Cubic trigonometric nonuniform spline curves and surfaces
type: Item
instance of: scholarly article
title: Cubic trigonometric nonuniform spline curves and surfaces
zbMATH Open document ID: 1400.65012
DOI: 10.1155/2016/7067408
author: Lanlan Yan
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: A class of cubic trigonometric nonuniform spline basis functions with a local shape parameter is constructed. Their totally positive property is proved. The associated spline curves inherit most properties of usual polynomial \(B\)-spline curves and enjoy some other advantageous properties for engineering design. They have \(C^2\) continuity at single knots. For equidistant knots, they have \(C^3\) continuity and \(C^5\) continuity for particular choice of shape parameter. They can express freeform curves as well as ellipses. The associated spline surfaces can exactly represent the surfaces of revolution. Thus the curve and surface representation scheme unifies the representation of freeform shape and some analytical shapes, which is popular in engineering.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 6953500
Wikidata QID: Q59141131
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7067408
OpenAlex ID: W2256010282
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description: scientific article; zbMATH DE number 6953500