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# Communications in Information and Systems

## Volume 22 (2022)

### Number 1

### FC-NURBS curves: fullness control non-uniform rational B-spline curves

Pages: 131 – 146

DOI: https://dx.doi.org/10.4310/CIS.2022.v22.n1.a6

#### Authors

#### Abstract

We present an approach to design non-uniform rational B-spline (NURBS) curves with fullness control and name the resulting curves as FC-NURBS curves. Given a point sequence and associated fullness parameters, firstly we construct a rational quadratic Bézier curve based on each adjacent three points and the fullness parameter of the middle point. Then using de Casteljau algorithm we divide each rational Bézier curve into two halves. Finally, all these halves are used to construct a $C^m$ continuous FC-NURBS curve by combining rational polynomial blending functions. Each segment of FC-NURBS curves is a rational polynomial curve, and thus FC-NURBS curves can be converted to NURBS curves exactly. Each end segment of FC-NURBS curve is defined by neighboring three points in the point sequence and the fullness parameter of the middle point, and each non-end segment is ruled by adjacent four points in the point sequence and the fullness parameters of the two interior points. The fullness parameters, determining the proximity between the curve and corresponding points, effectively improve the local shape control ability of FC-NURBS curves. Some numerical examples are further offered to demonstrate the efficiency of our approach.

The research of C. Deng was supported by the National Natural Science Foundation of China (No. 61872121), and the Zhejiang Provincial Science and Technology Program in China (No. 2021C01108).

The research of Z. Wang was supported by the National Natural Science Foundation of China (No. 61872121).

The research of J. Liu was supported by the Natural Science Foundation of Zhejiang Province (No. LQ17A010009).

The research of H. Xu was supported by the Ningbo Natural Science Foundation (No. 2019A610033).

The research of Q. Hu was supported by the Natural Science Foundation of Zhejiang Province (No. LY19F020004).

Received 15 September 2020

Published 7 February 2022