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Infinite Interpolation on Triangles
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    Abstract:

    Constructing triangle surface which interpolates the boundary curve and cross-boundary slopes on a triangle is the basic problem in computer aided geometric design, computer graphics and so on. This problem is called infinite interpolation on triangle. In this paper, a survey on the existing methods of constructing infinite interpolation surfaces on triangles is given, and a comparison is made between the methods by using examples. The open problems in the existing methods of infinite interpolation on triangles are discussed.

    Reference
    [1]Barnhill RE,Birkhoff G,Gordon WJ.Smooth interpolation in triangles.Journal of Approximation Theory,1973,8:114-128.
    [2]Barnhill RE,Gregory JA.Compatible smooth interpolation in triangles.Journal of Approximation Theory,1975,15:214-225.
    [3]Barnhill RE,Gregory JA.Polynomial interpolation to boundary data on triangles.Mathematics of Computation,1975,29:726-735.
    [4]Gregory JA.Smooth interpolation without twist constraints.In:Barnhill RE,Riesenfeld RF,eds.Computer Aided Geometric Design.New York:Academic Press,1974.71-88
    [5]Gregory JA.A blending function interpolant for triangles,In:Multivariate Approximation.New York:Academic Press,1978.279-287.
    [6]Charrot P,Gregory JA.A pentagonal surface patch for computer aided geometric design.Computer Aided Geometric Design,1984,1(1):87-94
    [7]Gregory JA.C1 rectangular and non-rectangular surface patches.In:Barnhill RE,Boehm W,eds.Surfaces in Computer Aided Geometric Design.Amsterdam:North-Holland,1983.25-33.
    [8]Sabin MA.Parametric surface equations for non-rectangular regions.BAC Weybridge VTO/MS/147,1968.
    [9]Sabin M.Non-Rectangular surface patches suitable for inclusion in a B-spline surface.In:Proc.of the Eruographics'83.North-Holland,1983.57-69.
    [10]Sabin MA.Some negative results in N-sided patches.Computer Aided Design,1986,18(1):38-44.
    [11]Hosaka M,Kimura F.Non-Four-Sided patch expressions with control points.Computer Aided Geometric Design,1984,1:75-86
    [12]Gregory JA.N-Sided surface patches.In:Gregory JA,ed.The Mathematics of Surfaces.Oxford:Oxford University Press,1986,217-232.
    [13]Varady T.Survey and new results in n-sided patch generation.In:Martin RR,ed.The Mathematics of Surfaces II.Oxford:Oxford University Press,1987.203-235.
    [14]Nielson GM.The side vertex method for interpolation in triangles.Journal of Approximation Theory,1979,25:318-336.
    [15]Hagen H.Geometric surface patches without twist constraints.Computer Aided Geometric Design,1986,3(3):179-184.
    [16]Hagen H.Curvature continuous triangular interpolants.In:Lyche T,Schumaker L,eds.Methods in CAGD.Oslo:Academic Press,1989.373-384.
    [17]Nielson GM.A transfinite,visually continuous,triangular interpolant.In:Farin G,ed.Geometric Modeling,Applications and New Trends.Philadelphia:SIAM,1987.235-246.
    [18]Wang CY.C1 rational interpolation over an arbitrary triangle.Computer Aided Design,1983,15(1):33-36.
    [19]Hosaka M,Kimura F.Non-Four-Sided patch expressions with control points.Computer Aided Geometric Design,1984,1:75-86.
    [20]Loop C,DeRose TD.A multisided generalization of Bezier surfaces.ACM Trans.on Graphics,1989,8(3):204-234.
    [21]Loop C,DeRose TD.Generalized B-spline surfaces of arbitrary topology.Proc.Siggraph'90,1990,24(4):347-356
    [22]Warren J.Creating multisided rational Bezier surfaces using base points.ACM Trans.on Graphics,1992,11(2):127-139.
    [23]Foley TA,Opitz K.Hybrid cubic Bézier triangle patches.In:Lyche T,Schumaker L,eds.Mathematical Methods for Computer Aided Geometric Design II.Academic Press,1992.275-286.
    [24]Kuriyama S.Surface modeling with an irregular network of curves via sweeping and blending.Computer Aided Design,1994,26(8):597-606.
    [25]Varady T.Overlap patches:A new scheme for interpolating curve networks with n-sided regions.Computer Aided Geometric Design,1991,8(1):7-27.
    [26]Zhang C,Agui T,Nagahashi H,Nagao T.A new method for smooth interpolation without twist constraints.IEICE Trans.on Information and Systems,1993,E76-D(2):243-250.
    [27]Zhang C,Cheng F.Triangular patch modeling using combination method.Computer Aided Geometric Design,2002,19(8):645-662.
    [28]Yang XQ,Zhang CM,Wang JY.C1 polynomial interpolation surface of degree 4 on a triangle.Journal of Computer-Aided Design and Computer Graphics,2003,15(5):583-587 (in Chinese with English abstract).
    [29]Zhang CM,Ji XH,Yang XQ.Constructing triangular patch by basic approximation operator plus additional interpolation operator.Science in China Series F,2005,48(2):263-272.
    [30]Beier KP,Chen Y.The highlight-line algorithm for real-time surface-quality assessment.Computer-Aided Design,1994,26(4):268-278.
    [31]Franke R.A critical comparison of some methods for interpolation of scattered data.Technical Report,NPS-53-79-003,Naval Postgraduate School,1979.
    [32]Lawson CL.Software for C1 surface interpolation.In:Rice JR,ed.Mathematical Software III.New York:Academic Press,1977.161-194.
    [28]杨兴强,张彩明,汪嘉业.三角形域上C1连续的四次插值曲面.计算机辅助设计与图形学学报,2003,15(5):583-587.
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徐琳.三角形域上的超限插值方法.软件学报,2007,18(2):430-441

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History
  • Received:May 18,2006
  • Revised:January 19,2007
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