Differential Geometry of Intersection Curves

2009 ◽  
pp. 161-180
Author(s):  
Nicholas M. Patrikalakis ◽  
Takashi Maekawa
Keyword(s):  
Differential Geometry ◽  
Intersection Curves

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 Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space

2016 ◽  
Vol 308 ◽  
pp. 20-38 ◽  
Author(s):  
O. Aléssio ◽  
M. Düldül ◽  
B. Uyar Düldül ◽  
Nassar H. Abdel-All ◽  
Sayed Abdel-Naeim Badr
Keyword(s):  
Differential Geometry ◽  
Transversal Intersection ◽  
Intersection Curves

Differential geometry of transversal intersection curves of hypersurfaces in ℝ5

2017 ◽  
Vol 15 (2) ◽  
pp. 147-162 ◽  
Author(s):  
Mohamd Saleem Lone ◽  
Osmar Aléssio ◽  
Mohammed Jamali ◽  
Mohammad Hasan Shahid
Keyword(s):  
Differential Geometry ◽  
Transversal Intersection ◽  
Intersection Curves

Differential geometry of non-transversal intersection curves of three parametric hypersurfaces in Euclidean 4-space

2014 ◽  
Vol 31 (9) ◽  
pp. 712-727 ◽  
Author(s):  
Osmar Aléssio ◽  
Mustafa Düldül ◽  
Bahar Uyar Düldül ◽  
Sayed Abdel-Naeim Badr ◽  
Nassar H. Abdel-All
Keyword(s):  
Differential Geometry ◽  
Transversal Intersection ◽  
Intersection Curves

Applicable Differential Geometry

1987 ◽  
Author(s):  
M. Crampin ◽  
F. A. E. Pirani
Keyword(s):  
Differential Geometry
Sign in / Sign up

Export Citation Format

Share Document