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NURBS surface fitting using orthogonal coordinate transform for rapid product development

Seok-Hyung Bae, Byoung K. Choi
2002 Computer-Aided Design  
Presented in the paper is a method of ®tting NURBS surfaces for rotational freeform shapes: (1) cloud-of-points data (COP-data) representing a rotational freeform shape are transformed into an orthogonal  ...  Compared to the existing'direct' ®tting methods, the proposed method has some distinctive advantages: it provides a natural means to parameterization, enables to recover exact NURBS geometry when the COP-data  ...  Acknowledgements The Ministry of Science and Technology of Korean government has supported the research.  ... 
doi:10.1016/s0010-4485(01)00198-1 fatcat:jir2xtpdffh4lie3adxlve3vwe

An effective third-order local fitting patch and its application

Zhong Li, Brian Barsky, Xiaogang Jin
2009 2009 IEEE International Conference on Shape Modeling and Applications  
Furthermore, we define the principal geodesic torsion of each vertex on the mesh model and estimate it through this local fitting patch.  ...  Compared to other estimation algorithms, this weighted bicubic B zier patch more accurately obtains the normal vector and curvature estimation of a triangular mesh model.  ...  ACKNOWLEDGEMENTS The authors gratefully appreciate the anonymous referees for the useful comments and suggestions which improved this paper considerably.  ... 
doi:10.1109/smi.2009.5170157 dblp:conf/smi/LiBJ09 fatcat:gzz332vvxvb57jwj3y45tt6d24

A Low Dimensional Framework for Exact Polygon-to-Polygon Occlusion Queries [article]

Denis Haumont, Otso Makinen, Shaun Nirenstein
2005 Symposium on Rendering  
In this paper, we present a new algorithm that simplifies implementation and computation by operating only on the skeletons of the polyhedra instead of the multi-dimensional face lattice usually used for  ...  Despite the importance of from-region visibility computation in computer graphics, efficient analytic methods are still lacking in the general 3D case.  ...  Debeir for all their help. This work is partially supported by a grant of the 'Région wallonne' (Belgium).  ... 
doi:10.2312/egwr/egsr05/211-222 fatcat:n3jy67r25zbj3ou7q6tow7q7rq

Marginal Independence Models [article]

Tobias Boege, Sonja Petrović, Bernd Sturmfels
2021 arXiv   pre-print
We develop the numerical algebra of parameter estimation, using both Euclidean distance and maximum likelihood, and we present a comprehensive database of small models.  ...  We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex.  ...  She is eternally grateful for the hospitality of her hosts and everyone at the institute.  ... 
arXiv:2112.10287v1 fatcat:voihufwtcncovju6nky4t42gxm

CAD-based computer vision: from CAD models to relational graphs

P.J. Flynn, A.K. Jain
1991 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we focus on the topic of mode&building for 3-D objects.  ...  If a solid model of an object to be recognized is already available in a manufacturing database, then we should be able to infer automatically a model appropriate for  ...  ACKNOWLEDGMENT The authors wish to thank the anonymous referees for 1271 very valuable comments, and Dr. P. Besl for providing scanconversion software. PI  ... 
doi:10.1109/34.67642 fatcat:gzvqjviklrcqfknqu2fkerhzgm

An Active Contour for Range Image Segmentation

Khaldi Amine
2012 Signal & Image Processing An International Journal  
In this paper a new classification of range image segmentation method is proposed according to the criterion of homogeneity which obeys the segmentation, then, a deformable modeltype active contour "Snake  ...  Abstract -In this paper a new classification of range image segmentation method is proposed according to the criterion of homogeneity which obeys the segmentation, then, a deformable model-type active  ...  and the major inconvenient is the appearance of regions (segments) parasites. − Maitre and Hügli [13] have a fusion method based on normal (gradient) to the surface normal are calculated on the facets  ... 
doi:10.5121/sipij.2012.3302 fatcat:yeutcvcs4fccnopwe7owd3rxje

The Method of Archimedes in the geometry of quadrics [article]

Ion I. Dinca
2006 arXiv   pre-print
Interestingly enough, The Method of Archimedes (lost for 7 centuries and rediscovered in the same year as Bianchi's discovery (1906), so unknown to Bianchi) applies word by word in both spirit and the  ...  (isometric) to quadrics and surfaces geometrically linked to these, thus providing a wealth of integrable systems and projective transformations of their solutions.  ...  Note that the method at the level of points of facets was known to Bianchi and Lie; however, they had never used the full method, at the level of the planes of the facets too (for this reason the 'of course  ... 
arXiv:math/0612375v1 fatcat:qyt6legcg5bo7p4mnnvbffvty4

On nondegeneracy of curves [article]

