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Point inversion and projection for NURBS curve: control polygon approach

Ying Liang Ma, W.T. Hewitt
Proceedings of Theory and Practice of Computer Graphics, 2003.  
Projecting a test point to a NURBS curve finds the closest point on the curve and point inversion finds the corresponding parameter for this test point.  ...  For point projection, we extract candidate Bézier subcurves based on the relationship between the test point and the control polygon of the Bézier subcurve.  ...  Introduction Both point projection and point inversion are common problems for interactively selecting a NURBS curve and curve fitting.  ... 
doi:10.1109/tpcg.2003.1206938 dblp:conf/tpcg/MaH03 fatcat:zps4wunetvhbxd6lj7ame5e47e

An Approach to Computing Multipoint Inversion and Multiray Surface Intersection on Parametric Surface

Pei Jingyu, Wang Xiaoping, Zhang Leen
2019 Mathematical Problems in Engineering  
This article presents a method for multipoint inversion and multiray surface intersection problem on the parametric surface.  ...  By combining tracing along the surface and classical Newton iteration, it can solve point inversion and ray-surface intersection issues concerning a large number of points or rays in a stable and high-speed  ...  For NURBS curve and surface, Johnson and Cohen [12] concentrated on the polygonal model for finding the minimum distance between two geometric objects.  ... 
doi:10.1155/2019/3790762 fatcat:ronzbqj7zvga7hvbkanrxfjvxi

Scalar and Parametric Spline Curves and Surfaces [chapter]

Horacio Florez, Belsay Borges
2018 Topics in Splines and Applications  
Another traditional requirement implies creating a curve that mimics a given array of points, namely, a polyline.  ...  Indeed, a global interpolant often experiences inflection points and sudden changes in curvature.  ...  Acknowledgements We acknowledge the financial support of the project "Reduced-Order Parameter Estimation for Underbody Blasts" funded by Army Research Laboratory.  ... 
doi:10.5772/intechopen.74929 fatcat:b43lvnwokzfnjcy44m5s6fetz4

Matrix weighted rational curves and surfaces

Xunnian Yang
2016 Computer Aided Geometric Design  
and its control polygon. which is similar to the rational algorithm for robust computation of points on rational Bézier curves (Farin, 2001).  ...  A geometric approach to construct rational curves and surfaces is the technique of dual Bézier curves and surfaces which treat the Bézier control points as control lines or control planes (Hoschek, 1983  ... 
doi:10.1016/j.cagd.2015.11.005 fatcat:ky2ymwhsrrbixmohr5dd465nfe

Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces

Huanyu Liao, Pavan Kumar Vaitheeswaran, Tao Song, Ganesh Subbarayan
2020 Algorithms  
Beginning with a first-order algorithm, sequentially refined procedures culminating in a second-order projection algorithm are described for NURBS curves and surfaces.  ...  To address this challenge, we present in this paper an algebraic procedure to project a point on to Non-uniform rational B-spline (NURBS) curves and surfaces.  ...  Acknowledgments: The authors wish to thank the reviewers for their suggestions that improved the manuscript. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13040082 fatcat:lrjgjjmfprgtzogbc56m6ib3li

Restructuring surface tessellation with irregular boundary conditions

Tsung-Hsien Wang, Ramesh Krishnamurti, Kenji Shimada
2014 Frontiers of Architectural Research  
The objective of this approach is to provide an alternative way for freeform surface manifestation from a well-structured discrete model of the given surface.  ...  For example, irregularly shaped panels form at the trimmed edges.  ...  Control polygons govern control points, which are used to interpolate ultimate surface presentation.  ... 
doi:10.1016/j.foar.2014.06.001 fatcat:r7t6s5n645cxdjgrp62plkwew4

Practical Ray Tracing of Trimmed NURBS Surfaces

William Martin, Elaine Cohen, Russell Fish, Peter Shirley
2000 Journal of Graphics Tools  
A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel.  ...  Thanks also to Brian Smits for helpful discussions, feedback, and encouragement, to Steve Parker for invaluable aid with parallelization and some of the nastier debugging, and to Amy Gooch for comments  ...  This work was supported in part by NSF grant 9720192 (CISE New Technologies), DARPA grant F33615-96-C-5621, and the NSF Science and Technology Center for Computer Graphics and Scientific Visualization  ... 
doi:10.1080/10867651.2000.10487519 fatcat:n7xxhc3wx5e2nmr3sipzj65cna

Hybrid Functional-Neural Approach for Surface Reconstruction

Andrés Iglesias, Akemi Gálvez
2014 Mathematical Problems in Engineering  
These neural and functional networks are applied in an iterative fashion for further surface refinement.  ...  This paper introduces a new hybrid functional-neural approach for surface reconstruction.  ...  Acknowledgments This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project ref. no.  ... 
doi:10.1155/2014/351648 fatcat:lbgi7iyfrnc6lmozotxrqqd67q

Analytical methods for polynomial weighted convolution surfaces with various kernels

