| Article ID: | iaor20081418 |
| Country: | Cuba |
| Volume: | 27 |
| Issue: | 3 |
| Start Page Number: | 261 |
| End Page Number: | 275 |
| Publication Date: | Sep 2006 |
| Journal: | Revista de Investigacin Operacional |
| Authors: | Hernndez-Mederos Victoria, Madrigal Jorge Estrada-Sarlabous Dionne Len |
In this paper we obtain a necessary and sufficient condition for local injectivity of a 2D triangular cubic Bezier function. The condition can be easily checked since it reduces the analysis of the local injectivity to determine if a quartic plane algebraic curve cuts a triangle. An original algorithm to test if a plane algebraic curve of any degree passes through a triangle was developed to verify the previous condition. The algorithm is based on subdivision and range analysis for a triangular region. Additionally, we obtain a sufficient condition for local injectivity of a 2D triangular cubic Bezier function.