3
$\begingroup$

Bug persisting in 11.3


I found RegionMember quite useful in retrieving the condition for which a point $(x,y)$ belongs to a region. Thus, this command works:

RegionMember[Disk[{0, 0}, 3, {-\[Pi]/2, \[Pi]/4}]][{x, y}]

$$(x|y)\in \mathbb{R}\land x^2+y^2\leq 9\land \frac{x}{3}\geq 0\land -\frac{y}{3 \sqrt{2}}\geq -\frac{x}{3 \sqrt{2}}$$

However, it does not for this self-intersecting polygon:

RegionMember[Polygon[{{0, 0}, {1, 1}, {0, 1}, {1, 0}}]][{x, y}]

MMA returns

{}[{x, y}]

or

RegionMember[Polygon[{{0, 0}, {1, 1}, {0, 1}, {1, 0}}],{x, y}]

MMA returns the same:

RegionMember[Polygon[{{0, 0}, {1, 1}, {0, 1}, {1, 0}}], {x, y}]

Anyone could explain why RegionMember fails in this case. The region seems to be not complicated.

$\endgroup$
5
  • 2
    $\begingroup$ Looks like a bug to me. The documentation doesn't list any sort of restrictions, like self-intersections. Because it's not documented, then I would say it is not working as described. Particularly this: RegionMember[Polygon[{{0, 0}, {1, 1}, {0, 1}, {1, 0}}]] $\endgroup$
    – ktm
    Commented Jan 29, 2018 at 20:56
  • $\begingroup$ If we apply DiscretizeRegion to the polygon, then we get a region that works with RegionMember. $\endgroup$
    – LouisB
    Commented Jan 30, 2018 at 6:24
  • $\begingroup$ @LouisB what you propose does not work for me (MMA ver. 11.2). Further, why the need of discretizing the polygon and not the disk? $\endgroup$ Commented Jan 30, 2018 at 11:41
  • $\begingroup$ I have just contacted support for assistance $\endgroup$ Commented Jan 30, 2018 at 13:17
  • $\begingroup$ Perhaps RegionMember[RegionUnion@@Rationalize[Graphics`PolygonUtils`SimplePolygonPartition[Polygon[{{0,0},{1,1},{0,1},{1,0}}]]],{x,y}]. $\endgroup$
    – chyanog
    Commented Jun 17, 2018 at 7:33

1 Answer 1

2
$\begingroup$

The fact that the one-argument form returns an empty list is simply a bug.

For sufficiently complicated algorithm, it may be hard/impossible to return a useful answer. This true even of self-intersecting polygons, though this particular one is admittedly not that complicated. But then it should return unevaluated, rather than an empty list.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.