Xiaogang Jin, Chiew-Lan Tai
2002 Computers & graphics  
We derive the closed-form formulae for most classical kernel functions, namely Gaussian, inverse linear, inverse squared, Cauchy, and quartic functions, and compare their computational complexity.  ...  Convolution surface has the advantage of being crease-free and bulge-free over other kinds of implicit surfaces.  ...  We are grateful to Andrei Sherstyuk for his help on convolution surfaces and to anonymous reviewers for their constructive suggestions. This work received support from Hong  ... 
doi:10.1016/s0097-8493(02)00087-0 fatcat:swi77dey5zb7xkkmfyfz5mugye

3-dimensional pliable surfaces

M. Sheelagh T. Carpendale, David J. Cowperthwaite, F. David Fracchia
1995 Proceedings of the 8th annual ACM symposium on User interface and software technology - UIST '95  
The significance of this approach is that it utilizes precognitive perceptual cues about the three-dimensional surface to make the distortions comprehensible, and allows the user to interactively control  ...  The manipulation and blending of foci is accomplished using a fairly simple mathematical model based on gaussian curves.  ...  Thanks also to Brian Fisher for verifying our cognitive references, James Strickland and Charles Henrich for the map data, Tom Shermer and Art Liestman for ongoing support, and John Dill for helpful comments  ... 
doi:10.1145/215585.215978 dblp:conf/uist/CarpendaleCF95 fatcat:ycswmxqu7rau7bl5nb3oxuvo2q

Fine level feature editing for subdivision surfaces

Andrei Khodakovsky, Peter Schröder
1999 Proceedings of the fifth ACM symposium on Solid modeling and applications - SMA '99  
In particular, our approach addresses the problem of defining the path of such feature curves independent of the location of surface iso-parameter lines and global patch boundaries.  ...  In this paper we describe an algorithm and implementation allowing the interactive creation and manipulation of fine scale feature curves on subdivision surfaces.  ...  Very special thanks to Khrysaundt Koenig for living on the bleeding edge of our modeler. Thanks also to the folks at DesignWorks/USA, Steven Schkolne, and Jim Barry for many discussions on modeling.  ... 
doi:10.1145/304012.304033 dblp:conf/sma/KhodakovskyS99 fatcat:uppb464fvfgctn3nzqe4nm2tue

Ray-tracing triangular trimmed free-form surfaces

W. Sturzlinger
1998 IEEE Transactions on Visualization and Computer Graphics  
Trimming curves are described by a tree of trimming primitives such as squares, circles, polygons and free form curves combined with Boolean operations.  ...  This paper presents a new approach to rendering triangular algebraic free form surfaces.  ...  Bramsteidl for implementing parts of the software and to W. Barth, J. Volkert, D. Manocha, T. Whitted, T. Hudson, and G. Meenakshi for helpful comments on previous versions of this manuscript.  ... 
doi:10.1109/2945.722295 fatcat:gbdq54pgtzf2zdr4v7gulcd3wi

GPU-based trimming and tessellation of NURBS and T-Spline surfaces

Michael Guthe, Aákos Balázs, Reinhard Klein
2005 ACM SIGGRAPH 2005 Papers on - SIGGRAPH '05  
Figure 1 : Rendering of NURBS models (from left to right): animated trimmed NURBS surface (degree 5 × 5, 100 control points) with environment mapping; Mini model consisting of 629 trimmed surfaces; with  ...  Combining this new method with GPU-based tessellation of cubic rational surfaces allows a new rendering algorithm for arbitrary trimmed NURBS and T-Spline surfaces with prescribed error in screen space  ...  reduce p-buffer switches when rendering multiple trimmed surfaces, and Andreas Schilling for his valuable comments.  ... 
doi:10.1145/1186822.1073305 fatcat:holhtj73j5gj7cfbhmb2e35paa

GPU-based trimming and tessellation of NURBS and T-Spline surfaces

Michael Guthe, Ákos Balázs, Reinhard Klein
2005 ACM SIGGRAPH 2005 Sketches on - SIGGRAPH '05  
Figure 1 : Rendering of NURBS models (from left to right): animated trimmed NURBS surface (degree 5 × 5, 100 control points) with environment mapping; Mini model consisting of 629 trimmed surfaces; with  ...  Combining this new method with GPU-based tessellation of cubic rational surfaces allows a new rendering algorithm for arbitrary trimmed NURBS and T-Spline surfaces with prescribed error in screen space  ...  reduce p-buffer switches when rendering multiple trimmed surfaces, and Andreas Schilling for his valuable comments.  ... 
doi:10.1145/1187112.1187190 dblp:conf/siggraph/GutheBK05 fatcat:2ueaqgoub5hcbfwjef6ajaediy

Illustrating smooth surfaces

Aaron Hertzmann, Denis Zorin
2000 Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00  
An important feature of our approach is that any polygonal mesh can serve as input; the smooth surface that we render is inferred from the mesh.  ...  . • An algorithm for cusp detection and segmentation of silhouette curves into smooth parts with constant visibility (Section 4.2). • An algorithm for computing smooth direction fields on surfaces, suitable  ...  This research was supported in part by the NSF grant DGE-9454173 and the NYU Center for Advanced Technology.  ... 
doi:10.1145/344779.345074 dblp:conf/siggraph/HertzmannZ00 fatcat:ruzzekxgm5hunl75ewaaq6qvxe
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