate( poly, reverse(ind), error, eps ) )
tris == undef ? undef :
[for(tri=tris) reverse(tri) ];
// poly is supposed to be a 2d cw polygon
// implements a modified version of ear cut method for non-twisted polygons
// the polygons accepted by this function are (tecnically) the ones whose interior
// is homeomoph to the interior of a simple polygon
function _triangulate(poly, ind, eps=EPSILON, tris=[]) =
// the polygons accepted by this function are those decomposable in simple
// CW polygons.
function _triangulate(poly, ind, error, eps=EPSILON, tris=[]) =
len(ind)==3
? _degenerate_tri(select(poly,ind),eps)
? tris // if last 3 pts perform a degenerate triangle, ignore it
: concat(tris,[ind]) // otherwise, include it
: let( ear = _get_ear(poly,ind,eps) )
/*
let( x= [if(is_undef(ear)) echo(ind=ind) 0] )
is_undef(ear) ? tris :
*/
assert( ear!=undef,
assert( ! error || (ear != undef),
"The polygon has twists or all its vertices are collinear or non coplanar.")
ear == undef ? undef :
is_list(ear) // is it a degenerate ear ?
? len(ind) <= 4 ? tris :
_triangulate(poly, select(ind,ear[0]+3, ear[0]), eps, tris) // discard it
_triangulate(poly, select(ind,ear[0]+3, ear[0]), error, eps, tris) // discard it
: let(
ear_tri = select(ind,ear,ear+2),
indr = select(ind,ear+2, ear) // indices of the remaining path
)
_triangulate(poly, indr, eps, concat(tris,[ear_tri]));
_triangulate(poly, indr, error, eps, concat(tris,[ear_tri]));
// a returned ear will be:
@@ -1847,9 +1851,7 @@ function _get_ear(poly, ind, eps, _i=0) =
// otherwise check the next ear candidate
_i<lind-1 ? _get_ear(poly, ind, eps, _i=_i+1) :
// poly has no ears, look for wiskers
let(
wiskers = [for(j=idx(ind)) if(norm(poly[ind[j]]-poly[ind[(j+2)%lind]])<eps) j ]
)
let( wiskers = [for(j=idx(ind)) if(norm(poly[ind[j]]-poly[ind[(j+2)%lind]])<eps) j ] )
wiskers==[] ? undef : [wiskers[0]];
@@ -1873,12 +1875,12 @@ function _none_inside(idxs,poly,p0,p1,p2,eps,i=0) =
_tri_class([p2,p0,vert],eps)>=0 )
// or it is equal to p1 and some of its adjacent edges cross the open segment (p0,p2)
|| ( norm(vert-p1) < eps
&& ( _is_at_left(p0,[prev_vert,p1],eps)
&& _is_at_left(p2,[p1,next_vert],eps) )
&& _is_at_left(p0,[prev_vert,p1],eps) && _is_at_left(p2,[p1,prev_vert],eps)
&& _is_at_left(p2,[p1,next_vert],eps) && _is_at_left(p0,[next_vert,p1],eps)
)
)
? false
: _none_inside(idxs,poly,p0,p1,p2,eps,i=i+1);
: _none_inside(idxs,poly,p0,p1,p2,eps,i=i+1);
// Function: is_polygon_clockwise()