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Posted 29 June 2009 - 02:45 PM
Posted 29 June 2009 - 04:45 PM
Posted 29 June 2009 - 05:03 PM
Posted 29 June 2009 - 05:23 PM
Quote:
Original post by Emergent
Can't always be done. Not all quads can be transformed by an affine transformation to a unit square. In fact, only parallelograms can...
Of course, here I'm assuming you want to map a 2d quad to a 2d square. Do you actually want to infer perspective or something? Then you have more degrees of freedom...
Posted 29 June 2009 - 05:27 PM
Quote:
Original post by Dave Eberly
The perspective mapping between two *convex* quadrilaterals is described in this 1-page document: Perspective Mapping.
Posted 30 June 2009 - 01:19 AM
Posted 30 June 2009 - 03:09 AM
Quote:
Original post by Kuroyume0161 Quote:
Original post by Dave Eberly
The perspective mapping between two *convex* quadrilaterals is described in this 1-page document: Perspective Mapping.
How would this relate to matrix transformation? As I stated, this must go both ways with an inversion of the quad-to-unitsquare after some processing.
Thanks!
Posted 30 June 2009 - 03:12 PM
Quote:
Original post by Kuroyume0161
You assume correctly. :) A 3D quadrangle polygon has been transformed to the world center and 'placed' on the X-Z plane so that its y-values are 0.0f (essentially a 2D quadrangle). Now I want to matrix transform it to a unit square (on the same plane)
(u1,v1)------(u2,v2)Then to all points in triangle A you can perform the affine transformation
| . B |
| . |
| A . |
(u3, v3)-----(u4,v4)
Posted 30 June 2009 - 03:26 PM
Posted 30 June 2009 - 04:56 PM
Posted 01 July 2009 - 05:23 PM
Quote:
Original post by Emergent
Apologies... I wasn't familiar enough with homographies, so my whole previous post may be pointless. alvaro: I haven't thought about this much; can a homography map between any two quads in R^2? Are there any restrictions on the types of quads that can be mapped to each other?
Posted 01 July 2009 - 05:55 PM
Posted 02 July 2009 - 02:15 AM
Quote:
Original post by alvaro
Hmmm... It's been too long since I was comfortable with this subject. You can convert any projective reference into any other projective reference. Projective references in the plane are sets of 4 points such that any 3 are not collinear. It might be the case that the homography will send a line that intersects the quadrilateral to infinity, which might not satisfy your idea of "mapping between two quads". My intuition tells me this would happen when you try to map a convex quad to a non-convex quad, but I am not completely sure.
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