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2003•Mini-micro SystemsRequires access

A Fast Algorithm for Inserting a Series of Knots into a B-spline Curve Simultaneously

Zhiqiang Yao

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Abstract

Based on a new recurrent formula of discrete B-splines, a fast algorithm is presented for inserting a series of knots into a B-spline curve simultaneously. The time complexity of this algorithm is O(sk+n), where k is the order of B-spline curve and n+k+1 is the number of knots before inserting knots, s is the number of inserted knots. This algorithm can be applied to both endpoints-interpolating and non-endpoints-interpolating B-spline curves . And the positions of the inserted knots can be inside or outside the domain of B-spline curves.

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What this paper is about

Based on a new recurrent formula of discrete B-splines, a fast algorithm is presented for inserting a series of knots into a B-spline curve simultaneously. The time complexity of this algorithm is O(sk+n), where k is the order of B-spline curve and n+k+1 is the number of knots before inserting knots, s is the number of inserted knots. This algorithm can be applied to both endpoints-interpolating and non-endpoints-interpolating B-spline curves . And the positions of the inserted knots can be inside or outside the domain of B-spline curves.

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Available abstract

Based on a new recurrent formula of discrete B-splines, a fast algorithm is presented for inserting a series of knots into a B-spline curve simultaneously. The time complexity of this algorithm is O(sk+n), where k is the order of B-spline curve and n+k+1 is the number of knots before inserting knots, s is the number of inserted knots. This algorithm can be applied to both endpoints-interpolating and non-endpoints-interpolating B-spline curves . And the positions of the inserted knots can be inside or outside the domain of B-spline curves.

Key concepts: Mathematics, B-spline, Algorithm, Spline (mechanical), Series (stratigraphy), Combinatorics, Mathematical analysis, Physics

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