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Computing the minimum distance between two Bézier curves

Xiao-Diao Chen, Linqiang Chen, Yigang Wang, Gang Xu, Jun-Hai Yong, Jean-Claude Paul
2009 Journal of Computational and Applied Mathematics  
A sweeping sphere clipping method is presented for computing the minimum distance between two Bézier curves.  ...  The initial radius of the sweeping sphere can be set as the minimum distance between an end point and the other curve.  ...  Algorithm for computing the minimum distance between two Bézier curves. Input: Two Bézier curves. Output: The nearest point pair as well as the minimum distance d.  ... 
doi:10.1016/j.cam.2008.10.050 fatcat:hslgchmbrfgvtequygfyaql3xu

Optimal development of doubly curved surfaces

Guoxin Yu, Nicholas M. Patrikalakis, Takashi Maekawa
2000 Computer Aided Geometric Design  
Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed  ...  The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem.  ...  Acknowledgements Funding for this research was obtained in part from the New Industry Research Organization (NIRO), and from the MIT Sea Grant and Department of Ocean Engineering.  ... 
doi:10.1016/s0167-8396(00)00017-0 fatcat:vop5anvflbbrvovvj36hedzira

Inspection Strategies for Complex Curved Surfaces Using CMM [chapter]

R. Wirza, M. S. Bloor, J. Fisher
2002 Lecture Notes in Computer Science  
The accurate measurement of complex surfaces is difficult.  ...  This enables comparison with other surfaces, e.g.. the as-designed surface or the original unworn surface. The measurement of the knee prosthesis was taken as a case study.  ...  The Delaunay triangulation diagrams are constructed and finally, the Bezier interpolation surface is produced, which consists of a set of interpolation points with 1 rnrn space between each of them in  ... 
doi:10.1007/3-540-47789-6_19 fatcat:gfjujd7w3vdatni7s6ttslmj7i

MODELING SCATTERED FUNCTION DATA ON CURVED SURFACES

Chandrajit L. Bajaj, Guoliang Xu
1994 Fundamentals of Computer Graphics  
W e also present t wo di erent techniques for visualizing the graph of the function F.  ...  Our smooth polynomial approximations allows one to additionally control the local geometry of the modeled function F.  ...  Displaying Iso-contours of F on D We display the iso-contours on the domain surface by showing di erent colors in the region between two iso-contours.  ... 
doi:10.1142/9789814503860_0002 fatcat:tdidzpixz5cjvojvbvo4jca3ce

Interval methods for multi-point collisions between time-dependent curved surfaces

John M. Snyder, Adam R. Woodbury, Kurt Fleischer, Bena Currin, Alan H. Barr
1993 Proceedings of the 20th annual conference on Computer graphics and interactive techniques - SIGGRAPH '93  
Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics.  ...  We present an efficient and robust algorithm for finding points of collision between time-dependent parametric and implicit surfaces.  ...  Additional support was provided by NSF (ASC-89-20219), as part of the NSF/DARPA STC for Computer Graphics and Scientific Visualization.  ... 
doi:10.1145/166117.166158 dblp:conf/siggraph/SnyderWFCB93 fatcat:hlhzdwomzfax5d7pidm455gfwy

Page 7284 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
[Jones, Lee Kenneth] (1-LWL); Trutzer, V. (1-LWL) Computationally feasible high-resolution minimum-distance procedures which extend the maximum-entropy method.  ...  In terms of the requirements of computer aided garment design, we put forward a method for curved surface approximation in the mean of least squares.  ... 

Automatic Spray Trajectory Optimization on Bézier Surface

Wei Chen, Junjie Liu, Yang Tang, Huilin Ge
2019 Electronics  
Spray trajectory optimization consists of two parts: spray space path and end-effector moving speed.  ...  Spray the workpiece for Bezier triangular surface modeling and find the best initial trajectory of the spraying robot, establish the appropriate spraying model, plan the appropriate space path, and finally  ...  By the same token, the Bézier curves with the same distance are specified on the Bézier surface (which is the distance between two adjacent painting paths).  ... 
doi:10.3390/electronics8020168 fatcat:w74hzo7y6rcqdisogxtkby55m4

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  
The developed technique utilizes the resultant theory to construct implicit forms of parametric Bézier patches, level sets of which are termed algebraic level sets (ALS).  ...  Boolean compositions of the algebraic level sets are carried out using the theory of R-functions.  ...  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

