## Abstract

The de Casteljau algorithm for evaluating Bezier curves can be represented as a simple data-flow graph where nodes represent either control points or linear interpolation steps. By modifying this graph using an operation called 'pruning,' we generate new curve schemes called 'pruned Bezier curves' that retain many properties of Bezier curves, but have smaller data-flow graphs, and hence can be computed using fewer linear interpolation steps. Many properties of pruned Bezier curves can be determined simply by inspecting the shape of the data-flow graph. In particular, we show that if the frontier of the graph does not oscillate (in a certain easily determined way), then the corresponding curve scheme is variation diminishing.

Original language | English (US) |
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Pages (from-to) | 229-238 |

Number of pages | 10 |

Journal | Proceedings - Graphics Interface |

State | Published - May 1 1990 |

Event | Proceedings - Graphics Interface '90 - Halifax, NS, USA Duration: May 14 1990 → May 18 1990 |