It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator.
|Conference||International Conference on Mathematical Methods for Curves and Surfaces|
|Period||03/07/1997 → 08/07/1997|
|Sponsor||SINTEF, The Research Council of Norway, University of Oslo|
|Series||INNOVATIONS IN APPLIED MATHEMATICS|