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Boolean geometry bugfixes.

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Revar Desmera 2019-06-17 18:55:10 -07:00
parent 88314af127
commit 1ad126f85d
1 changed files with 98 additions and 77 deletions
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geometry.scad
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@ -19,11 +19,12 @@
// Arguments: // Arguments:
// point = The point to test. // point = The point to test.
// edge = Array of two points forming the line segment to test against. // edge = Array of two points forming the line segment to test against.
function point_on_segment2d(point, edge) = // eps = Acceptable variance. Default: `EPSILON` (1e-9)
point==edge[0] || point==edge[1] || // The point is an endpoint function point_on_segment2d(point, edge, eps=EPSILON) =
approx(point,edge[0],eps=eps) || approx(point,edge[1],eps=eps) || // The point is an endpoint
sign(edge[0].x-point.x)==sign(point.x-edge[1].x) // point is in between the sign(edge[0].x-point.x)==sign(point.x-edge[1].x) // point is in between the
&& sign(edge[0].y-point.y)==sign(point.y-edge[1].y) // edge endpoints && sign(edge[0].y-point.y)==sign(point.y-edge[1].y) // edge endpoints
&& point_left_of_segment2d(point, edge)==0; // and on the line defined by edge && approx(point_left_of_segment2d(point, edge),0,eps=eps); // and on the line defined by edge
// Function: point_left_of_segment2d() // Function: point_left_of_segment2d()
@ -41,11 +42,11 @@ function point_left_of_segment2d(point, edge) =
// Internal non-exposed function. // Internal non-exposed function.
function _point_above_below_segment(point, edge) = function _point_above_below_segment(point, edge, eps=EPSILON) =
edge[0].y <= point.y? ( edge[0].y <= point.y+eps? (
(edge[1].y > point.y && point_left_of_segment2d(point, edge) > 0)? 1 : 0 (edge[1].y > point.y-eps && point_left_of_segment2d(point, edge) > eps)? 1 : 0
) : ( ) : (
(edge[1].y <= point.y && point_left_of_segment2d(point, edge) < 0)? -1 : 0 (edge[1].y <= point.y+eps && point_left_of_segment2d(point, edge) < eps)? -1 : 0
); );
@ -131,11 +132,13 @@ function line_normal(p1,p2) =
// for each segment, so if it is in this range, then the intersection // for each segment, so if it is in this range, then the intersection
// lies on the segment. Otherwise it lies somewhere on the extension // lies on the segment. Otherwise it lies somewhere on the extension
// of the segment. // of the segment.
function _general_line_intersection(s1,s2) = function _general_line_intersection(s1,s2,eps=EPSILON) =
let( denominator = det2([s1[0],s2[0]]-[s1[1],s2[1]]), let(
t=det2([s1[0],s2[0]]-s2)/denominator, denominator = det2([s1[0],s2[0]]-[s1[1],s2[1]])
u=det2([s1[0],s1[0]]-[s1[1],s2[1]])/denominator) ) approx(denominator,0,eps=eps)? [undef,undef,undef] : let(
[denominator==0 ? undef : s1[0]+t*(s1[1]-s1[0]),t,u]; t = det2([s1[0],s2[0]]-s2) / denominator,
u = det2([s1[0],s1[0]]-[s1[1],s2[1]]) /denominator
) [s1[0]+t*(s1[1]-s1[0]), t, u];
// Function: line_intersection() // Function: line_intersection()
@ -147,7 +150,8 @@ function _general_line_intersection(s1,s2) =
// Arguments: // Arguments:
// l1 = First 2D line, given as a list of two 2D points on the line. // l1 = First 2D line, given as a list of two 2D points on the line.
// l2 = Second 2D line, given as a list of two 2D points on the line. // l2 = Second 2D line, given as a list of two 2D points on the line.
function line_intersection(l1,l2) = let( isect = _general_line_intersection(l1,l2)) isect[0]; function line_intersection(l1,l2,eps=EPSILON) =
let(isect = _general_line_intersection(l1,l2,eps=eps)) isect[0];
// Function: segment_intersection() // Function: segment_intersection()
@ -159,10 +163,10 @@ function line_intersection(l1,l2) = let( isect = _general_line_intersection(l1,l
// Arguments: // Arguments:
// s1 = First 2D segment, given as a list of the two 2D endpoints of the line segment. // s1 = First 2D segment, given as a list of the two 2D endpoints of the line segment.
