Sparse Pythagorean hodograph curves

Rachid Ait-Haddou; Marie Laurence Mazure

doi:10.1016/j.cagd.2017.04.002

Sparse Pythagorean hodograph curves

Rachid Ait-Haddou, Marie Laurence Mazure^*

^*Corresponding author for this work

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

5 Scopus citations

Abstract

We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.

Original language	English (US)
Pages (from-to)	84-103
Number of pages	20
Journal	Computer Aided Geometric Design
Volume	55
DOIs	https://doi.org/10.1016/j.cagd.2017.04.002
State	Published - Jul 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

(Complete) Müntz spaces
(Sparse) Pythagorean hodograph curves
Blossoms
Control polygons
Extended Chebyshev spaces
Shape parameters

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/j.cagd.2017.04.002

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title = "Sparse Pythagorean hodograph curves",

abstract = "We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.",

keywords = "(Complete) M{\"u}ntz spaces, (Sparse) Pythagorean hodograph curves, Blossoms, Control polygons, Extended Chebyshev spaces, Shape parameters",

author = "Rachid Ait-Haddou and Mazure, {Marie Laurence}",

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year = "2017",

month = jul,

doi = "10.1016/j.cagd.2017.04.002",

language = "English (US)",

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T1 - Sparse Pythagorean hodograph curves

AU - Ait-Haddou, Rachid

AU - Mazure, Marie Laurence

PY - 2017/7

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N2 - We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.

AB - We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.

KW - (Complete) Müntz spaces

KW - (Sparse) Pythagorean hodograph curves

KW - Blossoms

KW - Control polygons

KW - Extended Chebyshev spaces

KW - Shape parameters

UR - http://www.scopus.com/inward/record.url?scp=85019545215&partnerID=8YFLogxK

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DO - 10.1016/j.cagd.2017.04.002

M3 - Article

AN - SCOPUS:85019545215

SN - 0167-8396

VL - 55

SP - 84

EP - 103

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

ER -

Sparse Pythagorean hodograph curves

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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