Lecture 1 - Projections and Transformations (slides)

# most transformations we require are afne the most

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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. Homogeneous Cartesian ! Homogeneous Cartesian 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 lines. ! •  Most transformations we require are afﬁne, the most important being: ! –  Scaling! –  Rotation! –  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.

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