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Trimming for subdivision surfaces

Nathan Litke, Adi Levin, Peter Schröder
2001 Computer Aided Geometric Design  
It is based on the use of combined subdivision schemes to guarantee exact interpolation of trim curves.  ...  ., for NURBS) we construct a new control mesh with each trim operation. This causes a perturbation of the surface near the trim region, which we control through the use of multiresolution details.  ...  Acknowledgements This work has been supported in part by NSF (DMS-9874082, DMS-9872890, ACI-9982273), Alias|Wavefront, Microsoft, Intel, Lucent, and the Packard Foundation.  ... 
doi:10.1016/s0167-8396(01)00042-5 fatcat:qzawnnfxxvdg7eyxwrdsma4nxe

Taxonomy of interpolation constraints on recursive subdivision surfaces

Ahmad H. Nasri, Malcolm A. Sabin
2002 The Visual Computer  
It addresses surface interpolation constraints, building upon the concepts and categories introduced in the first paper, on interpolation constraints on recursive subdivision curves.  ...  This is the second of two papers which describe and classify situations which any complete study of interpolation constraints for a recursive subdivision surface needs to consider.  ...  Thanks are due to the American University of Beirut, the Lebanese National Council for Scientific Research, and the Royal Society of London for supporting this work.  ... 
doi:10.1007/s003710100155 fatcat:m5vbcowrdfgaflpw6df7ti5dhq

A survey of subdivision-based tools for surface modeling [chapter]

Ioana Boier-Martin, Denis Zorin, Fausto Bernardini
2005 Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing  
Subdivision surfaces have emerged as a powerful representation for surface modeling and design.  ...  In this paper we survey existing subdivision-based modeling methods with emphasis on interactive tools for styling and decoration of 3D models.  ...  The cutting process takes advantage of the natural parameterization of subdivision surfaces over their control meshes (see section 2) to approximate the intersection curve by alternating so-called Snapping  ... 
doi:10.1090/dimacs/067/01 dblp:conf/dimacs/Boier-MartinZB03 fatcat:5pqdfabmvzbj5aktapk2enku2u

Conversion of trimmed NURBS surfaces to Catmull–Clark subdivision surfaces

Jingjing Shen, Jiří Kosinka, Malcolm A. Sabin, Neil A. Dodgson
2014 Computer Aided Geometric Design  
By integrating the trimming curve as part of the desired limit surface boundary, our conversion can produce gap-free models.  ...  We take a NURBS surface and its trimming curves as input, from this we automatically compute a base mesh, the limit surface of which fits the trimmed NURBS surface to a specified tolerance.  ...  In this way, along each boundary of the subdivision surface, the boundary curve and the first derivative across the boundary are set up using both the original NURBS surface and intersection curves B as  ... 
doi:10.1016/j.cagd.2014.06.004 fatcat:dpx2epa3bnfbhgnze77y7fbfoy

Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design

Ahmad H. Nasri
2000 Computer Aided Geometric Design  
We formulate this problem and establish a general theory which has a number of applications in CAGD such as the generation of subdivision surfaces through predefined arbitrary network of curves.  ...  One of the main advantages of the proposed scheme is that the regions of the surface between the interpolated curves do not have to be rectangular-a limitation of existing tensor-product based CAD systems  ...  Acknowledgements This work was supported by a research grant from the American University of Beirut. The author would like to thank Prof. Abdallah Lyzzaik for his valuable comments.  ... 
doi:10.1016/s0167-8396(00)00015-7 fatcat:3dnlrk4ipvdutlpwxuryf5r3mq

Lofting curve networks using subdivision surfaces

S. Schaefer, J. Warren, D. Zorin
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface.  ...  Lofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface.  ...  This research was supported in part by NSF awards CCR-0093390, DMS-0138445, ACI-997814, ITR-0205671 and IBM University Partnership Award.  ... 
doi:10.1145/1057432.1057447 fatcat:q7afrdfw7ve4jalltd6e2on33i

Trimming implicit surfaces

Galina Pasko, Alexander Pasko
2004 The Visual Computer  
The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm.  ...  These twodimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface.  ...  The comments by an anonymous reviewer helped improve the paper.  ... 
doi:10.1007/s00371-004-0250-6 fatcat:b6esu3kd3rcshkb3vpcxpelmoq

