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boolean operations fixes

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This commit is contained in:
Adrian Mariano 2021-10-09 21:44:26 -04:00
parent 9670fc0e68
commit ec02676267
5 changed files with 214 additions and 99 deletions
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1
drawing.scad
View file

@ -167,6 +167,7 @@ module stroke(
trim, trim1, trim2,
convexity=10, hull=true
) {
no_children($children);
module setcolor(clr) {
if (clr==undef) {
children();

9
mutators.scad
View file

@ -1037,6 +1037,8 @@ module HSV(h,s=1,v=1,a=1) color(HSV(h,s,v),a) children();
// list = The list of items to iterate through.
// stride = Consecutive colors stride around the color wheel divided into this many parts.
// maxhues = max number of hues to use (to prevent lots of indistinguishable hues)
// shuffle = if true then shuffle the hues in a random order. Default: false
// seed = seed to use for shuffle
// Side Effects:
// Sets the color to progressive values along the ROYGBIV spectrum for each item.
// Sets `$idx` to the index of the current item in `list` that we want to show.
@ -1046,14 +1048,13 @@ module HSV(h,s=1,v=1,a=1) color(HSV(h,s,v),a) children();
// Example(2D):
// rgn = [circle(d=45,$fn=3), circle(d=75,$fn=4), circle(d=50)];
// rainbow(rgn) stroke($item, closed=true);
module rainbow(list, stride=1, maxhues)
module rainbow(list, stride=1, maxhues, shuffle=false, seed)
{
ll = len(list);
maxhues = first_defined([maxhues,ll]);
huestep = 360 / maxhues;
hues = [for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)];
echo(hues=hues);
s = [for (i=[0:1:ll-1]) [.5,.7,1][posmod(i,3)]];
huelist = [for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)];
hues = shuffle ? shuffle(huelist, seed=seed) : huelist;
for($idx=idx(list)) {
$item = list[$idx];
HSV(h=hues[$idx]) children();

2
paths.scad
View file

@ -1170,7 +1170,7 @@ function _assemble_a_path_from_fragments(fragments, rightmost=true, startfrag=0,
/// fragments = List of paths to be assembled into complete polygons.
/// eps = The epsilon error value to determine whether two points coincide. Default: `EPSILON` (1e-9)
function _assemble_path_fragments(fragments, eps=EPSILON, _finished=[]) =
len(fragments)==0? _finished :
len(fragments)==0? _finished :
let(
minxidx = min_index([
for (frag=fragments) min(subindex(frag,0))

