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G n filling orbicular N-sided holes using periodic B-spline surfaces

KanLe Shi, JunHai Yong, JiaGuang Sun, Jean-Claude Paul
2011 Science China Information Sciences  
The orbicular N -sided hole filling problem is usually introduced by filleting an end-point of a part with large radius.  ...  Then we compute the control points of the periodic B-spline surface using the sufficient G n continuity condition on the pole and the algorithm of extending parametric surfaces.  ...  The second category uses an energy minimization or constrained-optimization method to solve trimmed surfaces.  ... 
doi:10.1007/s11432-011-4248-1 fatcat:g3rdwexiejecxeru4la6ha24km

Multi-sided B-spline surfaces over curved, multi-connected domains

Márton Vaitkus, Tamás Várady, Péter Salvi, Ágoston Sipos
2021 Computer Aided Geometric Design  
A GBS patch can connect to tensorproduct B-spline surfaces with arbitrary G m continuity. It supports ribbons not only along the perimeter loop, but also around holes in the interior of the patches.  ...  Our implementation is based on a computationally efficient discretization.  ...  The base surface of the second model ( Fig. 1b) has several concave B-spline boundaries.  ... 
doi:10.1016/j.cagd.2021.102019 fatcat:5ne6hxdlbfep5d3yivc3miaobm

Reverse Engineering Point Clouds to Fit Tensor Product B-Spline Surfaces by Blending Local Fits [article]

Lavanya Sita Tekumalla, Elaine Cohen
2014 arXiv   pre-print
As our second contribution, we propose an end-to-end framework for smoothing, hole filling, parameterization, knot selection and B-spline fitting that addresses these issues, works robustly with large  ...  As our main contribution, we present a new method to obtain a tensor product B-spline representation from point cloud data by fitting surfaces to appropriately segmented data.  ...  We propose an end-to-end framework to reverse engineer point clouds with noisy data and holes in the data and fit tensor product B-spline surfaces that involves smoothing, hole filling, parameterization  ... 
arXiv:1411.5993v1 fatcat:kuegx3kvcnh7pj26huw2ydhw5i

Designing B-Spline Surfaces with Haptics Based on Variational Technique

Xiaodong Liu
2014 Computer-Aided Design and Applications  
Based on an energy minimization method or variational B-Spline technique, the paper presents the technique of using a haptic device to design B-Spline surfaces.  ...  ., points and curves, and in real time, the system generates energy-minimization B-Spline surfaces in response to haptic operations.  ...  Fig. 3 : 3 Waterproof surfaces created by VBS kernel: (a)/(b) each boundary consists of n curves. VBS kernel uses one single rectangular B-Spline surface to fill the hole.  ... 
doi:10.1080/16864360.2014.881177 fatcat:ir3pzkljenbinmnw7ky6coxfri

Symmetry and template guided completion of damaged skulls

Xin Li, Zhao Yin, Li Wei, Shenghua Wan, Wei Yu, Maoqing Li
2011 Computers & graphics  
to fill holes.  ...  We propose a skull completion framework based on symmetry and surface matching.  ...  to fill holes on M.  ... 
doi:10.1016/j.cag.2011.01.015 fatcat:pj5qxcibbraojonsmcsxzfy2eu

Design of Functionally Graded Lattice Structures using B-splines for Additive Manufacturing

Archak Goel, Sam Anand
2019 Procedia Manufacturing  
This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC).  ...  Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, information based on a real time basis and, necessarily, much more efficient.  ...  size of B is equal to m+1 n Column size of B is equal to n+1 N B-spline surface basis functions along parameter u M B-spline surface basis functions along parameter v Unit cell design Fig. 1 . 1 Fig  ... 
doi:10.1016/j.promfg.2019.06.193 fatcat:7s6wk725kffyve6s72js37akc4

The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models

Dominik Schillinger, Martin Ruess
2014 Archives of Computational Methods in Engineering  
femur bone, the analysis of volumetric structures based on CAD boundary representations, and the isogeometric treatment of trimmed NURBS surfaces.  ...  These include the finite cell method with B-spline and NURBS basis functions, the treatment of geometric nonlinearities for large deformation analysis, the weak enforcement of boundary and coupling conditions  ...  The results for the plate with a spherical hole demonstrate that the finite cell method works very well with both integrated Legendre and B-spline basis functions and that both p-and B-spline versions  ... 
doi:10.1007/s11831-014-9115-y fatcat:h47y5t7jivdnra6pznl7tdnija

