> but the distinction does matter in > contains(), where we also use the word "interior".
Actually, scratch that - I can't really think of an example where the topological interior of the rectangle is contained in the topological interior of the curve but there is a point inside the rectangle that is not inside the curve (using the definition of "inside" in awt.Shape). ----- Original Message ----- > Hi Jim. > > > So, if you don't equate our "inside" term with topological > > "interior" > > then there is no conflict with the fact that both fields use the > > term > > boundary (and I think both use them compatibly). > > Well, I never really confused our use of "inside" with the topological > "interior". I think "inside", in our case, is very clearly defined in > awt.Shape. My problem was because we actually use the word "interior" > in > some methods' documentation (like intersects(double, > double,double,double)). > So I wasn't sure if "interior" there was a synonym for "inside" as > defined > in awt.Shape or whether it meant the same thing as in topology. They > may > actually be equivalent in the case of intersects() (but even so, we > should > be consistent with our wording), > > Regards, > Denis. > > ----- Original Message ----- > > Hi Denis, > > > > On 1/24/2011 3:41 PM, Denis Lila wrote: > > >> Perhaps the problem is less with the word "boundary" than it > > >> is with confusing our use of the word inside to describe the > > >> concept of filling and containment with the topological concept > > >> that a set has an interior in addition to (and mostly separate > > >> from) > > >> its boundary? > > > > > > That was exactly the problem. We classify every point as either > > > inside > > > or outside, and I'm used to the interior, exterior, and boundary > > > being > > > disjoint. > > > > Right, my point was that the problem here isn't that we use the word > > boundary, since when we use it we do acknowledge that there are > > points > > "on" the boundary. The problem is that our definition of "inside" is > > not similar to the topological definition of "interior". > > > > Topology has interior, boundary, and exterior as disjoint sets. > > > > Our definitions have inside and outside as disjoint sets, and we use > > the > > word boundary only to describe how to determine which points are > > divided > > into inside and outside - and I think our definition of boundary is > > compatible with the topological concept. It's just that when we > > refer > > to "inside" it may contain some points on the boundary, unlike the > > topological "interior" which would not. > > > > > > > Our "inside" is the topological "interior" unioned with the set of > > points in/on the topological "boundary" that satisfy the "interior > > is > > below or to the right" property. > > > > Inside == Interior + ~half of Boundary > > Outside == Exterior + ~half of Boundary > > > > Interior+Boundary+Exterior == whole plane > > No 2 of Interior, Boundary, or Exterior intersect > > > > Inside+Outside == whole plane > > Inside does not intersect Outside > > > > Inside is a superset of Interior > > Outside is a superset of Exterior > > Both Inside and Outside intersect Boundary > > > > ...jim