Modeling on triangulations with geodesic curves

Dimas Martínez Morera, Paulo Cezar Carvalho, Luiz Velho
2008 The Visual Computer  
The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive the convex hull property of geodesic Bézier curves.  ...  In the first part of this paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations.  ...  VISGRAF Laboratory is sponsored by CNPq, FAPERJ, FINEP and IBM Brazil.  ... 
doi:10.1007/s00371-008-0298-9 fatcat:fod52va6zjcynacenhuxlpt3nu

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.  ...  Other generous support was provided by the Sloan Foundation, the Okawa Foundation, an IBM partnership award, and Alias|wavefront.  ... 
doi:10.1145/304012.304033 dblp:conf/sma/KhodakovskyS99 fatcat:uppb464fvfgctn3nzqe4nm2tue

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
An algorithm for the local interpolation of a cubic curve mesh by a piecewise bi quartic C 1 surface is described.  ...  The boundary curves of a patch are polynomial curves which h a ve their B ezier polygon given by the boundary polygons of the control net of the patch.  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

Geodesic Bezier Curves: a Tool for Modeling on Triangulations

Dimas Martinez Morera, Paulo Cezar Carvalho, Luiz Velho
2007 Computer Graphics and Image Processing (SIBGRAPI), Proceedings of the Brazilian Symposium on  
Modeling on the surface of a cow. From left: the control polygons of some curves and a C 1 spline, the corresponding curves, a region is filled and other is trimmed, final result.  ...  As a natural generalization of Bézier curves, the new curves are as smooth as possible. We discuss the construction of C 0 and C 1 piecewise Bézier splines.  ...  VISGRAF Laboratory is sponsored by CNPq, FAPERJ, FINEP and IBM Brazil.  ... 
doi:10.1109/sibgra.2007.4368170 fatcat:qefiwon6qban3ljok44e2hfyze

Geodesic Bezier Curves: a Tool for Modeling on Triangulations

Dimas Martinez Morera, Paulo Cezar Carvalho, Luiz Velho
2007 XX Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI 2007)  
Modeling on the surface of a cow. From left: the control polygons of some curves and a C 1 spline, the corresponding curves, a region is filled and other is trimmed, final result.  ...  As a natural generalization of Bézier curves, the new curves are as smooth as possible. We discuss the construction of C 0 and C 1 piecewise Bézier splines.  ...  VISGRAF Laboratory is sponsored by CNPq, FAPERJ, FINEP and IBM Brazil.  ... 
doi:10.1109/sibgrapi.2007.38 dblp:conf/sibgrapi/MoreraCV07 fatcat:onccpu3eoncm5npkpkzloojmp4

Lofting Curve Networks using Subdivision Surfaces [article]

S. Schaefer, J. Warren, D. Zorin
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface.  ...  Lofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface.  ...  Acknowledgements This research was supported in part by NSF awards CCR-0093390, DMS-0138445, ACI-997814, ITR-0205671 and IBM University Partnership Award.  ... 
doi:10.2312/sgp/sgp04/105-116 fatcat:g7jpkgpqf5hczb35tdfgo4uarq

Restructuring surface tessellation with irregular boundary conditions

Tsung-Hsien Wang, Ramesh Krishnamurti, Kenji Shimada
2014 Frontiers of Architectural Research  
In this paper, the surface tessellation problem is explored, in particular, the task of meshing a surface with the added consideration of incorporating constructible building components.  ...  When a surface is tessellated into discrete counterparts, certain unexpected conditions usually occur at the boundary of the surface, in particular, when the surface is being trimmed.  ...  Boundary-driven curve intersection When boundary-driven curves (BDCurves) are created, they are grouped by origin, namely, by the directions along which they were derived.  ... 
doi:10.1016/j.foar.2014.06.001 fatcat:r7t6s5n645cxdjgrp62plkwew4

Subdivided Linear and Curved Meshes Preserving Features of a Linear Mesh Model

Albert Jiménez-Ramos, Abel Gargallo-Peiró, Xevi Roca
2020 Zenodo  
The examples show that it is possible to refine and obtain smooth curves and surfaces while preserving sharp features determined by vertices and polylines.  ...  There is no need for underlying target geometry, it is only needed a straight- edged mesh with boundary entities marked to characterize the geometry features, and a list of features to recast.  ...  The work of the third author has been partially supported by the Spanish Ministerio de Economía y Competitividad under the personal grant agreement RYC-2015-01633. Special thanks to Eloi Ruiz-Gironés.  ... 
doi:10.5281/zenodo.3653357 fatcat:ruvxwscd4fh5ri5c46r7iipzya
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