Convexity and positivity of bivariate quadratic Bézier surfaces over a rectangle

Autor:	You-dong Ding
Rok vydání:	2001
Předmět:	Bézier surface Pure mathematics Quadratic equation Discriminant General Mathematics Quartic function Mathematical analysis General Engineering Zero (complex analysis) Bézier curve Rectangle Convexity Mathematics
Zdroj:	Journal of Shanghai University (English Edition). 5:20-28
ISSN:	1863-236X 1007-6417
Popis:	With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I⊂(−∞, +∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bezier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::16f08d1fe9f8e4ebc839bf4b06770c7c https://doi.org/10.1007/s11741-001-0021-9 Zobrazit plný text záznamu Full text from SpringerLink