In this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension. In particular, throughout this paper we will focus on the derivation of 6-point interpolating schemes that turn out to be unique in combining vital ingredients like C²-continuity, simplicity of definition, ease of implementation, user independency, tension control and ability to reproduce salient trigonometric and transcendental curves.

Romani, L. (2009). From approximating subdivision schemes for exponential splines to high-performance interpolating algorithms. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 224(1), 383-396 [10.1016/j.cam.2008.05.013].

From approximating subdivision schemes for exponential splines to high-performance interpolating algorithms

ROMANI, LUCIA
2009

Abstract

In this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension. In particular, throughout this paper we will focus on the derivation of 6-point interpolating schemes that turn out to be unique in combining vital ingredients like C²-continuity, simplicity of definition, ease of implementation, user independency, tension control and ability to reproduce salient trigonometric and transcendental curves.
Articolo in rivista - Articolo scientifico
Binary subdivision; Laurent polynomial formalism; Interpolation; Analytical shapes reproduction; Tension control
English
383
396
Romani, L. (2009). From approximating subdivision schemes for exponential splines to high-performance interpolating algorithms. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 224(1), 383-396 [10.1016/j.cam.2008.05.013].
Romani, L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/7669
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