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Mathematics for 3D Game Programming and Computer Graphics, Third Edition by Eric Lengyel

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Chapter 4. Transforms

Throughout any 3D graphics engine architecture, it is often necessary to transform a set of vectors from one coordinate space to another. For instance, vertex coordinates for a model may be stored in object space, but need to be transformed to camera space before the model can be rendered. In this chapter, we concern ourselves with linear transformations among different Cartesian coordinate frames. Such transformations include simple scales and translations, as well as arbitrary rotations.

Linear Transformations

Suppose that we have established a 3D coordinate system C consisting of an origin and three coordinate axes, in which a point P has the coordinates 〈x, y, z〉. The values x, y, and z can be thought of as the distances ...

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