271
regions.scad
View file

@ -74,13 +74,22 @@ function check_and_fix_path(path, valid_dim=undef, closed=false, name="path") =
// Function: sanitize_region()
// Usage:
// r_fixed = sanitize_region(r);
// r_fixed = sanitize_region(r, [nonzero], [eps]);
// Description:
// Takes a malformed input region that contains self-intersecting polygons or polygons
// that cross each other and converts it into a properly defined region without
// these defects.
function sanitize_region(r) = exclusive_or([for(poly=r) each polygon_parts(poly)]);
// Arguments:
// r = region to sanitize
// nonzero = set to true to use nonzero rule for polygon membership. Default: false
// eps = Epsilon for geometric comparisons. Default: `EPSILON` (1e-9)
// Examples:
//
function sanitize_region(r,nonzero=false,eps=EPSILON) =
assert(is_region(r))
exclusive_or(
[for(poly=r) each polygon_parts(poly,nonzero,eps)],
eps=eps);
// Module: region()
@ -100,12 +109,12 @@ function sanitize_region(r) = exclusive_or([for(poly=r) each polygon_parts(poly)
// region(rgn);
module region(r)
{
no_children($children);
r = is_path(r) ? [r] : r;
points = flatten(r);
paths = [
for (i=[0:1:len(r)-1]) let(
start = default(sum([for (j=[0:1:i-1]) len(r[j])]),0)
) [for (k=[0:1:len(r[i])-1]) start+k]
];
lengths = [for(path=r) len(path)];
starts = [0,each cumsum(lengths)];
paths = [for(i=idx(r)) count(s=starts[i], n=lengths[i])];
polygon(points=points, paths=paths);
}
@ -143,12 +152,13 @@ function point_in_region(point, region, eps=EPSILON, _i=0, _cnt=0) =
// region = region to check
// eps = tolerance for geometric omparisons. Default: `EPSILON` = 1e-9
function is_region_simple(region, eps=EPSILON) =
[for(p=region) if (!is_path_simple(p,closed=true,eps)) 1] == []
&&
[for(p=region) if (!is_path_simple(p,closed=true,eps)) 1] == [];
/* &&
[for(i=[0:1:len(region)-2])
if (_path_region_intersections(region[i], list_tail(region,i+1), eps=eps) != []) 1
] ==[];
*/
// Function: are_regions_equal()
// Usage:
@ -221,10 +231,11 @@ function old_path_region_intersections(path, region, closed=true, eps=EPSILON) =
// find the intersection points of a path and the polygons of a
// region; only crossing intersections are caught, no collinear
// intersection is returned.
function _path_region_intersections(path, region, closed=true, eps=EPSILON) =
function _path_region_intersections(path, region, closed=true, eps=EPSILON, extra=[]) =
let( path = closed ? close_path(path,eps=eps) : path )
_sort_vectors(
[for(si = [0:1:len(path)-2]) let(
[ each extra,
for(si = [0:1:len(path)-2]) let(
a1 = path[si],
a2 = path[si+1],
nrm = norm(a1-a2)
@ -278,11 +289,11 @@ function _path_region_intersections(path, region, closed=true, eps=EPSILON) =
// paths = split_path_at_region_crossings(path, region);
// color("#aaa") region(region);
// rainbow(paths) stroke($item, closed=false, width=2);
function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON) =
function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON, extra=[]) =
let(
path = deduplicate(path, eps=eps),
region = [for (path=region) deduplicate(path, eps=eps)],
xings = _path_region_intersections(path, region, closed=closed, eps=eps),
xings = _path_region_intersections(path, region, closed=closed, eps=eps, extra=extra),
crossings = deduplicate(
concat([[0,0]], xings, [[len(path)-1,1]]),
eps=eps
@ -317,35 +328,90 @@ function split_path_at_region_crossings(path, region, closed=true, eps=EPSILON)
// right(5,square(i,center=true))];
// region_list = region_parts(R);
// rainbow(region_list) region($item);
function region_parts(region) =
let(
paths = sort(idx=0, [
for(i = idx(region)) let(
cnt = sum([
for (j = idx(region)) if (i!=j)
let(pt = lerp(region[i][0],region[i][1],0.5))
point_in_polygon(pt, region[j]) >=0 ? 1 : 0
])
) [cnt, region[i]]
]),
outs = [
for (candout = paths) let(
lev = candout[0],
parent = candout[1]
) if (lev % 2 == 0) [
clockwise_polygon(parent),
for (path = paths) if (
path[0] == lev+1 &&
point_in_polygon(
lerp(path[1][0], path[1][1], 0.5),
parent
) >= 0
) ccw_polygon(path[1])
]
]
) outs;
function old_region_parts(region) =
let(
paths = sort(idx=0,
[
for(i = idx(region))
let(
pt = mean([region[i][0],region[i][1]]),
cnt = sum([for (j = idx(region))
if (i!=j && point_in_polygon(pt, region[j]) >=0) 1])
)
[cnt, region[i]]
]),
outs = [
