Pythagorean-hodograph ovals of constant width

Rachid Ait-Haddou; Walter Herzog; Luc Biard

doi:10.1016/j.cagd.2007.10.008

Pythagorean-hodograph ovals of constant width

Rachid Ait-Haddou, Walter Herzog, Luc Biard^*

^*Corresponding author for this work

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

10 Scopus citations

Abstract

A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m > 4 and is based on the dual control structure of offsets of rational PH curves.

Original language	English (US)
Pages (from-to)	258-273
Number of pages	16
Journal	Computer Aided Geometric Design
Volume	25
Issue number	4-5
DOIs	https://doi.org/10.1016/j.cagd.2007.10.008
State	Published - May 2008
Externally published	Yes

Keywords

Constant width
Dual Bézier curve
Evolute and involute
Offset curve
Oval
PH curve
Rosette

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.2007.10.008

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title = "Pythagorean-hodograph ovals of constant width",

abstract = "A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m > 4 and is based on the dual control structure of offsets of rational PH curves.",

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author = "Rachid Ait-Haddou and Walter Herzog and Luc Biard",

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T1 - Pythagorean-hodograph ovals of constant width

AU - Ait-Haddou, Rachid

AU - Herzog, Walter

AU - Biard, Luc

PY - 2008/5

Y1 - 2008/5

N2 - A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m > 4 and is based on the dual control structure of offsets of rational PH curves.

AB - A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m > 4 and is based on the dual control structure of offsets of rational PH curves.

KW - Constant width

KW - Dual Bézier curve

KW - Evolute and involute

KW - Offset curve

KW - Oval

KW - PH curve

KW - Rosette

UR - http://www.scopus.com/inward/record.url?scp=41249097011&partnerID=8YFLogxK

U2 - 10.1016/j.cagd.2007.10.008

DO - 10.1016/j.cagd.2007.10.008

M3 - Article

AN - SCOPUS:41249097011

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VL - 25

SP - 258

EP - 273

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 4-5

ER -

Pythagorean-hodograph ovals of constant width

Abstract

Keywords

ASJC Scopus subject areas

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