scholarly journals Subdivision Depth Computation for Extra-Ordinary Catmull-Clark Subdivision Surface Patches

2006 ◽  
pp. 404-416 ◽  
Author(s):  
Fuhua (Frank) Cheng ◽  
Gang Chen ◽  
Jun-Hai Yong
Keyword(s):  
Subdivision Surface ◽  
Surface Patches ◽  
Subdivision Depth

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 Subdivision surface watermarking

2007 ◽  
Vol 31 (3) ◽  
pp. 480-492 ◽  
Author(s):  
Guillaume Lavoué ◽  
Florence Denis ◽  
Florent Dupont
Keyword(s):  
Subdivision Surface

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 Vision-based foothold contact reasoning using curved surface patches

2017 ◽  
Author(s):  
Dimitrios Kanoulas ◽  
Chengxu Zhou ◽  
Anh Nguyen ◽  
Georgios Kanoulas ◽  
Darwin G. Caldwell ◽  
...  
Keyword(s):  
Curved Surface ◽  
Surface Patches
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