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.

Ray tracing parametric surface patches utilizing numerical techniques and ray coherence

1986 ◽  
Vol 20 (4) ◽  
pp. 279-285 ◽  
Author(s):  
Kenneth I. Joy ◽  
Murthy N. Bhetanabhotla
Keyword(s):  
Ray Tracing ◽  
Parametric Surface ◽  
Numerical Techniques ◽  
Surface Patches

3-D prestack Kirchhoff beam migration for depth imaging

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1592-1603 ◽  
Author(s):  
Yonghe Sun ◽  
Fuhao Qin ◽  
Steve Checkles ◽  
Jacques P. Leveille
Keyword(s):  
Distributed Environment ◽  
Small Surface ◽  
Depth Imaging ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Surface Patches ◽  
Image Volume ◽  
Kirchhoff Depth Migration ◽  
Full Volume ◽  
Single Set

A beam implementation is presented for efficient full‐volume 3-D prestack Kirchhoff depth migration of seismic data. Unlike conventional Kirchhoff migration in which the input seismic traces in time are migrated one trace at a time into the 3-D image volume for the earth’s subsurface, the beam migration processes a group of input traces (a supergather) together. The requirement for a supergather is that the source and receiver coordinates of the traces fall into two small surface patches. The patches are small enough that a single set of time maps pertaining to the centers of the patches can be used to migrate all the traces within the supergather by Taylor expansion or interpolation. The migration of a supergather consists of two major steps: stacking the traces into a τ-P beam volume, and mapping the beams into the image volume. Since the beam volume is much smaller than the image volume, the beam migration cost is roughly proportional to the number of input supergathers. The computational speedup of beam migration over conventional Kirchhoff migration is roughly proportional to [Formula: see text], the average number of traces per supergather, resulting a theoretical speedup up to two orders of magnitudes. The beam migration was successfully implemented and has been in production use for several years. A factor of 5–25 speedup has been achieved in our in‐house depth migrations. The implementation made 3-D prestack full‐volume depth imaging feasible in a parallel distributed environment.

scholarly journals On-line construction of the upper envelope of triangles and surface patches in three dimensions

1996 ◽  
Vol 5 (6) ◽  
pp. 303-320 ◽  
Author(s):  
Jean-Daniel Boissonnat ◽  
Katrin T.G. Dobrindt
Keyword(s):  
Three Dimensions ◽  
Surface Patches ◽  
On Line ◽  
Line Construction
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