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https://github.com/BelfrySCAD/BOSL2.git
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split_path_at_region_crossings does not return zero length segments
faster code for path and region intersections
This commit is contained in:
Adrian Mariano
parent
b7c5b789b7
commit
dbee0abec6
2 changed files with 105 additions and 44 deletions
65
paths.scad
65
paths.scad
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@ -211,33 +211,34 @@ function _path_self_intersections(path, closed=true, eps=EPSILON) =
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let(
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path = cleanup_path(path, eps=eps),
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plen = len(path)
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) [
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for (i = [0:1:plen-(closed?2:3)], j=[i+2:1:plen-(closed?1:2)]) let(
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a1 = path[i],
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a2 = path[(i+1)%plen],
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b1 = path[j],
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b2 = path[(j+1)%plen],
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isect =
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(max(a1.x, a2.x) < min(b1.x, b2.x))? undef :
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(min(a1.x, a2.x) > max(b1.x, b2.x))? undef :
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(max(a1.y, a2.y) < min(b1.y, b2.y))? undef :
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(min(a1.y, a2.y) > max(b1.y, b2.y))? undef :
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)
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[
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for (i = [0:1:plen-(closed?2:3)])
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let(
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a1 = path[i],
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a2 = path[(i+1)%plen],
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maxax = max(a1.x,a2.x),
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minax = min(a1.x,a2.x),
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maxay = max(a1.y,a2.y),
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minay = min(a1.y,a2.y)
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)
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for(j=[i+2:1:plen-(closed?1:2)])
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let(
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c = a1-a2,
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d = b1-b2,
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denom = (c.x*d.y)-(c.y*d.x)
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) abs(denom)<eps? undef :
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let(
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e = a1-b1,
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t = ((e.x*d.y)-(e.y*d.x)) / denom,
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u = ((e.x*c.y)-(e.y*c.x)) / denom
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) [a1+t*(a2-a1), t, u]
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) if (
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(!closed || i!=0 || j!=plen-1) &&
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isect != undef &&
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isect[1]>=-eps && isect[1]<=1+eps &&
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isect[2]>=-eps && isect[2]<=1+eps
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) [isect[0], i, isect[1], j, isect[2]]
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b1 = path[j],
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b2 = path[(j+1)%plen],
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isect =
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maxax < b1.x && maxax < b2.x ||
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minax > b1.x && minax > b2.x ||
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maxay < b1.y && maxay < b2.y ||
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minay > b1.y && minay > b2.y
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? undef
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: _general_line_intersection([a1,a2],[b1,b2])
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)
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if ((!closed || i!=0 || j!=plen-1)
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&& isect != undef
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&& isect[1]>=-eps && isect[1]<=1+eps
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&& isect[2]>=-eps && isect[2]<=1+eps)
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[isect[0], i, isect[1], j, isect[2]]
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];
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@ -440,6 +441,14 @@ function resample_path(path, N, spacing, closed=false) =
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// closed = set to true to treat path as a polygon. Default: false
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// eps = Epsilon error value used for determine if points coincide. Default: `EPSILON` (1e-9)
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function is_path_simple(path, closed=false, eps=EPSILON) =
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[for(i=[0:1:len(path)-(closed?2:3)])
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let(v1=path[i+1]-path[i],
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v2=select(path,i+2)-path[i+1],
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normv1 = norm(v1),
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normv2 = norm(v2)
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)
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if (/*approx(normv1,0) || approx(normv2,0) ||*/ approx(v1*v2/normv1/normv2,-1)) 1] == []
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&&
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_path_self_intersections(path,closed=closed,eps=eps) == [];
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@ -1043,10 +1052,10 @@ function _tag_self_crossing_subpaths(path, nonzero, closed=true, eps=EPSILON) =
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// polygon(path);
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// right(27)rainbow(polygon_parts(path)) polygon($item);
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// move([16,-14])rainbow(polygon_parts(path,nonzero=true)) polygon($item);
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function polygon_parts(path, nonzero=false, closed=true, eps=EPSILON) =
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function polygon_parts(path, nonzero=false, eps=EPSILON) =
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let(
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path = cleanup_path(path, eps=eps),
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tagged = _tag_self_crossing_subpaths(path, nonzero=nonzero, closed=closed, eps=eps),
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tagged = _tag_self_crossing_subpaths(path, nonzero=nonzero, closed=true, eps=eps),
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kept = [for (sub = tagged) if(sub[0] == "O") sub[1]],
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outregion = _assemble_path_fragments(kept, eps=eps)
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) outregion;
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84
regions.scad
84
regions.scad
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@ -109,7 +109,7 @@ module region(r)
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// Function: point_in_region()
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// Usage:
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// point_in_region(point, region);
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// check = point_in_region(point, region);
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// Description:
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// Tests if a point is inside, outside, or on the border of a region.
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// Returns -1 if the point is outside the region.
