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The Convergence of the Geometric Interpolation Algorithm
CAD Computer Aided Design, 2010The geometric interpolation algorithm is proposed by Maekawa et al. in [Maekawa T, Matsumoto Y, Namiki K. Interpolation by geometric algorithm. Computer-Aided Design 2007;39:313-23]. Without solving a system of equations, the algorithm generates a curve (surface) sequence, of which the limit curve (surface) interpolates the given data points.
Hongwei Lin
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Geometric Hermite Interpolation
Computer Aided Geometric Design, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Klaus Höllig, J. Koch
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On Geometric Interpolation by Polynomial Curves
SIAM Journal on Numerical Analysis, 2004In this paper, geometric interpolation by parametric polynomial curves is considered. Discussion is focused on the case where the number of interpolated points is equal to r + 2, and n=r denotes the degree of the interpolating polynomial curve. The interpolation takes place in $\mathbb R^d$ with d=n.
Jernej Kozak, Emil Žagar
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GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION
International Journal of Modern Physics C, 2009 Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both ...
Kim, Pilwon
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Geometric Hermite Interpolation for Space Curves
Computer Aided Geometric Design, 2001This paper considers the geometric Hermite interpolation for spacial curves by parametric quartic Bézier curve. In additon to position and tangent direction, the curvature vector is prescribed at each knot. We prove that under appropriate assumptions the interpolant exists locally with one degree of freedom.
Jianhong Shi
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Discrete Smooth Interpolation in Geometric Modelling
CAD Computer Aided Design, 1992In such fields as geology and biology, a common problem is that of modelling complex surfaces that are defined by data of various types. Classical modelling techniques based on Bézier and spline interpolations can account for only some of these types of data.
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Fast Study Quadric Interpolation in the Conformal Geometric Algebra Framework
Electronics, 2022 Interpolating trajectories of points and geometric entities is an important problem for kinematics. To describe these trajectories, several algorithms have been proposed using matrices, quaternions, dual-quaternions, and the Study quadric; the last one ...
Susana Ortega-Cisneros +1 more
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Interpolation by geometric algorithm
Computer-Aided Design, 2007We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the ...
Takashi Maekawa +2 more
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Geometric interpolants with different degrees of smoothness
International Journal of Computer Mathematics, 2010Geometric interpolation is a basic task in geometric modelling. In this paper, the geometric interpolant with different degrees of smoothness is introduced. The method provides the lower degree, flexile interpolation curves and construction is simple. Moreover, convexity, regularity and the construction of some special geometric interpolants are also ...
Chun-Gang Zhu, Ren-Hong Wang 0001
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Convergence Analysis for B-Spline Geometric Interpolation
Computers and Graphics, 2012Guiqing Li
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