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Representing spheres and ellipsoids using periodic NURBS surfaces with fewer control vertices

Kaihuai Qin, Wenping Wang, Zesheng Tang
Proceedings Pacific Graphics '98. Sixth Pacific Conference on Computer Graphics and Applications (Cat. No.98EX208)  
The method for periodic curves is extended to derive a compact and symmetric representation of the sphere or the ellipsoid using a piecewise bi-quadratic NURBS surface with only eight distinct control  ...  A new kind of NURBS representation for periodic curves is introduced.  ...  Now using the C pseudocode in Figure 2 , we can give Algorithm 1 for an NURBS surface of degree 2×2 with eight vertices to represent the sphere precisely.  ... 
doi:10.1109/pccga.1998.732121 dblp:conf/pg/QinTW98 fatcat:7ui3yvh2wnghta2m2uyacq76yi

Smoothly deformable spheres

Daniel Schmitter, Pablo García-Amorena, Michael Unser
2016 SIGGRAPH ASIA 2016 Technical Briefs on - SA '16  
NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation.  ...  We present a new method to construct deformable closed surfaces, which includes the exact sphere, by combining the best of two worlds: a smooth and interpolating model with a continuously varying tangent  ...  We are greatful to Zsuzsanna Püspöki for help with the figures and to Irina Radu for the help with the video.  ... 
doi:10.1145/3005358.3005377 fatcat:4bbf7xjb2ndztk3qkjqly3r2pu

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

D. Schmitter, P. García-Amorena, M. Unser
2017 Computational Visual Media  
Our formulation is considerably simpler than NURBS and requires fewer parameters than polygon meshes.  ...  NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation.  ...  We are grateful to Zsuzsanna Püspöki for help with the figures and to Irina Radu for help with the video.  ... 
doi:10.1007/s41095-017-0086-4 fatcat:5ylo4rr5lnhwvasqsxf6gwnjfi

Isogeometric analysis using T-splines

Y. Bazilevs, V.M. Calo, J.A. Cottrell, J.A. Evans, T.J.R. Hughes, S. Lipton, M.A. Scott, T.W. Sederberg
2010 Computer Methods in Applied Mechanics and Engineering  
We review T-splines as a surface design methodology and then develop it for engineering analysis applications.  ...  We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis.  ...  Acknowledgements We wish to thank Omar Ghattas for helpful insights into the relationship between isogeometric analysis and high-performance computing. J.A. Evans  ... 
doi:10.1016/j.cma.2009.02.036 fatcat:r5k7zhjdrrfltdkauqy6azz4oe

Spline-Based Deforming Ellipsoids for Interactive 3D Bioimage Segmentation

Ricard Delgado-Gonzalo, Nicolas Chenouard, Michael Unser
2013 IEEE Transactions on Image Processing  
The proposed 3D snake can approximate blob-like objects with good accuracy and can perfectly reproduce spheres and ellipsoids, irrespective of their position and orientation.  ...  We introduce a parametric design that relies on exponential B-spline bases and allows us to build snakes that are able to reproduce ellipsoids.  ...  Our snake is characterized by fewer control points than nonparametric snakes and can approximate any blob-like structure with arbitrary precision.  ... 
doi:10.1109/tip.2013.2264680 pmid:23708807 fatcat:bzkc776w5jgpvlqdhapi7wkojy

An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

A.R. Owens, J.A. Welch, J. Kópházi, M.D. Eaton
2017 Computer Methods in Applied Mechanics and Engineering  
This is achieved by the use of automatic mesh generation software that generates surface and volumetric meshes of finite elements from the underlying Non-Uniform Rational B-Spline (NURBS) surface descriptions  ...  To preserve the CAD geometry, the same NURBS used in the CAD program are used as the shape and test functions in the spatial discretisation of the PDE.  ...  In accordance with EPSRC funding requirements, all supporting data used to create figures and tables in this paper may be accessed at the following URL: http://doi.org/10.5281/zenodo.259450.  ... 
doi:10.1016/j.cma.2017.01.036 fatcat:67v72mjzlbh37jglirjev3vgam

Making Use of 3D Models for Plant Physiognomic Analysis: A Review

Abhipray Paturkar, Gourab Sen Sen Gupta, Donald Bailey
2021 Remote Sensing  
In this paper, we investigate the techniques and algorithms used at various stages of processing and analysing 3D models of plants, and identify their current limiting factors.  ...  However, a review of approaches, algorithms, and techniques used for 3D plant physiognomic analysis is lacking.  ...  Non-uniform Rational Basis Splines NURBS are mathematical models commonly used for producing and representing smooth surfaces and curves in computer graphics.  ... 
doi:10.3390/rs13112232 fatcat:y65narwvcnc2tmwazk6ci23se4

Geometric modeling based on triangle meshes

Mario Botsch, Mark Pauly, Christian Rossl, Stephan Bischoff, Leif Kobbelt
2006 ACM SIGGRAPH 2006 Courses on - SIGGRAPH '06  
Being 2-simplices, triangles are the conceptually simplest primitives for representing surfaces, and thus allow for the implementation of very efficient geometry processing algorithms.  ...  The right configuration, although being non-manifold in the strict sense, can be handled by most data structures. where g is the genus of the surface and intuitively represents the number of handles of  ...  ., a set of NURBS patches, the same techniques for quality control can be used that are applied for smooth surfaces [HHS * 92].  ... 
doi:10.1145/1185657.1185839 dblp:conf/siggraph/BotschPRBK06 fatcat:osmn4jpgcbdf7f6n5zirkunl7q