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@ -126,6 +126,37 @@ function point_in_region(point, region, eps=EPSILON, _i=0, _cnt=0) =
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// Function: is_region_simple()
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// Usage:
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// bool = is_region_simple(region, [eps]);
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// Description:
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// Returns true if the region is entirely non-self-intersecting, meaning that it is
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// formed from a list of simple polygons that do not intersect each other.
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// Arguments:
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// region = region to check
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// eps = tolerance for geometric omparisons. Default: `EPSILON` = 1e-9
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function is_region_simple(region, eps=EPSILON) =
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[for(p=region) if (!is_path_simple(p)) 1] == []
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&&
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[for(i=[0:1:len(region)-2]) if (_path_region_intersections(region[i],[for(j=[i+1:1:len(region)-1]) region[j]]) != []) 1] ==[];
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function approx_sign(x) = approx(x,0) ? 0 : sign(x);
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function do_segments_intersect(s1,s2) =
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let(
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a1=cross(s1[1]-s1[0], s2[0]-s1[1]),
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a2=cross(s1[1]-s1[0], s2[1]-s1[1]),
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a3=cross(s2[1]-s2[0], s1[0]-s2[1]),
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a4=cross(s2[1]-s2[0], s1[1]-s2[1])
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)
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approx_sign(a1)!=approx_sign(a2) && approx_sign(a3)!=approx_sign(a4);
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// Note: parallel intersecting lines seem to have all the a's equal approx to zero
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// Function: polygons_equal()
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// Usage:
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// b = polygons_equal(poly1, poly2, [eps])
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@ -196,28 +227,49 @@ function __regions_equal(region1, region2, i) =
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__regions_equal(region1, region2, i+1);
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/// Internal Function: _region_path_crossings()
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/// Internal Function: _path_region_intersections()
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/// Usage:
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/// _region_path_crossings(path, region);
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/// _path_region_intersections(path, region);
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/// Description:
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/// Returns a sorted list of [SEGMENT, U] that describe where a given path is crossed by a second path.
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/// Returns a sorted list of [SEGMENT, U] that describe where a given path intersects the region
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// in a single point. (Note that intersections of collinear segments, where the intersection is another segment, are
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// ignored.)
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/// Arguments:
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/// path = The path to find crossings on.
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/// region = Region to test for crossings of.
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/// closed = If true, treat path as a closed polygon. Default: true
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/// eps = Acceptable variance. Default: `EPSILON` (1e-9)
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function _region_path_crossings(path, region, closed=true, eps=EPSILON) =
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function _path_region_intersections(path, region, closed=true, eps=EPSILON) =
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let(
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segs = pair(closed? close_path(path) : cleanup_path(path))
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)
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sort([for (si = idx(segs), p = close_region(region), s2 = pair(p))
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let (
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isect = _general_line_intersection(segs[si], s2, eps=eps)
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)
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if (!is_undef(isect[0]) && isect[1] >= 0-eps && isect[1] < 1+eps
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&& isect[2] >= 0-eps && isect[2] < 1+eps )
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[si, isect[1]]
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]);
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sort(
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[for(si = idx(segs))
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let(
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a1 = segs[si][0],
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a2 = segs[si][1],
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maxax = max(a1.x,a2.x),
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minax = min(a1.x,a2.x),
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maxay = max(a1.y,a2.y),
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minay = min(a1.y,a2.y)
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)
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for(p=close_region(region), s2=pair(p))
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let(
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b1 = s2[0],
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b2 = s2[1],
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isect =
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maxax < b1.x && maxax < b2.x ||
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minax > b1.x && minax > b2.x ||
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maxay < b1.y && maxay < b2.y ||
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minay > b1.y && minay > b2.y
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? undef
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: _general_line_intersection([a1,a2],[b1,b2],eps)
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)
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if (isect && isect[1]>=-eps && isect[1]<=1+eps
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&& isect[2]>=-eps && isect[2]<=1+eps)
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[si,isect[1]]
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]
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);
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// Function: split_path_at_region_crossings()
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@ -241,7 +293,7 @@ function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON)
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let(
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path = deduplicate(path, eps=eps),
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region = [for (path=region) deduplicate(path, eps=eps)],
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xings = _region_path_crossings(path, region, closed=closed, eps=eps),
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xings = _path_region_intersections(path, region, closed=closed, eps=eps),
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crossings = deduplicate(
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concat([[0,0]], xings, [[len(path)-1,1]]),
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eps=eps
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@ -254,7 +306,7 @@ function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON)
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)
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]
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)
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subpaths;
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[for(s=subpaths) if (len(s)>1) s];
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// Function: split_nested_region()
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@ -986,7 +1038,7 @@ function intersection(regions=[],b=undef,c=undef,eps=EPSILON) =
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// circle(d=40);
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// }
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function exclusive_or(regions=[],b=undef,c=undef,eps=EPSILON) =
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b!=undef? exclusive_or(concat([regions],[b],c==undef?[]:[c]),eps=eps) :
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b!=undef? exclusive_or([regions, b, if(is_def(c)) c],eps=eps) :
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len(regions)<=1? regions[0] :
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exclusive_or(
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let(regions=[for (r=regions) is_path(r)? [r] : r])
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