A Novel Facial Feature Point Localization Method on 3D Faces

Peng Guan, Yaoliang Yu, Liming Zhang
2007 2007 IEEE International Conference on Image Processing  
Bezier Surface is introduced to represent local structure of different feature points and global shape model is utilized to constrain the local search result.  ...  Experimental results based on comparison of our method and curvature analysis show the feasibility and efficiency of the new idea.  ...  Acknowledgement This work is supported by a grant from the National Science Foundation (NSF 60571052), China.  ... 
doi:10.1109/icip.2007.4379248 dblp:conf/icip/GuanYZ07 fatcat:fdldn5aozre7norhdvudc7qxa4

Double Cubic Singular Blend Bézier Surfaces

Peipei Ji, Guicang Zhang, Kai Wang
2019 Journal of Mathematics and Informatics  
Secondly, the properties of two cubic singular Bézier surfaces are studied, and the geometric meaning of the mixed parameters is studied and its influence on the shape of the surface is discussed.  ...  In the end, the splicing conditions of two cubic singular Bézier surfaces in parameter splicing and geometric splicing are presented.  ...  ,ଶ ܲ ଷ,ଷ ሱۛۛۛۛۛሮ are the fixed points of point ߙ ଶ,ଶ .If the four corners of a surface are ܳ , , ܳ ,ଵ , ܳ ଵ, and ܳ ଵ,ଵ , and the directed distance between the two points is recorded by ܲ ଵ ܲ , and If ,  ... 
doi:10.22457/jmi.146av17a4 fatcat:c2ogpoys4naq5bda377zru56ly

Data structures to support Bézier-based modelling

Hanan Samet, Robert E. Webber
1991 Computer-Aided Design  
The low level issues deal with the interaction between the representation of the individual patches and the representation of the collection of patches.  ...  The high level discussion consists of two parts. The first deals with how to maintain the topological integrity of the objects being modelled.  ...  ACKNOWLEDGEMENTS lhe support of the National ~ciem e Foundation under Grant IRI-88-02457 is gratefully acknowledged  ... 
doi:10.1016/0010-4485(91)90086-c fatcat:afcgjlrwircrdc65zidhegjrfm

Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm L2

Qian-Qian Hu, Guo-Jin Wang
2008 Journal of Computational and Applied Mathematics  
And the approximation error of this degree-reduced surface is minimum and can get a precise expression before processing of degree reduction.  ...  The new idea is to use orthonormality of triangular Jacobi polynomials and the transformation relationship between bivariate Jacobi and Bernstein polynomials.  ...  Acknowledgments The authors thank to the referees for their helpful suggestions and comments. This work is supported by the Na-  ... 
doi:10.1016/j.cam.2007.04.022 fatcat:kprehi6fr5fblcu6ogtwhb6fra

SLIME: A new deformable surface

A. J. Stoddart, A. Hilton, J. Illingworth
1994 Procedings of the British Machine Vision Conference 1994  
The method is based on a generalization of biquadratic B-splines, and has a comparable computational cost to methods based on traditional tensor product B-splines.  ...  For example a rectangular grid of control points cannot be evenly distributed over a sphere, and singularities occur at the poles.  ...  Acknowledgements George Matas is acknowledged for the use of his fast and efficient graph library. Paul Hoad is acknowledged for assistance in preparing diagrams using his package Xmgf.  ... 
doi:10.5244/c.8.28 dblp:conf/bmvc/StoddartHI94 fatcat:mtauy66xd5dtbd52hkebn2pswi

Force and Contact Location Shading Methods for Use Within Two- and Three-Dimensional Polygonal Environments

Andrew J. Doxon, David E. Johnson, Hong Z. Tan, William R. Provancher
2011 Presence - Teleoperators and Virtual Environments  
Two haptic shading algorithms were developed to address this issue and successfully extend the use of the CLD to 2D and 3D polygonal environments.  ...  It was found that the addition of contact location feedback significantly increased user sensitivity to edges and that the use of shading algorithms was able to significantly reduce the number of polygons  ...  The authors thank Jaeyoung Park for suggesting a more concise method of expressing the angular fraction used within the 2D algorithm (see Appendix).  ... 
doi:10.1162/pres_a_00074 fatcat:p74o6tsoerh5lidsjk2aemrmae

429 Digital Style Design : Modeling System Based on Highlight Lines

Terukazu Ogoshi, Hideki Aoyama
2003 Proceedings of International Conference on Leading Edge Manufacturing in 21st century LEM21  
Process methods to define an evolute of the shape ofa modified cross section aTe classified according to the changes of the curvature.  ...  This paper deajs with a style design system developed for creating shapes with required highlight lines entered using the computer mouse.  ...  This process is equivaLent to the movement of the highlight line shown by normal line IVi at point P; on the curved surface to point Pj in the review ofthe cross sectional shape of the curved surface shown  ... 
doi:10.1299/jsmelem.2003.797 fatcat:ztug3fp4tvderof4ofekvhlwxu
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