koolish@bbn.COM (Richard Koolish) (12/24/87)
References for polygon clipping:
"Reentrant Polygon Clipping" by Ivan Sutherland and Gary Hodgman
CACM, Vol 17, No 1, January 1974
"An Analysis and Algorithm for Polygon Clipping" by You-Dong Liang
and Brian Barsky, CACM Vol 26, No 11, November 1983neiderer@amsaa-seer.brl.mil (Andrew Neiderer ) (04/23/91)
Will clipping a triangle to a rectangular region always result in a convex polygon (or no polygon at all) ? This seems reasonable to me, but I just want to make sure so that I can restrict scan- conversion to convex polygons. Thanks.
lambert@silver.cs.umanitoba.ca (Tim Lambert) (04/24/91)
>>>>> On 23 Apr 91 10:24:09 GMT, neiderer@amsaa-seer.brl.mil (Andrew Neiderer ) said: > Will clipping a triangle to a rectangular region always result > in a convex polygon (or no polygon at all) ? Yes, because the intersection of two convex sets is convex.
dfr@usna.NAVY.MIL (Prof. David F. Rogers) (04/25/91)
In article <LAMBERT.91Apr23232842@silver.cs.umanitoba.ca> lambert@silver.cs.umanitoba.ca (Tim Lambert) writes: >>>>>> On 23 Apr 91 10:24:09 GMT, neiderer@amsaa-seer.brl.mil (Andrew Neiderer ) said: > >> Will clipping a triangle to a rectangular region always result >> in a convex polygon (or no polygon at all) ? > >Yes, because the intersection of two convex sets is convex. No, it depends on whether you do an INTERIOR or an EXTERIOR clip. If you do and EXTERIOR clip you can get a concave polygon. Dave Rogers
markv@pixar.com (Mark VandeWettering) (05/08/91)
>>> Will clipping a triangle to a rectangular region always result >>> in a convex polygon (or no polygon at all) ? >>Yes, because the intersection of two convex sets is convex. >No, it depends on whether you do an INTERIOR or an EXTERIOR clip. >If you do and EXTERIOR clip you can get a concave polygon. Well, we generally do mean interior clips when we speak about clipping to a rectangular region. And anyway, the exterior of a rectangle is not a convex set, so the original statement is correct as stands. mark
dfr@usna.NAVY.MIL (Prof. David F. Rogers) (05/08/91)
In article <1991May7.181010.22047@pixar.com> markv@pixar.com (Mark VandeWettering) writes:
!!!! Will clipping a triangle to a rectangular region always result
!!!! in a convex polygon (or no polygon at all) ?
!
!!!Yes, because the intersection of two convex sets is convex.
!
!!No, it depends on whether you do an INTERIOR or an EXTERIOR clip.
!!If you do and EXTERIOR clip you can get a concave polygon.
!
!Well, we generally do mean interior clips when we speak about clipping
!to a rectangular region. And anyway, the exterior of a rectangle is
!not a convex set, so the original statement is correct as stands.
!
!mark
No, not necessarily, a simple example is any windowing system.
The intersection of two convex sets is convex IN THE CONTEXT OF
A BOOLIAN OPERATION. In the context of `clipping' this is not
true since clipping CAN be either interior or exterior.
Dave Rogerslambert@silver.cs.umanitoba.ca (Tim Lambert) (05/09/91)
AN = neiderer@amsaa-seer.brl.mil (Andrew Neiderer) TL = lambert@cs.umanitoba.ca (Tim Lambert) DR = dfr@usna.NAVY.MIL (Prof. David F. Rogers) MV = markv@pixar.com (Mark VandeWettering) AN> Will clipping a triangle to a rectangular region always result AN> a convex polygon (or no polygon at all) ? TL> Yes, because the intersection of two convex sets is convex. DR> No, it depends on whether you do an INTERIOR or an EXTERIOR clip. DR> If you do and EXTERIOR clip you can get a concave polygon. MV> Well, we generally do mean interior clips when we speak about clipping MV> to a rectangular region. And anyway, the exterior of a rectangle is MV> not a convex set, so the original statement is correct as stands. DR> No, not necessarily, a simple example is any windowing system. OK. Consider X. Clipping regions are lists of (non-intersecting) rectangles. No exterior clipping. (Of course, when you have one window partly obscuring another, you are really doing an exterior clip against the obscuring window, but that is not the way X looks at it.) I understand "clipping" to mean interior clipping and "exterior clipping to R" to mean clipping to the exterior of R. DR> The intersection of two convex sets is convex IN THE CONTEXT OF DR> A BOOLIAN OPERATION. In the context of `clipping' this is not DR> true since clipping CAN be either interior or exterior. I don't understand. Are you saying that in the context of clipping `intersection' sometimes means `difference'? Tim