De Casteljau Algorithm and Degree Elevation of Toric Surface Patches

2020 ◽  
Author(s):  
Jinggai Li ◽  
Ye Ji ◽  
Chungang Zhu
Keyword(s):  
Toric Surface ◽  
De Casteljau Algorithm ◽  
Degree Elevation ◽  
Surface Patches

scholarly journals Linear Precision for Toric Surface Patches

2009 ◽  
Vol 10 (1) ◽  
pp. 37-66 ◽  
Author(s):  
Hans-Christian Graf von Bothmer ◽  
Kristian Ranestad ◽  
Frank Sottile
Keyword(s):  
Toric Surface ◽  
Surface Patches

Curvature continuity conditions between adjacent toric surface patches

2018 ◽  
Vol 37 (7) ◽  
pp. 469-477
Author(s):  
Lanyin Sun ◽  
Chungang Zhu
Keyword(s):  
Toric Surface ◽  
Surface Patches ◽  
Curvature Continuity

An improved algorithm for checking the injectivity of 2D toric surface patches

2020 ◽  
Vol 79 (10) ◽  
pp. 2973-2986
Author(s):  
Ying-Ying Yu ◽  
Ye Ji ◽  
Chun-Gang Zhu
Keyword(s):  
Toric Surface ◽  
Surface Patches ◽  
Improved Algorithm

G1 continuity between toric surface patches

2015 ◽  
Vol 35-36 ◽  
pp. 255-267 ◽  
Author(s):  
Lan-Yin Sun ◽  
Chun-Gang Zhu
Keyword(s):  
Toric Surface ◽  
Surface Patches ◽  
G1 Continuity

Isogeometric analysis for trimmed CAD surfaces using multi-sided toric surface patches

2020 ◽  
Vol 79 ◽  
pp. 101847
Author(s):  
Xuefeng Zhu ◽  
Ye Ji ◽  
Chungang Zhu ◽  
Ping Hu ◽  
Zheng-Dong Ma
Keyword(s):  
Isogeometric Analysis ◽  
Toric Surface ◽  
Surface Patches

THE EXISTENCE OF SURFACE PATCHES FOR PERIODIC MINIMAL SURFACES

1990 ◽  
Vol 51 (C7) ◽  
pp. C7-265-C7-271 ◽  
Author(s):  
J. C.C. NITSCHE
Keyword(s):  
Minimal Surfaces ◽  
Surface Patches

Computation of Self-Intersections of Offsets of Be´zier Surface Patches

1997 ◽  
Vol 119 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Takashi Maekawa ◽  
Wonjoon Cho ◽  
Nicholas M. Patrikalakis
Keyword(s):  
Differential Geometry ◽  
Distance Function ◽  
Polynomial Equations ◽  
Intersection Curve ◽  
Parameter Domain ◽  
Surface Patches ◽  
Intersection Curves

Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

scholarly journals A de Casteljau Algorithm for -Bernstein-Stancu Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Nowak
Keyword(s):  
Bernstein Polynomials ◽  
Classical Case ◽  
Geometric Progression ◽  
De Casteljau Algorithm ◽  
Stancu Operators

This paper is concerned with a generalization of the -Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and -Bernstein case.

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