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

Geometrical Criteria to Guarantee Curvature Continuity of Blend Surfaces

1992 ◽  
Vol 114 (1) ◽  
pp. 201-210 ◽  
Author(s):  
Joseph Pegna ◽  
Franz-Erich Wolter
Keyword(s):  
Second Order ◽  
Geometric Design ◽  
Technical Requirement ◽  
Computer Aided Geometric Design ◽  
First Order ◽  
Surface Patches ◽  
Computer Aided ◽  
Curvature Continuity ◽  
Continuous Surface ◽  
Blend Surfaces

Computer Aided Geometric Design (CAGD) of surfaces sometimes presents problems that were not envisioned in classical differential geometry. This paper presents mathematical results that pertain to the design of curvature continuous blending surfaces. Curvature continuity across normal continuous surface patches requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve theorem proved here shows that, for the blend to be curvature continuous when it is already normal continuous, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. The geometric criteria presented may be helpful to the designer since curvature continuity is a technical requirement in hull or cam design problems. The usefulness of the linkage curve theorem is illustrated with a second order blending problem whose implementation will not be detailed here.

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

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

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.

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