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Discrete Beta-splines

Published:01 August 1987Publication History

ABSTRACT

Goodman (1985) and Joe (1986) have given explicit formulas for (cubic) Beta-splines on uniform knot sequences with varying ß1 and ß2 values at the knots, and nonuniform knot sequences with varying ß2 values at the knots, respectively. The advantage of the latter formula is that it can also be used for knot sequences with multiple knots. Discrete Beta-splines arise when a Beta-spline curve is subdivided, i.e. the knot sequence is refined so that the curve is expressed in terms of a larger number of control vertices and Beta-splines. We prove that discrete Beta-splines satisfy the same properties as discrete B-splines, and present an algorithm for computing discrete Beta-splines and the new control vertices using the explicit formula of Joe (1986).

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          cover image ACM Conferences
          SIGGRAPH '87: Proceedings of the 14th annual conference on Computer graphics and interactive techniques
          August 1987
          352 pages
          ISBN:0897912276
          DOI:10.1145/37401

          Copyright © 1987 ACM

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          Publication History

          • Published: 1 August 1987

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          SIGGRAPH '87 Paper Acceptance Rate33of140submissions,24%Overall Acceptance Rate1,822of8,601submissions,21%

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