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Computing the minimum distance between two Bézier curves
2009
Journal of Computational and Applied Mathematics
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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
2000
Computer Aided Geometric Design
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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]
2002
Lecture Notes in Computer Science
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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
1994
Fundamentals of Computer Graphics
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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
1993
Proceedings of the 20th annual conference on Computer graphics and interactive techniques - SIGGRAPH '93
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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
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[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
2019
Electronics
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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
2020
Algorithms
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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
2007
2007 IEEE International Conference on Image Processing
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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
2019
Journal of Mathematics and Informatics
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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
1991
Computer-Aided Design
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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
2008
Journal of Computational and Applied Mathematics
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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
1994
Procedings of the British Machine Vision Conference 1994
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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
2011
Presence - Teleoperators and Virtual Environments
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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
2003
Proceedings of International Conference on Leading Edge Manufacturing in 21st century LEM21
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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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