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An Interpolation Method with Weights and Relaxation Parameters

Chiew Lan Tai, Brian A. Barsky, Kia Fock Loe

Open publisher page 5 citations

Abstract

This paper presents a new interpolation method that is based on blending a nonuniform rational B-spline (NURB) curve with a singularly reparametrized (SR) linear spline. The resulting curve is called the alpha-spline. It has weights and relaxation parameters. Given the data points to be interpolated, a NURB curve is obtained by using these data points as its control points. The SR linear spline is then determined by imposing constraints on the alpha-spline to interpolate the data points. The alpha-spline is parametrically continuous. It involves only simple computation, and does not require solving linear systems. This approach is extended to produce interpolatory surfaces, and can be used as a modeling tool for deforming polygonal shapes into smooth spline surface models.

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What this paper is about

This paper presents a new interpolation method that is based on blending a nonuniform rational B-spline (NURB) curve with a singularly reparametrized (SR) linear spline. The resulting curve is called the alpha-spline. It has weights and relaxation parameters. Given the data points to be interpolated, a NURB curve is obtained by using these data points as its control points. The SR linear spline is then determined by imposing constraints on the alpha-spline to interpolate the data points. The alpha-spline is parametrically continuous. It involves only simple computation, and does not require solving linear systems. This approach is extended to produce interpolatory surfaces, and can be used as a modeling tool for deforming polygonal shapes into smooth spline surface models.

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Available abstract

This paper presents a new interpolation method that is based on blending a nonuniform rational B-spline (NURB) curve with a singularly reparametrized (SR) linear spline. The resulting curve is called the alpha-spline. It has weights and relaxation parameters. Given the data points to be interpolated, a NURB curve is obtained by using these data points as its control points. The SR linear spline is then determined by imposing constraints on the alpha-spline to interpolate the data points. The alpha-spline is parametrically continuous. It involves only simple computation, and does not require solving linear systems. This approach is extended to produce interpolatory surfaces, and can be used as a modeling tool for deforming polygonal shapes into smooth spline surface models.

Key concepts: Spline (mechanical), Spline interpolation, Interpolation (computer graphics), Mathematics, Smoothing spline, Curve fitting, Thin plate spline, Linear interpolation

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