Browse > Article
http://dx.doi.org/10.4134/CKMS.2002.17.2.331

GEOMETRIC CONIC SPLINE APPROXIMATION IN CAGD  

Ahn, Young-Joon (Department of Mathematics Ajou University)
Publication Information
Communications of the Korean Mathematical Society / v.17, no.2, 2002 , pp. 331-347 More about this Journal
Abstract
We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.
Keywords
conic spline; Chebyshev approximation; geometric Hermite interpolation; offset curve; convolution curve;
Citations & Related Records
연도 인용수 순위
  • Reference
1 /
[] / Curves and Surfaces for Computer Aided Geometric Design
2 Curvatures of the quadratic rational Bezier curves /
[] / Computers and Mathematics with Applications   DOI   ScienceOn
3 An O(h²ⁿ) Hermite approximation for conic sectons /
[ M.Floater ] / Computer Aided Geometric Design   DOI   ScienceOn
4 Best approximations of parametric curves by spline /
[ W.L.F.Degen;T.Lyche(ed.);L.L.Schumaker(ed.) ] / Mathematical Methods in CAGD and Image Processing
5 Good degree reduction of Bezier curves using Jacobi polynomials /
[ H.J.Kim;Y.J.Ahn ] / Computers and Mathematics with Applications   DOI   ScienceOn
6 Generation of configuration space obstales: The case of moving algebraic curves /
[ C.Bajaj;M.S.Kim ] / Algorithmica   DOI
7 High accuracy geometric Hermite interpolation /
[ C.de Boor;K.Hollig;M.Sabin ] / Computer Aided Geometric Design
8 The approximation of a composite Bezier cubic curve by a composite Bezier quadratic curve /
[ M.G.Cox;P.M.Harris ] / IMA J.Numerical Analysis
9 High accurate rational approximation of parametric curves /
[] / Computer Aided Geometric Design   DOI   ScienceOn
10 The rational Bezier representation for conics /
[ E.T.Lee ] / Geometric modeling : algorithms and new trends
11 Conic approximation of conic offsets /
[] / J.Symbolic Computation   DOI   ScienceOn
12 Approximating smooth planar curves by arc splines /
[ D.S.Meek;D.J.Walton ] / J.Computational and Applied Mathematics   DOI   ScienceOn
13 /
[ D.Braess ] / Nonlinear Approximation Theory
14 Geometric continuity /
[ J.A.Gregory;T.Lyche(ed.);L.L.Schumaker(ed.) ] / Mathematical Methods in CAGD
15 Approximation of circular arcs by Bezier curves /
[ Y.J.Ahn;H.O.Kim ] / J.Computational and Applied Mathematics   DOI   ScienceOn
16 Chebychev approximation of plane curves by splines /
[ E.F.Eisele ] / J.Approximation Theory   DOI   ScienceOn
17 Curvature continuity and offsets for piecewise conics /
[ G.Farin ] / ACM Trans.Graph.   DOI   ScienceOn
18 Techniques for conic splines /
[ T.Pratt ] / Proceedings of SIGGRAPH 85
19 Planar curve interpolation by piecewise conics of arbitrary type /
[ R.Schaback ] / Constructive Approximation   DOI   ScienceOn
20 /
[ J.K.Rice ] / The Approximation of Functions, Vol.Ⅱ - Advanced Topics
21 G¹arc spline approximations of quadratic Bezier curves /
[ Y.J.Ahn;H.O.Kim;K.Y.Lee ] / Computer-Aided Design
22 Conic Approximation of planar curves /
[ Y.J.Ahn ] / Computer-Aided Design   DOI   ScienceOn
23 Curve fitting with conic splines /
[ T.Pavlidis ] / ACM Trans.Graph.   DOI
24 Analysis of the offset to a parabola /
[ R.T.Farouki ] / Computer Aided Geometric Design   DOI   ScienceOn