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Update geometry.scad

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RonaldoCMP 2021-10-14 11:48:41 -03:00
parent 4d9a1d36ac
commit 6b542191ce
1 changed files with 11 additions and 7 deletions
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geometry.scad
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@ -488,7 +488,7 @@ function _covariance_evec_eval(points) =
evals = _eigenvals_symm_3(M), // eigenvalues in decreasing order evals = _eigenvals_symm_3(M), // eigenvalues in decreasing order
evec = _eigenvec_symm_3(M,evals,i=2) ) evec = _eigenvec_symm_3(M,evals,i=2) )
[pm, evec, evals[0] ]; [pm, evec, evals[0] ];
// Function: plane_from_points() // Function: plane_from_points()
// Usage: // Usage:
@ -1616,12 +1616,13 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// simple polygons with the same winding. These polygons may have "touching" vertices // simple polygons with the same winding. These polygons may have "touching" vertices
// (two vertices having the same coordinates, but distinct adjacencies) and "contact" edges // (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 // (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, returns an empty list. // 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 // 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 // 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 // can work for 3d non-planar polygons if they are close enough to planar but may otherwise
// issue an error for this case. // issue an error for this case.
// Arguments: // Arguments:
// poly = Array of vertices for the polygon. // poly = Array of vertices for the polygon.
// ind = A list indexing the vertices of the polygon in `poly`. // ind = A list indexing the vertices of the polygon in `poly`.
@ -1630,18 +1631,21 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// poly = star(id=10, od=15,n=11); // poly = star(id=10, od=15,n=11);
// tris = polygon_triangulate(poly); // tris = polygon_triangulate(poly);
// color("lightblue") for(tri=tris) polygon(select(poly,tri)); // 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("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1); // color("black") up(3) vnf_debug([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
// poly = [ [-10,0], [10,0], [0,10], [-10,0], [-4,4], [4,4], [0,2], [-4,4] ]; // poly = [ [-10,0], [10,0], [0,10], [-10,0], [-4,4], [4,4], [0,2], [-4,4] ];
// tris = polygon_triangulate(poly); // tris = polygon_triangulate(poly);
// color("lightblue") for(tri=tris) polygon(select(poly,tri)); // 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("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1); // color("black") up(3) vnf_debug([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
// poly = [ [0,0], [5,5], [-5,5], [0,0], [-5,-5], [5,-5] ]; // poly = [ [0,0], [5,5], [-5,5], [0,0], [-5,-5], [5,-5] ];
// tris = polygon_triangulate(poly); // tris = polygon_triangulate(poly);
// color("lightblue") for(tri=tris) polygon(select(poly,tri)); // 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("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1); // color("black") up(3) vnf_debug([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
@ -1649,6 +1653,7 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// [7,7], [7,3], [3,3] ]; // [7,7], [7,3], [3,3] ];
// tris = polygon_triangulate(poly); // see from the top // tris = polygon_triangulate(poly); // see from the top
// color("lightblue") for(tri=tris) polygon(select(poly,tri)); // 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("magenta") up(2) stroke(poly,.25,closed=true);
// color("black") up(3) vnf_debug([poly,[]],faces=false,size=1); // color("black") up(3) vnf_debug([poly,[]],faces=false,size=1);
// Example(3D): // Example(3D):
@ -1666,21 +1671,20 @@ function polygon_triangulate(poly, ind, eps=EPSILON) =
let( ind = is_undef(ind) ? count(len(poly)) : ind ) let( ind = is_undef(ind) ? count(len(poly)) : ind )
len(ind) == 3 len(ind) == 3
? _is_degenerate([poly[ind[0]], poly[ind[1]], poly[ind[2]]], eps) ? [] : ? _is_degenerate([poly[ind[0]], poly[ind[1]], poly[ind[2]]], eps) ? [] :
// no zero area // non zero area
assert( norm(scalar_vec3(cross(poly[ind[1]]-poly[ind[0]], poly[ind[2]]-poly[ind[0]]))) > 2*eps, assert( norm(scalar_vec3(cross(poly[ind[1]]-poly[ind[0]], poly[ind[2]]-poly[ind[0]]))) > 2*eps,
"The polygon vertices are collinear.") "The polygon vertices are collinear.")
[ind] [ind]
: len(poly[ind[0]]) == 3 : len(poly[ind[0]]) == 3
? // represents the polygon projection on its plane as a 2d polygon ? // represents the polygon projection on its plane as a 2d polygon
let( let(
ind = deduplicate_indexed(poly, ind, eps) ind = deduplicate_indexed(poly, ind, eps)
) )
len(ind)<3 ? [] : assert(len(ind)>=3 , "The polygon vertices are collinear.")
let( let(
pts = select(poly,ind), pts = select(poly,ind),
nrm = polygon_normal(pts) nrm = polygon_normal(pts)
) )
// here, instead of an error, it might return [] or undef
assert( nrm!=undef, assert( nrm!=undef,
"The polygon has self-intersections or its vertices are collinear or non coplanar.") "The polygon has self-intersections or its vertices are collinear or non coplanar.")
let( let(