Unformatted text preview: aphics Lecture 1: Slide 38! General Homogenous Coordinates General homogenous coordinates !
• In most cases the last ordinate will be 1 ! In most cases the last ordinate will be 1
• But in general it is a scale factor. !
But in general it is a scale factor.
px py pz
(px , py , pz , s) ()
s, s, s Graphics Lecture 1: Slide 39! 32 / 47 Afﬁne transformations !
• Afﬁne transformations are those that preserve parallel
• Most transformations we require are afﬁne, the most
important being: !
– Translation! • Other more complex transforms can be built from these. !
• An example of a non-afﬁne transformation: !
– Perspective projection (parallels not preserved). ! Graphics Lecture 1: Slide 40! Translation with with a matrix !
Translation a matrix
• We can apply a general translation by (tx, ty, tz) to the
points of a scene by using the following matrix
multiplication ! We c...
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This document was uploaded on 03/26/2014.
- Spring '14