for (candout = paths)
let(
lev = candout[0],
parent = candout[1]
)
if (lev % 2 == 0)
[
clockwise_polygon(parent),
for (path = paths)
if (
path[0] == lev+1
&& point_in_polygon(
lerp(path[1][0], path[1][1], 0.5)
,parent
) >= 0
)
ccw_polygon(path[1])
]
]
)
outs;
function inside(region, ins=[]) =
let(
i = len(ins)
)
i==len(region) ? ins
:
let(
pt=mean([region[i][0],region[i][1]])
)
i==0 ? inside(region,
[[0,
for(j=[1:1:len(region)-1]) point_in_polygon(pt,region[j])>=0 ? 1 : 0]])
: let(
prev = [for(j=[0:i-1]) point_in_polygon(pt,region[j])>=0 ? 1 : 0],
check = sum(bselect(ins,prev),repeat(0,len(region))),
next = [for(j=[i+1:1:len(region)-1]) check[j]>0 ? 1 : point_in_polygon(pt,region[j])>=0 ? 1 : 0]
)
inside(region, [
each ins,
[each prev, 0, each next]
]);
function region_parts(region) =
let(
inside = [for(i=idx(region))
let(pt = mean([region[i][0], region[i][1]]))
[for(j=idx(region)) i==j ? 0
: point_in_polygon(pt,region[j]) >=0 ? 1 : 0]
],
level = inside*repeat(1,len(region))
)
[ for(i=idx(region))
if(level[i]%2==0)
let(
possible_children = search([level[i]+1],level,0)[0],
keep=search([1], select(inside,possible_children), 0, i)[0]
)
[
clockwise_polygon(region[i]),
for(good=keep)
ccw_polygon(region[possible_children[good]])
]
];
// Section: Region Extrusion and VNFs
@ -647,7 +713,18 @@ function _point_dist(path,pathseg_unit,pathseg_len,pt) =
]);
function _offset_region(
function _offset_region(region, r, delta, chamfer, check_valid, quality,closed,return_faces,firstface_index,flip_faces) =
let(
//dg= echo(region=region),
reglist = [for(R=region_parts(region)) is_path(R) ? [R] : R],
//fdsa= echo(reglist),
ofsregs = [for(R=reglist)
[for(i=idx(R)) offset(R[i], r=u_mul(i>0?-1:1,r), delta=u_mul(i>0?-1:1,delta), chamfer=chamfer, check_valid=check_valid,
quality=quality,closed=true)]]
)
union(ofsregs);
function d_offset_region(
paths, r, delta, chamfer, closed,
check_valid, quality,
return_faces, firstface_index,
@ -785,7 +862,10 @@ function offset(
quality=1, return_faces=false, firstface_index=0,
flip_faces=false
) =
is_region(path)? (
is_region(path)? _offset_region(path,r=r,delta=delta,chamfer=chamfer,quality=quality,check_valid=check_valid)
/*
(
assert(!return_faces, "return_faces not supported for regions.")
let(
path = [for (p=path) clockwise_polygon(p)],
@ -805,7 +885,8 @@ function offset(
return_faces=return_faces, firstface_index=firstface_index,
flip_faces=flip_faces
)
) : let(rcount = num_defined([r,delta]))
)*/
: let(rcount = num_defined([r,delta]))
assert(rcount==1,"Must define exactly one of 'delta' and 'r'")
let(
chamfer = is_def(r) ? false : chamfer,
@ -904,37 +985,40 @@ function offset(
/// "S" - the subpath is on the region's border and the polygon and region are on the same side of the subpath
/// "U" - the subpath is on the region's border and the polygon and region meet at the subpath (from opposite sides)
/// The return has the form of a list with entries [TAG, SUBPATH]
function _tag_subpaths(path, region, eps=EPSILON) =
function _tag_subpaths(region1, region2, eps=EPSILON, SUtags=true) =
// We have to compute common vertices between paths in the region because
// they can be places where the path must be cut, even though they aren't
// found my the split_path function.
let(
subpaths = split_path_at_region_crossings(path, region, eps=eps),
tagged = [
for (subpath = subpaths)
points = flatten(region1),
tree = len(points)>0 ? vector_search_tree(points): undef
)
[for(path=region1)
let(
self_int = is_undef(tree)?[]:[for(i=idx(path)) if (len(vector_search(path[i], eps, tree))>1) [i,0]],
subpaths = split_path_at_region_crossings(path, region2, eps=eps, extra=self_int)
)
for (subpath = subpaths)
let(
midpt = mean([subpath[0], subpath[1]]),
rel = point_in_region(midpt,region2,eps=eps)
)
if(rel<0) ["O", subpath]
else if (rel>0) ["I", subpath]
else if (SUtags)
let(
midpt = mean([subpath[0], subpath[1]]),
rel = point_in_region(midpt,region,eps=eps)
)
rel<0? ["O", subpath]
: rel>0? ["I", subpath]
: let(
vec = unit(subpath[1]-subpath[0]),
perp = rot(90, planar=true, p=vec),
sidept = midpt + perp*0.01,
rel1 = point_in_polygon(sidept,path,eps=eps)>0,
rel2 = point_in_region(sidept,region,eps=eps)>0
sidept = midpt + 0.01*line_normal(subpath[0],subpath[1]),
rel1 = point_in_region(sidept,region1,eps=eps)>0,