Wouter Castryck, John Voight
2008 arXiv   pre-print
A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate.  ...  We also prove that the locus of nondegenerate curves inside the moduli space of curves of fixed genus g > 1 is min(2g+1,3g-3)-dimensional, except in case g=7 where it is 16-dimensional.  ...  This is a copy of [31, Figure 2 ], we include the list here for sake of self-containedness. It is an essential ingredient in the proofs of Lemma 4.1 and Proposition 9.1.  ... 
arXiv:0802.0420v2 fatcat:coq45mwkufemthsuguguprc5ja

Recognition of Curved Surfaces From "One-Dimensional" Tactile Data

Rinat Ibrayev, Yan-Bin Jia
2012 IEEE Transactions on Automation Science and Engineering  
For every surface model in a given database, a lookup table is constructed to store principal curvatures precomputed at points of discretization on the surface.  ...  This paper presents a method for recognition of 3D objects with curved surfaces from linear tactile data.  ...  ACKNOWLEDGMENT The authors thank J. Tian for generating the tactile data used in our experiments.  ... 
doi:10.1109/tase.2012.2194143 fatcat:fdpjpioknrfv7nvl7zsanevbaq

Knowledge-based deformable surface model with application to segmentation of brain structures in MRI

Amir Ghanei, Hamid Soltanian-Zadeh, Kost Elisevich, Jeffrey A. Fessler, Milan Sonka, Kenneth M. Hanson
2001 Medical Imaging 2001: Image Processing  
These data are combined together with a priori knowledge using Bayes method to estimate a probability density function (pdf) for the length of the structure in sagittal direction.  ...  We have developed a knowledge-based deformable surface for segmentation of medical images.  ...  ACKNOWLEDGEMENT The authors would like to thank Dr. Suresh Patel and Dr. Cylen Javidan-Nejad from Henry Ford Health System for their help in evaluation of the model.  ... 
doi:10.1117/12.431106 dblp:conf/miip/GhaneiSEF01 fatcat:wftwr3ixvnfillujnybi7jnzni

Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data [chapter]

Eric Albin, Ronnie Knikker, Shihe Xin, Christian Oliver Paschereit, Yves D'Angelo
2017 Lecture Notes in Computer Science  
An implicit method based on high-order differentiation to determine the mean, Gaussian and principal curvatures of implicit surfaces from a three-dimensional scalar field is presented and assessed.  ...  The method also determines normal vectors and principal directions.  ...  The first explicit method is classical and consists in fitting full quadric [12, 22] .  ... 
doi:10.1007/978-3-319-67885-6_1 fatcat:n4lyx4m35bhdvn5jn62dtckzdm

The Schläfli Fan [article]

Michael Joswig, Marta Panizzut, Bernd Sturmfels
2020 arXiv   pre-print
It reveals all possible patterns of lines on tropical cubic surfaces, thus serving as a combinatorial base space for the universal Fano variety.  ...  This article develops the relevant theory and offers a blueprint for the analysis of big data in tropical geometry.  ...  We thank Sara Lamboglia, Yue Ren and Emre Sertöz for their comments on a manuscript version of this article.  ... 
arXiv:1905.11951v2 fatcat:4d4xj4azzrh6dcm6gtvgwigeq4

Consistent topographic surface labelling

Richard C. Wilson, Edwin R. Hancock
1999 Pattern Recognition  
The key ingredient is to develop a constraint dictionary for the feasible con"gurations of the topographic labels that can occur on neighbouring faces of the surface mesh.  ...  Firstly, we develop a statistical model which allows label probabilities to be assigned to the di!erent topographic classes.  ...  a cubic patch.  ... 
doi:10.1016/s0031-3203(98)00146-0 fatcat:dab7srebznd33pggdpbbz6kirm

Refining surface curvature with relaxation labeling [chapter]

Richard C. Wilson, Edwin R. Hancock
1997 Lecture Notes in Computer Science  
In the first instance, we demonstrate how H ? K surface labelling can be realised using dictionary-based probabilistic relaxation.  ...  In the first instance, we demonstrate how H ? K surface labelling can be realised using dictionary-based probabilistic relaxation.  ...  Firstly, a local tangent plane is extracted by identifying the principal component axes for the surface point distribution over a support neighbourhood, Next, the plane-fit is refined using a cubic patch  ... 
doi:10.1007/3-540-63507-6_196 fatcat:2omkvsvsend2dge4twk2vfap44

The geometry of Siegel modular varieties [article]

K. Hulek, G. K. Sankaran
2000 arXiv   pre-print
This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces.  ...  Jacobi forms to modular forms; projective models of some special Siegel modular 3-folds; non-principally polarized abelian surfaces; and constructing degenerating families of abelian varieties.  ...  Even for principal polarization it may be necessary to make a base change if we want the central fibre P 0 to have no non-reduced components.  ... 
arXiv:math/9810153v2 fatcat:m5tytytkgvbufdzzuvielcnlsm
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