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1Announcements Is your account working yet? Watch out for ^M and missing newlines Assignment 1 is due next Thursday at midnight Check the webpage and newsgroup for answers to Questions about the Assignment Questions on Assignment 1?TransformationsVectors, bases, and matricesTranslation, rotation, scaling Postscript ExamplesHomogeneous coordinates3D transformations3D rotationsTransforming normalsNonlinear deformationsVectors, bases, and matricesTranslation, rotation, scaling Postscript ExamplesHomogeneous coordinates3D transformations3D rotationsTransforming normalsNonlinear deformationsAngel, Chapter 42Uses of Transformations Modeling transformations build complex models by positioning simple components transform from object coordinates to world coordinates Viewing transformations placing the virtual camera in the world specifying transformation from world coordinates to camera coordinates Animation vary transformations over time to create motionWORLDOBJECTCAMERAGeneral TransformationsQ = T(P)for pointsV = R(u)

2D Cartesian point (x,y). –For 3-D graphics, the 4D projective space point (x,y,z,w) maps to the 3D point (x,y,z) in the same way. Homogeneous 2D Transformations The basic 2D transformations become Translate: Scale: Rotate: Any affine transformation can be expressed as a combination of these. We can combine homogeneous transforms by ...

  Transformation, 2d transformations

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