// s2 = Second 2D segment, given as a list of the two 2D endpoints of the line segment. // s2 = Second 2D segment, given as a list of the two 2D endpoints of the line segment.
function segment_intersection(s1,s2) = // eps = Acceptable variance. Default: `EPSILON` (1e-9)
function segment_intersection(s1,s2,eps=EPSILON) =
let( let(
isect = _general_line_intersection(s1,s2), isect = _general_line_intersection(s1,s2,eps=eps)
eps=EPSILON
) isect[1]<0-eps || isect[1]>1+eps || isect[2]<0-eps || isect[2]>1+eps ? undef : isect[0]; ) isect[1]<0-eps || isect[1]>1+eps || isect[2]<0-eps || isect[2]>1+eps ? undef : isect[0];
@ -175,10 +179,10 @@ function segment_intersection(s1,s2) =
// Arguments: // Arguments:
// line = The unbounded 2D line, defined by two 2D points on the line. // line = The unbounded 2D line, defined by two 2D points on the line.
// segment = The bounded 2D line segment, given as a list of the two 2D endpoints of the segment. // segment = The bounded 2D line segment, given as a list of the two 2D endpoints of the segment.
function line_segment_intersection(line,segment) = // eps = Acceptable variance. Default: `EPSILON` (1e-9)
function line_segment_intersection(line,segment,eps=EPSILON) =
let( let(
isect = _general_line_intersection(line,segment), isect = _general_line_intersection(line,segment,eps=eps)
eps = EPSILON
) isect[2]<0-eps || isect[2]>1+eps ? undef : isect[0]; ) isect[2]<0-eps || isect[2]>1+eps ? undef : isect[0];
@ -342,7 +346,7 @@ function is_path(x) = is_list(x) && is_vector(x.x);
// is_closed_path(path, [eps]); // is_closed_path(path, [eps]);
// Description: // Description:
// Returns true if the first and last points in the given path are coincident. // Returns true if the first and last points in the given path are coincident.
function is_closed_path(path, eps=1e-6) = approx(path[0], path[len(path)-1], eps=eps); function is_closed_path(path, eps=EPSILON) = approx(path[0], path[len(path)-1], eps=eps);
// Function: close_path(path) // Function: close_path(path)
@ -350,7 +354,7 @@ function is_closed_path(path, eps=1e-6) = approx(path[0], path[len(path)-1], eps
// close_path(path); // close_path(path);
// Description: // Description:
// If a path's last point does not coincide with its first point, closes the path so it does. // If a path's last point does not coincide with its first point, closes the path so it does.
function close_path(path) = approx(path[0],path[len(path)-1])? path : concat(path,[path[0]]); function close_path(path, eps=EPSILON) = is_closed_path(path,eps=eps)? path : concat(path,[path[0]]);
// Function path_subselect() // Function path_subselect()
@ -385,7 +389,7 @@ function path_subselect(path,s1,u1,s2,u2) =
// assemble_path_fragments(subpaths); // assemble_path_fragments(subpaths);
// Description: // Description:
// Given a list of incomplete paths, assembles them together into complete closed paths if it can. // Given a list of incomplete paths, assembles them together into complete closed paths if it can.
function assemble_path_fragments(subpaths,_finished=[]) = function assemble_path_fragments(subpaths,eps=EPSILON,_finished=[]) =
len(subpaths)<=1? concat(_finished, subpaths) : len(subpaths)<=1? concat(_finished, subpaths) :
let( let(
path = subpaths[0], path = subpaths[0],
@ -393,7 +397,7 @@ function assemble_path_fragments(subpaths,_finished=[]) =
for (i=[1:1:len(subpaths)-1], rev1=[0,1], rev2=[0,1]) let( for (i=[1:1:len(subpaths)-1], rev1=[0,1], rev2=[0,1]) let(
idx1 = rev1? 0 : len(path)-1, idx1 = rev1? 0 : len(path)-1,
idx2 = rev2? len(subpaths[i])-1 : 0 idx2 = rev2? len(subpaths[i])-1 : 0
) if (approx(path[idx1], subpaths[i][idx2])) [ ) if (approx(path[idx1], subpaths[i][idx2], eps=eps)) [
i, concat( i, concat(
rev1? reverse(path) : path, rev1? reverse(path) : path,
select(rev2? reverse(subpaths[i]) : subpaths[i], 1,-1) select(rev2? reverse(subpaths[i]) : subpaths[i], 1,-1)
