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Invariant Fitting of Arbitrary Single-Extremum Surfaces

Andrew W. Fitzgibbon, Robert B. Fisher
1993 Procedings of the British Machine Vision Conference 1993  
In this paper we describe a new method of satisfying the requirement for high representational richness while retaining the ease of manipulation and recognition of single-extremum surface patches.  ...  Besl and Jain's variable order surface fitting algorithm [1] is a useful method of constructing a noise-free reconstruction of 2jD range images with a small number of primitive regions.  ...  Acknowledgements Funding for this work was provided by ACME grant GR/H/86905. The authors would like to thank the members of the Machine Vision Unit at Edinburgh University for their help and advice.  ... 
doi:10.5244/c.7.57 dblp:conf/bmvc/FitzgibbonF93 fatcat:2dcebqbil5hwdk2zf3223fczmq

A biquadratic reflectance model for radiometric image analysis

Boxin Shi, Ping Tan, Y. Matsushita, K. Ikeuchi
2012 2012 IEEE Conference on Computer Vision and Pattern Recognition  
We show applications of reflectometry using general diffuse surfaces and photometric stereo for general isotropic materials.  ...  We propose a compact biquadratic reflectance model to represent the reflectance of a broad class of materials precisely in the low-frequency domain.  ...  Tan was supported by the Singapore ASTAR grant R-263-000-592-305 and MOE grant R-263-000-555-112.  ... 
doi:10.1109/cvpr.2012.6247680 dblp:conf/cvpr/ShiTMI12 fatcat:6gdbdo3chbbtfdvgmwksiwc3hy

Curvature estimation scheme for triangle meshes using biquadratic Bézier patches

Anshuman Razdan, MyungSoo Bae
2005 Computer-Aided Design  
This paper compares commonly used discrete and continuous curvature estimation schemes. We also present a novel method which uses biquadratic Bézier patches as a local surface fitting technique.  ...  Since a triangle mesh is a piecewise linear surface, curvature has to be estimated. Several different schemes have been proposed, both discrete and continuous i.e. based on fitting surfaces locally.  ...  Special thanks to Sandeep Pulla for implementing the original Bézier method, Gerald Farin for contribution to the manuscript and John Femiani for review and corrections.  ... 
doi:10.1016/j.cad.2005.03.003 fatcat:s2pgbqeqircvvix2x2bjfi2hiy

Triangular Springs for Modeling Nonlinear Membranes

H. Delingette
2008 IEEE Transactions on Visualization and Computer Graphics  
Furthermore, when considering a quadratic strain function of stretch, we introduce a new type of springs called tensile biquadratic springs.  ...  In a second stage, we extend this equivalence to non-linear membranes (St Venant-Kirchhoff materials) on triangular meshes leading to triangular biquadratic and quadratic springs.  ...  Furthermore, when considering a quadratic strain function of stretch, we introduce a new type of springs called tensile biquadratic springs.  ... 
doi:10.1109/tvcg.2007.70431 pmid:18192713 fatcat:mcmoxstrfzdztebcsnvcnb5nqy

Page 2066 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Examples of the octtree building process are presented and discussed.” 8$8d:65028 65D10 65D07 DeVore, Ronald A. (1-SC); Yan, Zheng (1-SC) Error analysis for piecewise quadratic curve fitting algorithms  ...  The authors pro- pose two new algorithms. The first one preserves monotonicity and is of order three for monotone data.  ... 

Page 5694 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
Farin [Curves and surfaces for computer aided geometric design, second edition, Academic Press, Boston, MA, 1990; MR 91i:65036].  ...  It is employed as the foundation of this new method such that this new solid and surface model is reliable and com- patible with the solid modeling and surface modeling systems in most common use.  ... 

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
algorithm for the evaluation of a B spline segment from curves to surfaces.  ...  An algorithm for the local interpolation of a cubic curve mesh by a piecewise bi quartic C 1 surface is described.  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

Page 4322 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
Summary: “A cyclide patch is a surface patch for which the bound- ary curves are lines of curvature of the Dupin cyclide, and it is known that the patch is represented in biquadratic rational para- metric  ...  (English summary) Mathematical methods for curves and surfaces (Ulvik, 1994), 507-516, Vanderbilt Univ. Press, Nashville, TN, 1995.  ... 

