Practical Algorithms for 3D Computer Graphics, 2nd Edition

10.11. Texture coordinate generation 445

Note that the planar mapping described here uses th r ee p oints to define the

location of the map and therefore the opposite sid es are always par allel even

though the angle between P

α

and P

β

does not have to be 90

◦

.

It would be possible to define a map using four points, one at each corner

of the rectangle but it is considerably more complex to determine the mapping

coordinates from such a map because the opposite sides would not necessar-

ily be parallel. Haines [33] gives exp r es s ion s (without derivation) for a convex

quadrilateral mapping that could form the basis of the necessary procedure.

10.11.2 Cylindrical ...