-Transforms - Transformations Transformations Bedich Bene...

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Transformations Bed ř ich Beneš, Ph.D. Purdue University Department of Computer Graphics © Bedrich Benes Transformations transformations are essential closely related to Cg programs (vp) the following should be a review of well-known things (is it?) © Bedrich Benes Homogenous coordinates We use homogenous coordinates in 3D A=[x,y,z,w] The relation between homogenous and Cartesian coordinates is [x,y,z]=[x/w,y/w,z/w] for w=0 the [x,y,z,w] corresponds to a vector (x,y,z) © Bedrich Benes Homogenous coordinates Advantages of using homog. coords: Linear transformations (scale, shear, translate, rotate) can be represented by matrices 4x4 Projective transformation can be represented by matrices 4x4
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Transformations Having matrix A of type 4x4 and a vertex v=[x,y,z,w] The vertex transformation is represented by the matrix multiplication v’= A v to transform a vertex only the matrix must be specified © Bedrich Benes Transformations Example: A corresponds to the translation by the vector (X T ,Y T ,Z T ) A = 1 0 0 X T 0 1 0 Y T 0 0 1 Z T 0 0 0 1 © Bedrich Benes Transformations One of the first things ever performed by hardware is matrix-to-vector multiplication Every vertex must pass a various stages of transformations
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This note was uploaded on 02/19/2012 for the course CGT 411 taught by Professor Staff during the Spring '08 term at Purdue.

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-Transforms - Transformations Transformations Bedich Bene...

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