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.  ...  The new construction, based on reparameterization of the bi-2 spline data, yields well-distributed highlight lines for a range of challenging test data.  ...  First, the methods listed are not compatible with the CAD-industry's NURBS standard. Second, most CAD packages follow a different paradigm to fill multi-sided holes.  ... 
doi:10.1016/j.cag.2014.09.004 fatcat:53igukekaze3dbxuqayfvlnusy

Reconstruction of Branching Surface and Its Smoothness by Reversible Catmull-Clark Subdivision [chapter]

Kailash Jha
2009 Lecture Notes in Computer Science  
In branching, a particular layer has more than one contour, corresponds with the contour at the adjacent layer.  ...  In the current research a new algorithm has been developed to get surface from the contours having branches and a final smooth surface is obtained by reversible Catmull-Clark Subdivision.  ...  A brief overview of branching problems has been explained in reference [19] , which involves skinning, trimming and hole filling.  ... 
doi:10.1007/978-3-642-01973-9_85 fatcat:jke7aywmhfdj7edxauuiw2pgye

Condition number analysis and preconditioning of the finite cell method

F. de Prenter, C.V. Verhoosel, G.J. van Zwieten, E.H. van Brummelen
2017 Computer Methods in Applied Mechanics and Engineering  
Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells.  ...  Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC).  ...  B-spline bases.  ... 
doi:10.1016/j.cma.2016.07.006 fatcat:bugv5rma2zbz7okwlookclhjxi

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  
In this paper we survey existing subdivision-based modeling methods with emphasis on interactive tools for styling and decoration of 3D models.  ...  They address important limitations of traditional spline-based methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations.  ...  Surfaces obtained after trimming and embossing with sharp features using the method described in [BMZB02] .  ... 
doi:10.1090/dimacs/067/01 dblp:conf/dimacs/Boier-MartinZB03 fatcat:5pqdfabmvzbj5aktapk2enku2u

Fitting smooth surfaces to dense polygon meshes

Venkat Krishnamurthy, Marc Levoy
1996 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques - SIGGRAPH '96  
In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product B-spline surface patches with accompanying displacement maps.  ...  Finally, we fit a tensor product B-spline surface to the grid. We also output a displacement map for each mesh section, which represents the error between our fitted surface and the spring grid.  ...  Brian Curless for his range image integration software, David Addleman and George Dabrowski of Cyberware for the use of a scanner, Lincoln Hu and Christian Rouet of Industrial Light and Magic for advice on  ... 
doi:10.1145/237170.237270 dblp:conf/siggraph/KrishnamurthyL96 fatcat:m55rjqmkengdnnvn6ah7ox73ey

Review of heterogeneous material objects modeling in additive manufacturing

Bin Li, Jianzhong Fu, Jiawei Feng, Ce Shang, Zhiwei Lin
2020 Visual Computing for Industry, Biomedicine, and Art  
Prevalent heterogeneous object representations are generally categorized based on the different expression or data structure employed therein, and the state-of-the-art of process planning procedures for  ...  AM is reviewed via different vigorous solutions for part orientation, slicing methods, and path planning strategies.  ...  [62] , a volumetric representation was proposed for geometric modeling based on trimmed B-spline.  ... 
doi:10.1186/s42492-020-0041-6 pmid:32240443 fatcat:dinaoei6yngc5eza4t6feannny

Interactive Shape Modeling and Deformation [article]

Olga Sorkine, Mario Botsch
2009 Eurographics State of the Art Reports  
As such, our class is intended for both researchers and practitioners, helping to sift through the large body of work on interactive modeling by a systematic, hands-on overview.  ...  We focus on the essence of the underlying theory and principles, as well as the practical aspects of algorithm design and development involved in interactive shape editing.  ...  Parts of our course notes are based on the notes of a more general course on Geometric Modeling with Polygonal Meshes [BPK * 08] co-authored with them.  ... 
doi:10.2312/egt.20091068 fatcat:cmsgz7vlhjej7hh5wumxlpm4na

Construction of fair surfaces over irregular meshes

Geir Westgaard, Horst Nowacki
2001 Proceedings of the sixth ACM symposium on Solid modeling and applications - SMA '01  
The choice is based on the desired shape character.  ...  The set of available fairness criteria is able to measure surface characteristics related to curvature, variation of curvature, and higher order surface derivatives based on integral functionals of quadratic  ...  polygonal holes in the surface or mesh with proper edge joint, since the irregularity of the mesh can be ascribed to arbitrary n-sided mesh cells.  ... 
doi:10.1145/376957.376969 dblp:conf/sma/WestgaardN01 fatcat:viylrmrj7fflno5hcxuwmibch4
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