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is_valid_region detects vertex-edge contact

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This commit is contained in:
Adrian Mariano 2021-11-05 19:31:48 -04:00
parent 379f70a6e0
commit 924421fa22
2 changed files with 114 additions and 40 deletions
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4
paths.scad
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@ -522,13 +522,15 @@ function is_path_simple(path, closed, eps=EPSILON) =
let(closed=default(closed,false))
assert(is_path(path, 2),"Must give a 2D path")
assert(is_bool(closed))
// check for path reversals
[for(i=[0:1:len(path)-(closed?2:3)])
let(v1=path[i+1]-path[i],
v2=select(path,i+2)-path[i+1],
normv1 = norm(v1),
normv2 = norm(v2)
)
if (approx(v1*v2/normv1/normv2,-1)) 1] == []
if (approx(v1*v2/normv1/normv2,-1)) 1
] == []
&&
_path_self_intersections(path,closed=closed,eps=eps) == [];

150
regions.scad
View file

@ -14,17 +14,25 @@
// Section: Regions
// A region is a list of non-crossing simple polygons. Simple polygons are those without self intersections,
// and the polygons of a region can touch at corners, but their segments should not
// cross each other. The actual geometry of the region is defined by XORing together
// A region is a list of polygons meeting these conditions:
// .
// - Every polygon on the list is simpel, meaning it does not intersect itself
// - Two polygons on the list do not cross each other
// - A vertex of one polygon never meets the edge of another one except at a vertex
// .
// Note that this means vertex-vertex touching between two polygons is acceptable
// to define a region. Note, however, that regions with vertex-vertex contact usually
// cannot be rendered with CGAL.
// .
// The actual geometry of the region is defined by XORing together
// all of the polygons on the list. This may sound obscure, but it simply means that nested
// boundaries make rings in the obvious fashion, and non-nested shapes simply union together.
// Checking that the polygons on a list are simple and non-crossing can be a time consuming test,
// so it is not done automatically. It is your responsibility to ensure that your regions are
// Checking that a list of paths is a valid region, meaning that it satisfies all of the conditions
// above, can be a time consuming test, so it is not done automatically. It is your responsibility to ensure that your regions are
// compliant. You can construct regions by making a list of polygons, or by using
// boolean function operations such as union() or difference(), which all except paths, as
// well as regions, as their inputs. And if you must you
// can clean up an ill-formed region using make_region().
// boolean function operations such as union() or difference(), which all acccept paths, as
// well as regions, as their inputs. And if you must you can clean up an ill-formed region using make_region(),
// which will break up self-intersecting paths and paths that cross each other.
// Function: is_region()
@ -49,64 +57,128 @@ function is_region(x) = is_list(x) && is_path(x.x);
// Arguments:
// region = region to check
// eps = tolerance for geometric comparisons. Default: `EPSILON` = 1e-9
// Example(2D,noaxes): Two non-intersecting squares make a valid region:
// Example(2D,NoAxes): In all of the examples each path in the region appears in a different color. Two non-intersecting squares make a valid region.
// region = [square(10), right(11,square(8))];
// rainbow(region)stroke($item, width=.1,closed=true);
// back(12)text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,noaxes): Nested squares form a region
// rainbow(region)stroke($item, width=.2,closed=true);
// back(11)text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,NoAxes): Nested squares form a region
// region = [for(i=[3:2:10]) square(i,center=true)];
// rainbow(region)stroke($item, width=.1,closed=true);
// rainbow(region)stroke($item, width=.2,closed=true);
// back(6)text(is_valid_region(region) ? "region" : "non-region", size=2,halign="center");
// Example(2D,noaxes): Also a region:
// Example(2D,NoAxes): Also a region:
// region= [square(10,center=true), square(5,center=true), right(10,square(7))];
// rainbow(region)stroke($item, width=.1,closed=true);
// rainbow(region)stroke($item, width=.2,closed=true);
// back(8)text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,noaxes): The squares cross each other, so not a region
// Example(2D,NoAxes): The squares cross each other, so not a region
// object = [square(10), move([8,8], square(8))];
// rainbow(object)stroke($item, width=.1,closed=true);
// rainbow(object)stroke($item, width=.2,closed=true);
// back(17)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,noaxes): Not a region due to a self-intersecting (non-simple) hourglass path
// Example(2D,NoAxes): Not a region due to a self-intersecting (non-simple) hourglass path
// object = [move([-2,-2],square(14)), [[0,0],[10,0],[0,10],[10,10]]];
// rainbow(object)stroke($item, width=.1,closed=true);
// rainbow(object)stroke($item, width=.2,closed=true);
// move([-1.5,13])text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,noaxes): Breaking hourglass in half fixes it. Now it's a region:
// Example(2D,NoAxes): Breaking hourglass in half fixes it. Now it's a region:
// region = [move([-2,-2],square(14)), [[0,0],[10,0],[5,5]], [[5,5],[0,10],[10,10]]];
// rainbow(region)stroke($item, width=.1,closed=true);
// move([1,13])text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,noaxes): As with the "broken" hourglass, Touching at corners is OK. This is a region.
