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Chanderjit Bajaj - One of the best experts on this subject based on the ideXlab platform.

  • algebraic surface design with Hermite Interpolation
    ACM Transactions on Graphics, 1992
    Co-Authors: Chanderjit Bajaj
    Abstract:

    This paper presents an efficient algorithm called Hermite Interpolation, for constructing low-degree algebraic surfaces, which contain, with C 1 or tangent plane continuity, any given collection of points and algebraic space curves having derivative information. Positional as well as derivative constraints on an implicitly defined algebraic surface are translated into a homogeneous linear system, where the unknowns are the coefficients of the polynomial defining the algebraic surface. Computaional details of the Hermite Interpolation algorithm are presented along with several illustrative applications of the Interpolation technique to construction of joining or blending surfaces for solid models as well as fleshing surfaces for curved wire frame models. A heuristic approach to interactive shape control of implicit algebraic surfaces is also given, and open problems in algebraic surface design are discussed.

H. Takata - One of the best experts on this subject based on the ideXlab platform.

Seungpil Jeong - One of the best experts on this subject based on the ideXlab platform.

  • Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics
    Abstract and Applied Analysis, 2012
    Co-Authors: Seungpil Jeong
    Abstract:

    We present an algorithm for Hermite Interpolation using Mobius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solve Hermite Interpolation problems, since their lack of parameters makes the problems overdetermined. In this paper, we show that, for each Mobius transformation, we can introduce an extra parameter determined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex plane . Mobius transformations preserve the PH property of PH curves and are biholomorphic. Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics. We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop. We demonstrate the improved stability of these new interpolants compared with PH quintics.

  • Hermite Interpolation using ph curves with undetermined junction points
    Bulletin of The Korean Mathematical Society, 2012
    Co-Authors: Jae Hoon Kong, Seungpil Jeong
    Abstract:

    Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general C 1 Hermite Interpolation problems. We also extend the UJP method to solve C 2 Hermite Interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with C 1 junction points. Further generalizing the UJP method, we go on to solve C 2 Hermite Interpolation problems using two PH quintics with a C 1 junction point, and we also show the possibility of applying the modied UJP method to G 2 ( C 1 ) Hermite Interpolation.

  • c1 Hermite Interpolation with simple planar ph curves by speed reparametrization
    Computer Aided Geometric Design, 2008
    Co-Authors: Jae Hoon Kong, Seungpil Jeong
    Abstract:

    We introduce a new method of solving C^1 Hermite Interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t-c)^2^n^+^1+d. Next, we introduce a speed reparametrization. Finally, we show that, for C^1 Hermite data, we can use PH curves of type K(t-c)^2^n^+^1+d or strongly regular PH quintics satisfying the G^1 reduction of C^1 data, and use these curves to solve the original C^1 Hermite Interpolation problem.

Claus Schneider - One of the best experts on this subject based on the ideXlab platform.

K. Narikiyo - One of the best experts on this subject based on the ideXlab platform.