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Page 5720 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
Heike FaBbender (D-BRMN) 92j:65213 65Y25 65D07 65D17 Chui, Charles K. (1-TXAM-A); Lai, Ming Jun (1-UT) Algorithms for generating B-nets and graphically displaying spline surfaces on three- and four-directional  ...  surfaces on a three- or four-directional mesh.  ... 

Splines for Meshes with Irregularities

Jörg Peters
2019 SMAI Journal of Computational Mathematics  
This paper reviews and categorizes techniques for splines on meshes with irregularities.  ...  "Generalized" splines can use quad-dominant meshes as control nets both for modeling geometry and to support engineering analysis without additional meshing. 2010 Mathematics Subject Classification. 65N35  ...  Acknowledgements Many of the ideas and algorithms for splines on meshes with irregularities arose in collaboration with Ulrich Reif, Kȩstutis Karčiauskas and Thien Nguyen.  ... 
doi:10.5802/smai-jcm.57 fatcat:4vrditc7pna4bgo223bjxbep3e

Localized-hierarchy surface splines (LeSS)

Carlos Gonzalez-Ochoa, Jorg Peters
1999 Proceedings of the 1999 symposium on Interactive 3D graphics - SI3D '99  
Key characteristics of the approach are: (1) mesh pieces and surface pieces are related by strictly local averaging rules; (2) refinement rules depend only on direct, coarser-level ancestors and not on  ...  The environment offers localized hierarchical modeling at different levels of detail, direct surface manipulation, change of connectivity for extrusion and to form holes and bridges, and built-in tangent  ...  Acknowledgment: Our thanks to John Hughes and the referees for valuable pointers on how to improve the presentation.  ... 
doi:10.1145/300523.300524 dblp:conf/si3d/Gonzalez-OchoaP99 fatcat:gg4b4x3d6nf5nfxwopsjy5jhka

Combining 4- and 3-direction subdivision

Jörg Peters, Le-Jeng Shiue
2004 ACM Transactions on Graphics  
Remarkably, 4-3 surfaces can be proven to be C 1 and have bounded curvature everywhere. In regular mesh regions, they are C 2 and correspond to two closely-related box-splines of degree four.  ...  4-3 direction subdivision combines quad and triangle meshes.  ...  Finally, and this is a major point for graphics modeling, the A 4 spline avoids undesirable ripples in more directions than tensor-product bicubic splines.  ... 
doi:10.1145/1027411.1027415 fatcat:otuphppes5dr5aywgzecixstsy

Patching Catmull-Clark meshes

Jörg Peters
2000 Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00  
continuity and interpolate the limit of the extraordinary mesh node.  ...  The patches join parametrically ¾ and agree with the Catmull-Clark limit surface except in the immediate neighborhood of extraordinary mesh nodes; in such a neighborhood they join at least with tangent  ...  Acknowledgement: I thank the referees, David Lutterkort, Malcolm Sabin, Andy Shiue and Georg Umlauf at SurfLab for their constructive comments.  ... 
doi:10.1145/344779.344908 dblp:conf/siggraph/Peters00 fatcat:fe4uhngwzzhetl6h5zaml6cbei

Quad/Triangle Subdivision

Jos Stam, Charles Loop
2003 Computer graphics forum (Print)  
Our new scheme is a generalization of the well known Catmull-Clark and Loop subdivision algorithms.  ...  It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad-only meshes behave poorly with triangular schemes.  ...  agree exactly with regular bi-cubic B-splines and triangular Box splines of total degree four, respectively.  ... 
doi:10.1111/1467-8659.t01-2-00647 fatcat:35abxwtqonhlpl6ydggevwwuli

Haptic sculpting of dynamic surfaces

Frank Dachille, Hong Qin, Arie Kaufman, Jihad El-Sana
1999 Proceedings of the 1999 symposium on Interactive 3D graphics - SI3D '99  
This paper presents a novel haptic approach for the direct manipulation of physics-based B-spline surfaces.  ...  We aim to develop various haptic sculpting tools to expedite the direct manipulation of B-spline surfaces with haptic feedback and constraints.  ...  The authors wish to thank Justine Dachille for her review, ideas, and support.  ... 
doi:10.1145/300523.300535 dblp:conf/si3d/DachilleQKE99 fatcat:xizbgkag25gjrbzahlk6fc6jhu

Polynomial splines over hierarchical T-meshes

Jiansong Deng, Falai Chen, Xin Li, Changqi Hu, Weihua Tong, Zhouwang Yang, Yuyu Feng
2008 Graphical Models  
PHT-splines are a generalization of B-splines over hierarchical T-meshes.  ...  For example, PHT-splines are polynomial instead of rational; cross insertion/removal of PHT-splines is local and simple; and conversion between a NURBS surface and a PHTspline is very effective.  ...  Here the control nets of the TP B-spline patches are displayed in brown, and the patch boundaries are in light blue.  ... 
doi:10.1016/j.gmod.2008.03.001 fatcat:mjif3x2jkbfjhedj27ih5d424m