Geometric modeling based on polygonal meshes

Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Lévy, Stephan Bischoff, Christian Rössl
2007 ACM SIGGRAPH 2007 courses on - SIGGRAPH '07  
His current research interests include shape approximation, mesh generation, surface remeshing and surface reconstruction. Dr.  ...  He has published several papers in the area of geometry compression, mesh approximation, surface remeshing, mesh generation and surface parameterization.  ...  ., a set of NURBS patches, the same techniques for quality control can be used that are applied for smooth surfaces [HHS + 92]. .1: Isophotes.  ... 
doi:10.1145/1281500.1281640 dblp:conf/siggraph/BotschPKALBR07 fatcat:khwj3g4lu5eurovnvvt7hzenye

Geometric Modeling Based on Polygonal Meshes [article]

Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Levy
2008 Eurographics State of the Art Reports  
The course starts with a comparison of different surface representations, motivating the use of polygonal meshes.  ...  Moreover, the consequent use of triangle meshes avoids error-prone conversions, e.g., the meshing of CAD surfaces for numerical simulations.  ...  ., a set of NURBS patches, the same techniques for quality control can be used that are applied for smooth surfaces [HHS + 92].  ... 
doi:10.2312/egt.20081055 fatcat:yypmklz4lvexpox3z6iinvwun4

Modeling of Deformable Objects for Robotic Manipulation: A Tutorial and Review

Veronica E. Arriola-Rios, Puren Guler, Fanny Ficuciello, Danica Kragic, Bruno Siciliano, Jeremy L. Wyatt
2020 Frontiers in Robotics and AI  
We then use this as the basis for a review of existing work on learning and estimation of these models and on motion planning and control to achieve desired deformations.  ...  manipulation, and manipulation planning and control.  ...  SIP-STRIM was a strategic research initiative funded by Vinnova, Formas and the Swedish Energy Agency.  ... 
doi:10.3389/frobt.2020.00082 pmid:33501249 pmcid:PMC7805872 doaj:327f34dd8d004e8c8d815dcea38f79b6 fatcat:nwgep4tvgrgyppueryp3hg7xle

Strands and hair

Sunil Hadap, Marie-Paule Cani, Ming Lin, Tae-Yong Kim, Florence Bertails, Steve Marschner, Kelly Ward, Zoran Kačić-Alesić
2007 ACM SIGGRAPH 2007 courses on - SIGGRAPH '07  
Simplifying this geometry, using fewer vertices and rendering fewer strands, is one strategy for accelerating hair rendering.  ...  The base skeleton is the underlying control structure for each LOD representation and dictates the placement of control vertices used for subdivision.  ... 
doi:10.1145/1281500.1281689 dblp:conf/siggraph/HadapCL0BMWK07 fatcat:znzypovcwfarxkzrtkohs2ktde

Realistic hair simulation

Florence Bertails, Sunil Hadap, Marie-Paule Cani, Ming Lin, Tae-Yong Kim, Steve Marschner, Kelly Ward, Zoran Kačić-Alesić
2008 ACM SIGGRAPH 2008 classes on - SIGGRAPH '08  
Prerequisites: Familiarity with fundamentals of computer graphics, physical simulation and physically based rendering is strongly recommended but not mandatory.  ...  This class covers both recent and novel research ideas in hair animation and rendering, and presents time tested industrial practices that resulted in spectacular imagery.  ...  Simplifying this geometry, using fewer vertices and rendering fewer strands, is one strategy for accelerating hair rendering.  ... 
doi:10.1145/1401132.1401247 dblp:conf/siggraph/BertailsHCL0MWK08 fatcat:32hq6vl2vvgddedakivfy37enu

Towards the Virtual Physiological Human [article]

Nadia Magnenat-Thalmann, Benjamin Gilles, Hervé Delingette, Andrea Giachetti, Marco Agus
2007 Eurographics State of the Art Reports  
Three levels of complexity can be distinguished (geometry, function and control) where modelling and simulation methods take place.  ...  Human body representations have been used for centuries to help in understanding and documenting the shape and function of its compounding parts.  ...  Alternatively, muscles can be represented by their medial surfaces (1 resolution, 3821 vertices) with an average error of 0.6mm.  ... 
doi:10.2312/egt.20071062 fatcat:iyybqfp4nnadhfkaeagp6qr63q

Multiresolution by Repeated Invertible Averaging - With Applications in Digital Earth [article]

Troy F. Alderson, University Of Calgary, Faramarz Samavati
2019
These include curves in Euclidean and non-Euclidean spaces (particularly the surfaces of spheres and ellipsoids) as well as polygonal mesh surfaces.  ...  Generalizations of the approach include a modification that allows our framework to produce multiscale NURBS curves on the sphere and ellipsoid.  ...  Both B-Spline curves and NURBS curves may be represented in a multiscale manner on the ellipsoid (here an ellipsoid with a flattening factor of 0.5) using the RIA framework with an appropriate interpolation  ... 
doi:10.11575/prism/37274 fatcat:ypmvpqzib5ghhp2nkqqf5asshe
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