// rainbow(region)stroke($item, width=.2,closed=true);
// Example(2D,NoAxes): A single path corner touches an edge, so not a region:
// object = [[[-10,0], [-10,10], [20,10], [20,-20], [-10,-20],
// [-10,-10], [0,0], [10,-10], [10,0]]];
// rainbow(object)stroke($item, width=.3,closed=true);
// move([-4,12])text(is_valid_region(object) ? "region" : "non-region", size=3);
// Example(2D,NoAxes): Corners touch in the same path, so the path is not simple and the object is not a region.
// object = [[[0,0],[10,0],[10,10],[-10,10],[-10,0],[0,0],[-5,5],[5,5]]];
// rainbow(object)stroke($item, width=.3,closed=true);
// move([-10,12])text(is_valid_region(object) ? "region" : "non-region", size=3);
// Example(2D,NoAxes): The shape above as a valid region with two paths:
// region = [ [[0,0],[10,0],[10,10],[-10,10],[-10,0]],
// [[0,0],[5,5],[-5,5]] ];
// rainbow(region)stroke($item, width=.3,closed=true);
// move([-5.5,12])text(is_valid_region(region) ? "region" : "non-region", size=3);
// Example(2D,NoAxes): As with the "broken" hourglass, Touching at corners is OK. This is a region.
// region = [square(10), move([10,10], square(8))];
// rainbow(region)stroke($item, width=.1,closed=true);
// rainbow(region)stroke($item, width=.25,closed=true);
// back(12)text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,noaxes): A union is one way to fix the above example and get a region. (Note that union is run here on two simple paths, which are valid regions themselves and hence acceptable inputs to union.
// Example(2D,NoAxes): A union is one way to fix the above example and get a region. (Note that union is run here on two simple paths, which are valid regions themselves and hence acceptable inputs to union.
// region = union([square(10), move([8,8], square(8))]);
// rainbow(region)stroke($item, width=.1,closed=true);
// rainbow(region)stroke($item, width=.25,closed=true);
// back(12)text(is_valid_region(region) ? "region" : "non-region", size=2);
// Example(2D,noaxes): These two squares share part of an edge, hence not a region
// Example(2D,NoAxes): These two squares share part of an edge, hence not a region
// object = [square(10), move([10,2], square(7))];
// stroke(object[0], width=0.1,closed=true);
// color("red")dashed_stroke(object[1], width=0.1,closed=true);
// stroke(object[0], width=0.2,closed=true);
// color("red")dashed_stroke(object[1], width=0.25,closed=true);
// back(12)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,noaxes): These two squares share a full edge, hence not a region
// Example(2D,NoAxes): These two squares share a full edge, hence not a region
// object = [square(10), right(10, square(10))];
// stroke(object[0], width=0.1,closed=true);
// color("red")dashed_stroke(object[1], width=0.1,closed=true);
// stroke(object[0], width=0.2,closed=true);
// color("red")dashed_stroke(object[1], width=0.25,closed=true);
// back(12)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,noaxes): Sharing on edge on the inside, also not a regionn
// Example(2D,NoAxes): Sharing on edge on the inside, also not a regionn
// object = [square(10), [[0,0], [2,2],[2,8],[0,10]]];
// stroke(object[0], width=0.1,closed=true);
// color("red")dashed_stroke(object[1], width=0.1,closed=true);
// stroke(object[0], width=0.2,closed=true);
// color("red")dashed_stroke(object[1], width=0.25,closed=true);
// back(12)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,noaxes): Crossing at vertices is also bad
// Example(2D,NoAxes): Crossing at vertices is also bad