A tangent subdivision scheme

Evelyne Vanraes, Adhemar Bultheel
2006 ACM Transactions on Graphics  
In this paper we propose a new subdivision scheme based on uniform Powell-Sabin spline subdivision. For each vertex we have a control triangle tangent to the surface instead of a control point.  ...  Abstract In this paper we propose a new subdivision scheme based on uniform Powell-Sabin spline subdivision.  ...  Acknowledgement This work is partially supported by the Belgian Program on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister's Office for Science, Technology and Culture  ... 
doi:10.1145/1138450.1138458 fatcat:oxvst7psn5d25lnjgkvkio7skq

Lens-shaped surfaces and C 2 subdivision

Kestutis Karčiauskas, Jorg Peters
2009 Computing  
Since this conformal ring is of degree bi-2 rather than bi-3, it allows constructing a subdivision algorithm that works directly on the control net and generates C 2 limit surfaces of degree bi-4 for lens-shaped  ...  Mathematics Subject Classification (2000) Computer aided design (modeling of curves and surfaces) · Splines · Computer graphics and computational geometry Motivation The prescription of the original Catmull-Clark  ...  (a) B-spline layers (b) BB-net of a segment of the C 2 polar ring (c) BB-net of a segment of the C 2 central cap Fig. 19: Polar construction of a transition and n central patches of degree 6,5.  ... 
doi:10.1007/s00607-009-0060-9 fatcat:deykvpaqpbcvtpjlem3kzrua6i

Smooth multi-sided blending of biquadratic splines

Kȩstutis Karčiauskas, Jörg Peters
2015 Computers & graphics  
(a) Input: one planar and four cylindric pieces. (b) The input is pairwise blended by bi-2 splines and the remaining gap is filled by a G 1 cap consisting of five patches of degree bi-3.  ...  Biquadratic (bi-2) splines are the simplest choice for converting a regular quad meshes into smooth tensor-product spline surfaces.  ...  But while splines of degree bi-3 can model inflections along boundary curves, both hand-crafted and algorithmically-generated quad-meshes model inflections as transitions between (bi-linear) pieces so  ... 
doi:10.1016/j.cag.2014.09.004 fatcat:53igukekaze3dbxuqayfvlnusy

Dynamic Catmull-Clark subdivision surfaces

Hong Qin, C. Mandal, B.C. Vemuri
1998 IEEE Transactions on Visualization and Computer Graphics  
Recursive subdivision schemes have been extensively used in computer graphics, computer-aided geometric design, and scientific visualization for modeling smooth surfaces of arbitrary topology.  ...  Recursive subdivision generates a visually pleasing smooth surface in the limit from an initial user-specified polygonal mesh through the repeated application of a fixed set of subdivision rules.  ...  Malandain for the edge detection software, Dr. H. Hoppe and Dr. K. Pulli for the range data, and Dr. C.M. Leonard for the brain MRI data.  ... 
doi:10.1109/2945.722296 fatcat:7wa7vhcukzb5xc6oxkl7uh3gd4

Extending Catmull-Clark Subdivision and PCCM with Polar Structures

Ashish Myles, Kestutis Karciauskas, Jorg Peters
2007 15th Pacific Conference on Computer Graphics and Applications (PG'07)  
Both and polar subdivision [7] generalize bi-cubic spline subdivision.  ...  We complete and bring together two pairs of surface constructions that use polynomial pieces of degree (3, 3) to associate a smooth surface with a mesh.  ...  Except for constructing polar vertices and their 1-links, the refinement algorithm in [7] applies cubic spline refinement only in the longitudinal (radial) but not in the latitudinal (circular) direction  ... 
doi:10.1109/pg.2007.11 dblp:conf/pg/MylesKP07 fatcat:g2v35esu7vgtzmox445vp7jjdm

On the Local Linear Independence of Generalized Subdivision Functions

Jörg Peters, Xiaobin Wu
2006 SIAM Journal on Numerical Analysis  
Given a control net, the spanning functions of one spatial coordinate of a generalized subdivision surface are called nodal functions.  ...  It proves the conjectured global independence of the nodal functions of both algorithms, disproves local linear independence (for higher valences), and establishes linear independence on every surface  ...  The presentation benefited from the kind suggestions of the reviewers and the editor.  ... 
doi:10.1137/050627496 fatcat:urd3umkfuvf6plivcl4splp5p4

Improved shape for refinable surfaces with singularly parameterized irregularities

Kȩstutis Karčiauskas, Jörg Peters
2017 Computer-Aided Design  
Independently, in the context of iso-geometry, Takacs and Jüttler [11] discussed singular spline constructions for analysis and observed that specific linear combinations of singular splines can be sufficiently  ...  Akin to subdivision surfaces, singularlyparameterized functions on the surfaces are straightforward to refine.  ...  Acknowledgments This work was supported in part by NSF grant CCF-1117695 and NIH R01 LM011300-01.  ... 
doi:10.1016/j.cad.2017.05.004 pmid:29129934 pmcid:PMC5679004 fatcat:ralxuskndvg63fl2yr4ihyxthy
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