[OpenJDK 2D-Dev] CubicCurve2D.solveCubic and containment/intersection bugs.

[Denis Lila]

> 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