rel2 = point_in_region(sidept,region2,eps=eps)>0
)
rel1==rel2? ["S", subpath] : ["U", subpath]
]
) tagged;
function _tag_region_subpaths(region1, region2, eps=EPSILON) =
[for (path=region1) each _tag_subpaths(path, region2, eps=eps)];
];
function _tagged_region(region1,region2,keep1,keep2,eps=EPSILON) =
let(
tagged1 = _tag_region_subpaths(region1, region2, eps=eps),
tagged2 = _tag_region_subpaths(region2, region1, eps=eps),
tagged1 = _tag_subpaths(region1, region2, eps=eps),
tagged2 = _tag_subpaths(region2, region1, eps=eps),
tagged = [
for (tagpath = tagged1) if (in_list(tagpath[0], keep1)) tagpath[1],
for (tagpath = tagged2) if (in_list(tagpath[0], keep2)) tagpath[1]
@ -963,14 +1047,14 @@ function _tagged_region(region1,region2,keep1,keep2,eps=EPSILON) =
// color("green") region(union(shape1,shape2));
function union(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? union(concat([regions],[b],c==undef?[]:[c]), eps=eps) :
len(regions)<=1? regions[0] :
union(
let(regions=[for (r=regions) quant(is_path(r)? [r] : r, 1/65536)])
concat(
[_tagged_region(regions[0],regions[1],["O","S"],["O"], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]]
),
eps=eps
len(regions)==0? [] :
len(regions)==1? regions[0] :
let(regions=[for (r=regions) quant(is_path(r)? [r] : r, 1/65536)])
union([
_tagged_region(regions[0],regions[1],["O","S"],["O"], eps=eps),
for (i=[2:1:len(regions)-1]) regions[i]
],
eps=eps
);
@ -996,13 +1080,13 @@ function difference(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? difference(concat([regions],[b],c==undef?[]:[c]), eps=eps) :
len(regions)==0? [] :
len(regions)==1? regions[0] :
difference(
let(regions=[for (r=regions) quant(is_path(r)? [r] : r, 1/65536)])
concat(
[_tagged_region(regions[0],regions[1],["O","U"],["I"], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]]
),
eps=eps
regions[0]==[] ? [] :
let(regions=[for (r=regions) quant(is_path(r)? [r] : r, 1/65536)])
difference([
_tagged_region(regions[0],regions[1],["O","U"],["I"], eps=eps),
for (i=[2:1:len(regions)-1]) regions[i]
],
eps=eps
);
@ -1024,9 +1108,11 @@ function difference(regions=[],b=undef,c=undef,eps=EPSILON) =
// for (shape = [shape1,shape2]) color("red") stroke(shape, width=0.5, closed=true);
// color("green") region(intersection(shape1,shape2));
function intersection(regions=[],b=undef,c=undef,eps=EPSILON) =
// echo(regions=regions)
b!=undef? intersection(concat([regions],[b],c==undef?[]:[c]),eps=eps)
: len(regions)==0 ? []
: len(regions)==1? regions[0]
: regions[0]==[] || regions[1]==[] ? []
: let(regions=[for (r=regions) quant(is_path(r)? [r] : r, 1/65536)])
intersection([
_tagged_region(regions[0],regions[1],["I","S"],["I"],eps=eps),
@ -1063,17 +1149,14 @@ function intersection(regions=[],b=undef,c=undef,eps=EPSILON) =
// }
function exclusive_or(regions=[],b=undef,c=undef,eps=EPSILON) =
b!=undef? exclusive_or([regions, b, if(is_def(c)) c],eps=eps) :
len(regions)<=1? regions[0] :
exclusive_or(
let(regions=[for (r=regions) is_path(r)? [r] : r])
concat(
[union([
difference([regions[0],regions[1]], eps=eps),
difference([regions[1],regions[0]], eps=eps)
], eps=eps)],
[for (i=[2:1:len(regions)-1]) regions[i]]
),
eps=eps
len(regions)==0? [] :
len(regions)==1? regions[0] :
let(regions=[for (r=regions) is_path(r)? [r] : r])
exclusive_or([
_tagged_region(regions[0],regions[1],["I","O"],["I","O"],eps=eps),
for (i=[2:1:len(regions)-1]) regions[i]
],
eps=eps
);

30
tests/test_regions.scad
View file

@ -10,3 +10,33 @@ module test_is_region() {
assert(!is_region("foo"));
}
test_is_region();
module test_union() {
R1 = [square(10,center=true), square(9,center=true)];
R2 = [square(9,center=true)];
assert(are_regions_equal(union(R1,R2), [square(10,center=true)]));
}
test_union();
module test_intersection() {
R1 = [square(10,center=true), square(9,center=true)];
R6 = [square(9.5,center=true), square(9,center=true)];
assert(are_regions_equal(intersection(R6,R1), R6));
assert(are_regions_equal(intersection(R1,R6), R6));
}
test_intersection();
module test_difference() {
R5 = [square(10,center=true), square(9,center=true),square(4,center=true)];
R4 = [square(9,center=true), square(3,center=true)];
assert(are_regions_equal(difference(R5,R4),
[square(10,center=true), square(9, center=true), square(3,center=true)]));
}
test_difference();