Graphics Gems V (IBM Version)

Introduction to Modeling and Transformation

The gems in this section describe algebraic models and their transformations. In most cases a linear algebra underlies the derivations, supporting a natural extension to higher dimensions, as with gems II.4 and II.7 of the previous section.

In the first gem ( III.1), Alciatore and Miranda apply the method of least squares to fit a line to a set of points. What is unique is that perpendicular distance is chosen to create a true isotropic fit, not a conventional fit by abscissa. Hill and Roberts ( III.2) review modeling methods related to the marching cubes method in which slope discontinuities and their ambiguities arise. These occur at the adjoining boundaries between the discrete cells that collectively ...