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![]() ![]() ![]() ![]() ![]() Next: 2.10.1 Controlling the Viewport Up: 2 OpenGL Operation Previous: 2.9 Rectangles
2.10 Coordinate TransformationsVertices, normals, and texture coordinates are transformed before their coordinates are used to produce an image in the framebuffer. We begin with a description of how vertex coordinates are transformed and how this transformation is controlled. Figure 2.6 diagrams the sequence of transformations that are applied to vertices. The vertex coordinates that are presented to the GL are termed object coordinates. The model-view matrix is applied to these coordinates to yield eye coordinates. Then another matrix, called the projection matrix, is applied to eye coordinates to yield clip coordinates. A perspective division is carried out on clip coordinates to yield normalized device coordinates. A final viewport transformation is applied to convert these coordinates into window coordinates.
Object coordinates,
eye coordinates,
and clip coordinates are four-dimensional,
consisting of x, y, z, and w coordinates (in that order).
The model-view and perspective matrices are thus
If a vertex in object coordinates is given by
Similarly, if P is the projection matrix, then the vertex's clip coordinates are The vertex's normalized device coordinates are then
David Blythe Sat Mar 29 02:23:21 PST 1997
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