@ -403,12 +407,14 @@ function assemble_path_fragments(subpaths,_finished=[]) =
) len(matches)==0? ( ) len(matches)==0? (
assemble_path_fragments( assemble_path_fragments(
select(subpaths,1,-1), select(subpaths,1,-1),
concat(_finished, [path]) eps=eps,
_finished=concat(_finished, [path])
) )
) : is_closed_path(matches[0][1])? ( ) : is_closed_path(matches[0][1], eps=eps)? (
assemble_path_fragments( assemble_path_fragments(
[for (i=[1:1:len(subpaths)-1]) if(i != matches[0][0]) subpaths[i]], [for (i=[1:1:len(subpaths)-1]) if(i != matches[0][0]) subpaths[i]],
concat(_finished, [matches[0][1]]) eps=eps,
_finished=concat(_finished, [matches[0][1]])
) )
) : ( ) : (
assemble_path_fragments( assemble_path_fragments(
@ -416,7 +422,8 @@ function assemble_path_fragments(subpaths,_finished=[]) =
[matches[0][1]], [matches[0][1]],
[for (i = [1:1:len(subpaths)-1]) if(i != matches[0][0]) subpaths[i]] [for (i = [1:1:len(subpaths)-1]) if(i != matches[0][0]) subpaths[i]]
), ),
_finished eps=eps,
_finished=_finished
) )
); );
@ -469,11 +476,12 @@ function simplify_path_indexed(points, path, eps=EPSILON) =
// Arguments: // Arguments:
// point = The point to check position of. // point = The point to check position of.
// path = The list of 2D path points forming the perimeter of the polygon. // path = The list of 2D path points forming the perimeter of the polygon.
function point_in_polygon(point, path) = // eps = Acceptable variance. Default: `EPSILON` (1e-9)
function point_in_polygon(point, path, eps=EPSILON) =
// Does the point lie on any edges? If so return 0. // Does the point lie on any edges? If so return 0.
sum([for(i=[0:1:len(path)-1]) point_on_segment2d(point, select(path, i, i+1))?1:0])>0 ? 0 : sum([for(i=[0:1:len(path)-1]) point_on_segment2d(point, select(path, i, i+1), eps=eps)?1:0])>0 ? 0 :
// Otherwise compute winding number and return 1 for interior, -1 for exterior // Otherwise compute winding number and return 1 for interior, -1 for exterior
sum([for(i=[0:1:len(path)-1]) _point_above_below_segment(point, select(path, i, i+1))]) != 0 ? 1 : -1; sum([for(i=[0:1:len(path)-1]) _point_above_below_segment(point, select(path, i, i+1), eps=eps)]) != 0 ? 1 : -1;
// Function: point_in_region() // Function: point_in_region()
@ -487,10 +495,11 @@ function point_in_polygon(point, path) =
// Arguments: // Arguments:
// point = The point to test. // point = The point to test.
// region = The region to test against. Given as a list of polygon paths. // region = The region to test against. Given as a list of polygon paths.
function point_in_region(point, region, _i=0, _cnt=0) = // eps = Acceptable variance. Default: `EPSILON` (1e-9)
function point_in_region(point, region, eps=EPSILON, _i=0, _cnt=0) =
(_i >= len(region))? ((_cnt%2==1)? 1 : -1) : let( (_i >= len(region))? ((_cnt%2==1)? 1 : -1) : let(
pip = point_in_polygon(point, region[_i]) pip = point_in_polygon(point, region[_i], eps=eps)
) pip==0? 0 : point_in_region(point, region, _i+1, _cnt + (pip>0? 1 : 0)); ) approx(pip,0,eps=eps)? 0 : point_in_region(point, region, eps=eps, _i=_i+1, _cnt = _cnt + (pip>eps? 1 : 0));
// Function: pointlist_bounds() // Function: pointlist_bounds()
@ -544,7 +553,7 @@ function is_region(x) = is_list(x) && is_path(x.x);
// close_region(region); // close_region(region);
// Description: // Description:
// Closes all paths within a given region. // Closes all paths within a given region.
function close_region(region) = [for (path=region) close_path(path)]; function close_region(region, eps=EPSILON) = [for (path=region) close_path(path, eps=eps)];
// Function: region_path_crossings() // Function: region_path_crossings()
@ -555,60 +564,68 @@ function close_region(region) = [for (path=region) close_path(path)];
// Arguments: // Arguments:
// path = The path to find crossings on. // path = The path to find crossings on.
