Graphics Gems V (IBM Version)

IV.9

Linear Form Curves

Shoemake Ken,     University of Pennsylvania Philadelphia, Pennsylvania. E-mail address: [e-mail]

Introduction

Straight lines are simple curves: easy to understand, and easy to manipulate. A generalization, the multilinear form, underlies the common curves of computer graphics ( Ramshaw 1987, Barry and Goldman 1988). This gem uses multilinearity and symmetry to explain Lagrange polynomials, Bézier and B-spline curves, the de Casteljau and de Boor algorithms, and Catmull–Rom splines; and it unites all these in a single routine. Though space prevents it here, these methods can also be applied to other curves, to rectangular and triangular surface patches, and to geometric continuity.

Curves from ...