منابع مشابه
Exploring Expo-Rational B-splines for Curves and Surfaces
We introduce expo-rational B-splines for curves and surfaces and explore for the first time some properties of these new splines which depend not only on their knot vector but also on their intrinsic parameters and the geometry and parametrization of the local curves/surfaces. We consider several examples, discuss some computational aspects, and address potential applications in shape design. §
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This is the first one in a sequence of several papers dedicated to the development of applications of Euler Beta-function B-splines (BFBS) to Computer-aided Geometric Design (CAGD) and, in particular, for geometric modelling of parametric curves, surfaces and volume deformations. This study is an analogue of the study conducted in [12, 10] for the case of expo-rational Bsplines (ERBS). An impor...
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A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...
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Duality of curves is an important aspect of the “classical” algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using the development of an algebraic “mechanism”, based on “distortion” values, geometric and convexity properties are analyzed. Specifically, we discuss some significant aspe...
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The dual of an algebraic curve C in RP defined by the polynomial equation f(x, y, z) = 0 is the locus of points ( ∂f ∂x (a, b, c) : ∂f ∂y (a, b, c) : ∂f ∂z (a, b, c) ) where (a : b : c) ∈ C. The dual can alternatively be defined geometrically as the image under reciprocation of the envelope of tangent lines to the curve. It is known that the dual of an algebraic curve is also an algebraic curve...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1991
ISSN: 0021-9045
DOI: 10.1016/0021-9045(91)90109-n