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

[Denis Lila]

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), but the distinction does matter in
contains(), where we also use the word "interior".

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