The conditions of convexity for Bernstein–Bézier surfaces over triangles

Liu, Zhi; Tan, Jieqing; Chen, Xiao-yan; Zhang, Li

doi:10.1016/j.cagd.2010.05.004

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Some Particular Sets Of Sufficient Conditions For Convexity1

§1 Introduction1

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2011

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Cited by 4 publications

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“…Proof: We apply Theorem 2.2 with The remaining conditions can be reformulated in a similar way, and we obtain the conditions derived in [31]. By Corollary 2.4 this set of conditions is weaker than (2.16).…”

Section: Some Particular Sets Of Sufficient Conditions For Convexitymentioning

confidence: 89%

“…Therefore, an important subproblem is to find sets of (sufficient) convexity conditions for polynomials in Bernstein-Bézier representation. Particular sets of linear convexity conditions have been derived in [6,8,26,31]; sets of nonlinear conditions have been described in [9,38], and methods based on convexity of the control net and subdivision can be found in [15,18,20,21].…”

Section: §1 Introductionmentioning

confidence: 99%

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