ON LOCAL INJECTIVITY OF 2D TRIANGULAR CUBIC BEZIER FUNCTIONS

Abstract

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.