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point_in_polygon optimization

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Adrian Mariano 2021-11-01 17:34:18 -04:00
parent 3a367c3faf
commit 7bac9a484d
1 changed files with 33 additions and 27 deletions
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60
geometry.scad
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@ -1583,6 +1583,7 @@ function _point_above_below_segment(point, edge) =
? (edge[1].y > 0 && cross(edge[0], edge[1]-edge[0]) > 0) ? 1 : 0
: (edge[1].y <= 0 && cross(edge[0], edge[1]-edge[0]) < 0) ? -1 : 0;
function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// Original algorithms from http://geomalgorithms.com/a03-_inclusion.html
assert( is_vector(point,2) && is_path(poly,dim=2) && len(poly)>2,
@ -1597,39 +1598,44 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
:
// Does the point lie on any edges? If so return 0.
let(
on_brd = [
for (i = [0:1:len(poly)-1])
let( seg = select(poly,i,i+1) )
if (!approx(seg[0],seg[1],eps) )
_is_point_on_line(point, seg, SEGMENT, eps=eps)? 1:0
]
segs = pair(poly,true),
on_border = [for (seg=segs)
if (norm(seg[0]-seg[1])>eps && _is_point_on_line(point, seg, SEGMENT, eps=eps)) 1]
)
sum(on_brd) > 0? 0 :
nonzero
? // Compute winding number and return 1 for interior, -1 for exterior
let(
windchk = [
for(i=[0:1:len(poly)-1])
let( seg=select(poly,i,i+1) )
if (!approx(seg[0],seg[1],eps=eps))
_point_above_below_segment(point, seg)
on_border != [] ? 0 :
nonzero // Compute winding number and return 1 for interior, -1 for exterior
? let(
winding = [
for(seg=segs)
let(
p0=seg[0]-point,
p1=seg[1]-point
)
if (norm(p0-p1)>eps)
p0.y <=0
? p1.y > 0 && cross(p0,p1-p0)>0 ? 1 : 0
: p1.y <=0 && cross(p0,p1-p0)<0 ? -1: 0
]
) sum(windchk) != 0 ? 1 : -1
)
sum(winding) != 0 ? 1 : -1
: // or compute the crossings with the ray [point, point+[1,0]]
let(
n = len(poly),
cross = [
for(i=[0:n-1])
let(
p0 = poly[i]-point,
p1 = poly[(i+1)%n]-point
)
if (
( (p1.y>eps && p0.y<=eps) || (p1.y<=eps && p0.y>eps) )
&& -eps < p0.x - p0.y *(p1.x - p0.x)/(p1.y - p0.y)
) 1
for(seg=segs)
let(
p0 = seg[0]-point,
p1 = seg[1]-point
)
if (
( (p1.y>eps && p0.y<=eps) || (p1.y<=eps && p0.y>eps) )
&& -eps < p0.x - p0.y *(p1.x - p0.x)/(p1.y - p0.y)
)
1
]
) 2*(len(cross)%2)-1;
)
2*(len(cross)%2)-1;
// Function: polygon_triangulate()