// region = Region to test for crossings of. // region = Region to test for crossings of.
function region_path_crossings(path, region) = sort([ // eps = Acceptable variance. Default: `EPSILON` (1e-9)
function region_path_crossings(path, region, eps=EPSILON) = sort([
for (s1=enumerate(pair_wrap(path)), path=region, s2=pair_wrap(path)) let( for (s1=enumerate(pair_wrap(path)), path=region, s2=pair_wrap(path)) let(
isect = _general_line_intersection(s1.y,s2), isect = _general_line_intersection(s1[1],s2,eps=eps)
eps = 1e-9
) if ( ) if (
!is_undef(isect) && !is_undef(isect) &&
isect[1] >= 0-eps && isect[1] < 1-eps && isect[1] >= 0-eps && isect[1] < 1-eps &&
isect[2] >= 0-eps && isect[2] < 1-eps isect[2] >= 0-eps && isect[2] < 1-eps
) [s1.x, isect[1]] ) [s1[0], isect[1]]
]); ]);
function _split_path_at_region_crossings(path, region, eps=1e-6) = function _split_path_at_region_crossings(path, region, eps=EPSILON) =
let( let(
path = deduplicate(path, eps=eps), path = deduplicate(path, eps=eps),
region = [for (path=region) deduplicate(path, eps=eps)], region = [for (path=region) deduplicate(path, eps=eps)],
crossings = deduplicate(concat( crossings = deduplicate(
[[0,0]], concat(
region_path_crossings(path, region), [[0,0]],
[[len(path)-2,1]] region_path_crossings(path, region),
)) [[len(path)-2,1]]
),
eps=eps
)
) [for (p = pair(crossings)) path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1])]; ) [for (p = pair(crossings)) path_subselect(path, p[0][0], p[0][1], p[1][0], p[1][1])];
function _tag_subpaths(path, region) = function _tag_subpaths(path, region, eps=EPSILON) =
let( let(
subpaths = _split_path_at_region_crossings(path, region), subpaths = _split_path_at_region_crossings(path, region, eps=eps),
tagged = [ tagged = [
for (subpath = subpaths) let( for (sub = subpaths) let(
subpath = deduplicate(sub)
) if (len(sub)>1) let(
midpt = lerp(subpath[0], subpath[1], 0.5), midpt = lerp(subpath[0], subpath[1], 0.5),
rel = point_in_region(midpt,region) rel = point_in_region(midpt,region,eps=eps)
) rel<0? ["O", subpath] : rel>0? ["I", subpath] : let( ) rel<0? ["O", subpath] : rel>0? ["I", subpath] : let(
sidept = midpt + rot(90, planar=true, p=normalize(subpath[0][1]-subpath[0][0])*0.01), vec = normalize(subpath[1]-subpath[0]),
rel2 = (point_in_region(sidept,region)>0) == (point_in_region(sidept,region)>0) perp = rot(90, planar=true, p=vec),
) rel2? ["S", subpath] : ["U", subpath] sidept = midpt + perp*0.01,
rel1 = point_in_polygon(sidept,path,eps=eps)>0,
rel2 = point_in_region(sidept,region,eps=eps)>0
) rel1==rel2? ["S", subpath] : ["U", subpath]
] ]
) tagged; ) tagged;
function _tag_region_subpaths(region1, region2) = function _tag_region_subpaths(region1, region2, eps=EPSILON) =
[for (path=region1) each _tag_subpaths(path, region2)]; [for (path=region1) each _tag_subpaths(path, region2, eps=eps)];
function _tagged_region(region1,region2,keep1,keep2) = function _tagged_region(region1,region2,keep1,keep2,eps=EPSILON) =
let( let(
region1 = close_region(region1), region1 = close_region(region1, eps=eps),
region2 = close_region(region2), region2 = close_region(region2, eps=eps),
tagged1 = _tag_region_subpaths(region1,region2), tagged1 = _tag_region_subpaths(region1, region2, eps=eps),
tagged2 = _tag_region_subpaths(region2,region1), tagged2 = _tag_region_subpaths(region2, region1, eps=eps),
tagged = concat( tagged = concat(
[for (tagpath = tagged1) if (in_list(tagpath[0], keep1)) tagpath[1]], [for (tagpath = tagged1) if (in_list(tagpath[0], keep1)) tagpath[1]],
[for (tagpath = tagged2) if (in_list(tagpath[0], keep2)) tagpath[1]] [for (tagpath = tagged2) if (in_list(tagpath[0], keep2)) tagpath[1]]
), ),
outregion = assemble_path_fragments(tagged) outregion = assemble_path_fragments(tagged, eps=eps)
) outregion; ) outregion;
@ -624,15 +641,16 @@ function _tagged_region(region1,region2,keep1,keep2) =
// shape2 = move([ 8, 8,0], p=circle(d=50)); // shape2 = move([ 8, 8,0], p=circle(d=50));
// for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true); // for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true);
