On local injectivity of 2D triangular cubic Bezier functions

In this paper we obtain a 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 another sufficient condition for local injectivity of a 2D triangular cubic Bezier function. RESUMEN En este articulo presentamos una condicion suficiente para la inyectividad local de una funcion triangular de Bezier cubica en 2D. En este caso el analisis de la inyectividad local se reduce a determinar si una curva algebraica plana de grado 4 pasa por un triangulo. Para verificar la condicion anterior, presentamos un algoritmo novedoso para detectar si una curva algebraica plana de grado arbitrario pasa por un triangulo. El algoritmo utiliza tecnicas de subdivision y analisis de rango de una funcion. Ademas, presentamos otra condicion suficiente para la inyectividad local de una funcion triangular de Bezier en 2D.

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