Adaptive Smooth Scattered-data Approximation for Large-scale Terrain Visualization [article]

Martin Bertram, Xavier Tricoche, Hans Hagen
2003 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
We provide numerical results for two terrain data sets, demonstrating that our algorithm works efficiently and accurate for large data sets with highly non-uniform sampling densities.  ...  The resulting surface components are locally approximated by a smooth B-spline surface obtained by knot removal.  ...  Acknowledgements The Crater Lake and Seattle datasets used to test our method were provided by U.S. Geological Survey (USGS).  ... 
doi:10.2312/vissym/vissym03/177-184 fatcat:gswefpxe7zhh3fqjytrphs7jxy

Page 2122 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
surfaces and B-spline surfaces), nonlinear spline curves, smooth- ing for the grid, and the intrinsic affine invariants of parametric curves in affine spaces.  ...  We give a proof of this fact and propose an algorithm for construction of a piecewise-linear function that has this property.” {For the entire collection see MR 85g:94002.} Watson, G.  ... 

High-order approximation of conic sections by quadratic splines

Michael Floater
1995 Computer Aided Geometric Design  
Given a segment of a conic section in the form of a rational Bézier curve, a quadratic spline approximation is constructed and an explicit error bound is derived.  ...  The approximation method and error bound are also applied to an important subclass of rational biquadratic surfaces which includes the sphere, ellipsoid, torus, cone and cylinder.  ...  I would also like to thank the referees for helpful comments and suggestions for improving the readability of this paper.  ... 
doi:10.1016/0167-8396(94)00037-s fatcat:tvcicthprrhnjn2yuosbk7knr4

A B-spline-based approach to heterogeneous objects design and analysis

Pinghai Yang, Xiaoping Qian
2007 Computer-Aided Design  
In the design module, a new approach for intuitively modelling of multi-material objects, termed heterogeneous lofting, is presented.  ...  In this paper, we present an integrated design and analysis approach for heterogeneous object realization, which employs a unified design and analysis model based on B-spline representation and allows  ...  Acknowledgements The authors are grateful for anonymous reviewers' and Dr. Larry Byrd's constructive comments.  ... 
doi:10.1016/j.cad.2006.10.005 fatcat:76rffe3cfje2bn2ewp3reftyja

Improved quadratic normal vector interpolation for realistic shading

Yuan-Chung Lee, Chein-Wei Jen
2001 The Visual Computer  
Previous quadratic interpolation for normal vectors generates visual artifacts for archtype curves and triangle scan conversion.  ...  Interpolation for normal vectors is an important stage of Phong shading. Linear interpolation cannot represent the geometry of surfaces adequately in some situations.  ...  The authors would like to acknowledge the valuable suggestions from Wen-Chang Yeh and Kun-Bin Lee as well as the reviewers.  ... 
doi:10.1007/s003710100111 fatcat:b5cfjdzgyvgodct5rckhglfuxq

Analysis of Algorithms Generalizing B-Spline Subdivision

Jörg Peters, Ulrich Reif
1998 SIAM Journal on Numerical Analysis  
A new set of tools for verifying smoothness of surfaces generated by stationary subdivision algorithms is presented.  ...  The tools are sufficiently versatile and easy to wield to allow, as an application, a full analysis of algorithms generalizing biquadratic and bicuble B-spline subdivision.  ...  Figure 11 : 11 Masks for the Catmull-Clark algorithm. a new edge point, and one for the new location of a former vertex, see Figure 11. So, the variables at disposal are the weights 0.,13",0.+13+,=1.  ... 
doi:10.1137/s0036142996304346 fatcat:6lpxcjyowfburhk53vwudasyfi

Fast and Accurate Redistancing by Directional Optimization

Matt Elsey, Selim Esedoḡlu
2014 SIAM Journal on Scientific Computing  
A fast and accurate algorithm for the reinitialization of the signed distance function in two and three spatial dimensions is presented.  ...  The algorithm has computational complexity O(N log N ) for the reinitialization of N grid points.  ...  Acknowledgments This work was supported, in part, by grants from the National Science Foundation: DMS-0748333, DMS-0713767, and OISE-0967140, and by the Rackham Predoctoral Fellowship.  ... 
doi:10.1137/120889447 fatcat:r2cwswye4zcs5el4rooznlceai
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