Numerical Calculations in Clifford Algebra

19Perspective Projection

Often, illustrations of simple three‐dimensional objects such as a cube or tetrahedron can be drawn in projection onto two dimensions by eye, either without attempting to incorporate the effects of perspective, or including those effects in an artistic manner, not resorting to the calculation of individual coordinates. As the objects become more complicated, it becomes harder to make them appear visually correct. Perspective projection is used here as a simple example of the application of the Clifford numerical suite for performing a geometric operation.

19.1 Theory

Perspective projection can be interpreted as the shadows of objects cast by the sun onto a plane. In Figure 19.1, the sun stands vertically above the point in the horizontal plane (small rectangle). Rays from the sun pass through points in three‐dimensional space casting shadows on the tilted shadow‐plane (large rectangle). The shadow‐plane is tilted so that its normal is pointing towards ...