Transforming Vertices
Vertex transformations (such as rotations, translations, scaling, and shearing) and projections (such as perspective and orthographic) can all be represented by applying an appropriate 4 × 4 matrix to the coordinates representing the vertex. If v represents a homogeneous vertex and M is a 4 × 4 transformation matrix, then Mv is the image of v under the transformation by M. (In computer-graphics applications, the transformations used are usually nonsingular—in other words, the matrix M can be inverted. This isn’t required, but some problems arise with singular matrices.)
After transformation, all transformed vertices are clipped so that x, y, and z are in the range [–w, w] (assuming w > 0). Note that this range corresponds ...
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