// color("green") region(union(shape1,shape2)); // color("green") region(union(shape1,shape2));
function union(regions=[],b=undef,c=undef) = function union(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? union(concat([regions],[b],c==undef?[]:[c])) : b!=undef? union(concat([regions],[b],c==undef?[]:[c]), eps=eps) :
len(regions)<=1? regions[0] : len(regions)<=1? regions[0] :
union( union(
let(regions=[for (r=regions) is_path(r)? [r] : r]) let(regions=[for (r=regions) is_path(r)? [r] : r])
concat( concat(
[_tagged_region(regions[0],regions[1],["O","S"],["O"])], [_tagged_region(regions[0],regions[1],["O","S"],["O"], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]] [for (i=[2:1:len(regions)-1]) regions[i]]
) ),
eps=eps
); );
@ -649,15 +667,16 @@ function union(regions=[],b=undef,c=undef) =
// shape2 = move([ 8, 8,0], p=circle(d=50)); // shape2 = move([ 8, 8,0], p=circle(d=50));
// for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true); // for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true);
// color("green") region(difference(shape1,shape2)); // color("green") region(difference(shape1,shape2));
function difference(regions=[],b=undef,c=undef) = function difference(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? difference(concat([regions],[b],c==undef?[]:[c])) : b!=undef? difference(concat([regions],[b],c==undef?[]:[c]), eps=eps) :
len(regions)<=1? regions[0] : len(regions)<=1? regions[0] :
difference( difference(
let(regions=[for (r=regions) is_path(r)? [r] : r]) let(regions=[for (r=regions) is_path(r)? [r] : r])
concat( concat(
[_tagged_region(regions[0],regions[1],["O","U"],["I"])], [_tagged_region(regions[0],regions[1],["O","U"],["I"], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]] [for (i=[2:1:len(regions)-1]) regions[i]]
) ),
eps=eps
); );
@ -673,15 +692,16 @@ function difference(regions=[],b=undef,c=undef) =
// shape2 = move([ 8, 8,0], p=circle(d=50)); // shape2 = move([ 8, 8,0], p=circle(d=50));
// for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true); // for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true);
// color("green") region(intersection(shape1,shape2)); // color("green") region(intersection(shape1,shape2));
function intersection(regions=[],b=undef,c=undef) = function intersection(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? intersection(concat([regions],[b],c==undef?[]:[c])) : b!=undef? intersection(concat([regions],[b],c==undef?[]:[c]),eps=eps) :
len(regions)<=1? regions[0] : len(regions)<=1? regions[0] :
intersection( intersection(
let(regions=[for (r=regions) is_path(r)? [r] : r]) let(regions=[for (r=regions) is_path(r)? [r] : r])
concat( concat(
[_tagged_region(regions[0],regions[1],["I","S"],["I"])], [_tagged_region(regions[0],regions[1],["I","S"],["I"],eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]] [for (i=[2:1:len(regions)-1]) regions[i]]
) ),
eps=eps
); );
@ -697,18 +717,19 @@ function intersection(regions=[],b=undef,c=undef) =
// shape2 = move([ 8, 8,0], p=circle(d=50)); // shape2 = move([ 8, 8,0], p=circle(d=50));
// for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true); // for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, close=true);
// color("green") region(exclusive_or(shape1,shape2)); // color("green") region(exclusive_or(shape1,shape2));
function exclusive_or(regions=[],b=undef,c=undef) = function exclusive_or(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? exclusive_or(concat([regions],[b],c==undef?[]:[c])) : b!=undef? exclusive_or(concat([regions],[b],c==undef?[]:[c]),eps=eps) :
len(regions)<=1? regions[0] : len(regions)<=1? regions[0] :
exclusive_or( exclusive_or(
let(regions=[for (r=regions) is_path(r)? [r] : r]) let(regions=[for (r=regions) is_path(r)? [r] : r])
concat( concat(
[union([ [union([
difference([regions[0],regions[1]]), difference([regions[0],regions[1]], eps=eps),
difference([regions[1],regions[0]]) difference([regions[1],regions[0]], eps=eps)
])], ], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]] [for (i=[2:1:len(regions)-1]) regions[i]]
) ),
eps=eps
); );