Convexity and Positivity of Bivariate Quadratic Bezier Surfaces over a Rectangle

摘要

With the help of several discriminants about he zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonegativity of the quartic polynomial over an interval I<(-∞, +∞) was derived. Based on these conclu- sions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bezier surface over a rectangle were ob- tained. A simple sufficient condition was deduced also and finally several examples were given.