Second order spiral splines

Lyle Noakes

doi:10.1016/j.cagd.2019.05.004

Second order spiral splines

Lyle Noakes

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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Abstract

Second order spiral splines are C² unit-speed planar curves that can be used to interpolate a list Y of n+1 points in R² at times specified in some list T, where n≥2. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.

Original language	English
Pages (from-to)	69-83
Number of pages	15
Journal	Computer Aided Geometric Design
Volume	72
DOIs	https://doi.org/10.1016/j.cagd.2019.05.004
Publication status	Published - 1 Jun 2019

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10.1016/j.cagd.2019.05.004

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title = "Second order spiral splines",

abstract = "Second order spiral splines are C2 unit-speed planar curves that can be used to interpolate a list Y of n+1 points in R2 at times specified in some list T, where n≥2. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.",

keywords = "Clothoidal splines, Convex, Elastic splines, Spiral splines, Tridiagonal",

author = "Lyle Noakes",

year = "2019",

month = jun,

day = "1",

doi = "10.1016/j.cagd.2019.05.004",

language = "English",

volume = "72",

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journal = "Computer Aided Geometric Design",

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AU - Noakes, Lyle

PY - 2019/6/1

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N2 - Second order spiral splines are C2 unit-speed planar curves that can be used to interpolate a list Y of n+1 points in R2 at times specified in some list T, where n≥2. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.

AB - Second order spiral splines are C2 unit-speed planar curves that can be used to interpolate a list Y of n+1 points in R2 at times specified in some list T, where n≥2. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.

KW - Clothoidal splines

KW - Convex

KW - Elastic splines

KW - Spiral splines

KW - Tridiagonal

UR - https://www.scopus.com/pages/publications/85067172849

U2 - 10.1016/j.cagd.2019.05.004

DO - 10.1016/j.cagd.2019.05.004

M3 - Article

AN - SCOPUS:85067172849

SN - 0167-8396

VL - 72

SP - 69

EP - 83

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

ER -

Second order spiral splines

Abstract

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