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Article
Tangents and Curvatures of Matrix-valued Subdivision Curves and Their Applications to Curve Design
Applicable Analysis
(2016)
Abstract
Subdivision provides an efficient method to generate smooth curves and surfaces. Recently, matrix-valued subdivision schemes were introduced to provide more flexibility and smaller subdivision templates for curve and surface design. For matrix-valued subdivision, the input is a set of vectors with the first components being the vertices of the control polygon (or the control net for surface subdivision) and the other components being the so-called control (or shape) parameters. It was observed that the control parameters can change the shape of limiting curve/surfaces significantly. However, how to choose these parameters has not been fully discussed in the literature. In this paper, we address this issue for matrix-valued curve subdivision by providing easy-to-implement formulas for normals and curvature of subdivision curves and a method for defining shape parameters. We also do some analysis using data from a sample planar curve.
Disciplines
Publication Date
August 2, 2016
DOI
10.1080/00036811.2015.1068298
Citation Information
Qingtang Jiang and James J. Smith. "Tangents and Curvatures of Matrix-valued Subdivision Curves and Their Applications to Curve Design" Applicable Analysis Vol. 95 Iss. 8 (2016) p. 1671 - 1699 Available at: http://works.bepress.com/qingtang-jiang/16/