Shading by Quaternion Interpolation

Anders Hast

The purpose of this paper is to show that linear interpolation of quaternions can be used for true Phong shading and also for related techniques that use frames, like bump mapping and anisotropic shading. Quaternion interpolation for shading has not been proposed in literature and the reason might be that it turns out to be mostly of academic interest, and it will here be explained why. Furthermore some pros and cons of interpolation using quaternions will be discussed. The effect of using this approach is that the square root in the normalization process disappears. The square root is now implemented in modern graphics hardware in such way that it is very fast. However for other types of platforms, especially hand held devices, the square root is computationally expensive and any software algorithm that could produce true Phong shading without the square root might turn out to be useful. It will be shown that linear interpolation of quaternion could be useful for bump mapping as well. However, quaternion arithmetic operations are not implemented in modern graphics hardware, and are therefore not useful until this is done.