// object = [square(10), [[10,0],[0,10],[8,13],[13,8]]];
// rainbow(object)stroke($item, width=.1,closed=true);
// rainbow(object)stroke($item, width=.2,closed=true);
// back(14)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,NoAxes): One path touches another in the middle of an edge
// object = [square(10), [[10,5],[15,0],[15,10]]];
// rainbow(object)stroke($item, width=.2,closed=true);
// back(11)text(is_valid_region(object) ? "region" : "non-region", size=2);
// Example(2D,NoAxes): The path touches the side, but the side has a vertex at the contact point so this is a region
// poly1 = [ each square(30,center=true), [15,0]];
// poly2 = right(10,circle(5,$fn=4));
// poly3 = left(0,circle(5,$fn=4));
// poly4 = move([0,-8],square([10,3]));
// region = [poly1,poly2,poly3,poly4];
// rainbow(region)stroke($item, width=.25,closed=true);
// move([-5,16.5])text(is_valid_region(region) ? "region" : "non-region", size=3);
// color("black")move_copies(region[0]) circle(r=.4);
// Example(2D,NoAxes): The path touches the side, but not at a vertex so this is not a region
// poly1 = fwd(4,[ each square(30,center=true), [15,0]]);
// poly2 = right(10,circle(5,$fn=4));
// poly3 = left(0,circle(5,$fn=4));
// poly4 = move([0,-8],square([10,3]));
// object = [poly1,poly2,poly3,poly4];
// rainbow(object)stroke($item, width=.25,closed=true);
// move([-9,12.5])text(is_valid_region(object) ? "region" : "non-region", size=3);
// color("black")move_copies(object[0]) circle(r=.4);
// Example(2D,NoAxes): The inner path touches the middle of the edges, so not a region
// poly1 = square(20,center=true);
// poly2 = circle(10,$fn=8);
// object=[poly1,poly2];
// rainbow(object)stroke($item, width=.25,closed=true);
// move([-10,11.4])text(is_valid_region(object) ? "region" : "non-region", size=3);
// Example(2D,NoAxes): The above shape made into a region using difference():
// poly1 = square(20,center=true);
// poly2 = circle(10,$fn=8);
// region = difference(poly1,poly2);
// rainbow(region)stroke($item, width=.25,closed=true);
// move([-5,11.4])text(is_valid_region(region) ? "region" : "non-region", size=3);
function is_valid_region(region, eps=EPSILON) =
let(region=force_region(region))
assert(is_region(region), "Input is not a region")
// no short paths
[for(p=region) if (len(p)<3) 1] == []
&&
// all paths are simple
[for(p=region) if (!is_path_simple(p,closed=true,eps=eps)) 1] == []
&&
// paths do not cross each other
[for(i=[0:1:len(region)-2])
if (_polygon_crosses_region(list_tail(region,i+1),region[i], eps=eps)) 1] == [];
if (_polygon_crosses_region(list_tail(region,i+1),region[i], eps=eps)) 1] == []
&&
// one path doesn't touch another in the middle of an edge
[for(i=idx(region), j=idx(region))
if (i!=j) for(v=region[i], edge=pair(region[j],wrap=true))
let(
v1 = edge[1]-edge[0],
v0 = v - edge[0],
t = v0*v1/(v1*v1)
)
if (abs(cross(v0,v1))<eps*norm(v1) && t>eps && t<1-eps) 1
]==[];
// internal function:
@ -135,7 +207,7 @@ function _polygon_crosses_region(region, poly, eps=EPSILON) =
// We extend the notion of the simple path to regions: a simple region is entirely
// non-self-intersecting, meaning that it is formed from a list of simple polygons that
// don't intersect each other at all---not even with corner contact points.
// Regions with corner contact are valid but may fail CGA. Simple regions
// Regions with corner contact are valid but may fail CGAL. Simple regions
// should not create problems with CGAL.
// Arguments:
// region = region to check