OpenGL® Programming Guide: The Official Guide to Learning OpenGL®, Version 4.5 with SPIR-V, Ninth Edition

Appendix E. Homogeneous Coordinates and Transformation Matrices

This appendix presents a brief discussion of homogeneous coordinates, stated in a different way from Chapter 5, “Viewing Transformations, Culling, Clipping, and Feedback.” It also summarizes the forms of the transformation matrices used for rotation, scaling, translation, perspective, and orthographic projection discussed in detail in Chapter 5. For a more detailed discussion on projection, see The Real Projective Plane, by H. S. M. Coxeter, 3rd ed. (Springer, 1992). To see how to use the library accompanying this book, see Chapter 5.

In the discussion that follows, the term homogeneous coordinates always means three-dimensional homogeneous coordinates, although projective geometries ...