Coincidence condition of two Bézier curves of an arbitrary degree

Xiao-Diao Chen; Chao Yang; Weiyin Ma

doi:10.1016/j.cag.2015.07.013

Coincidence condition of two Bézier curves of an arbitrary degree

Xiao-Diao Chen^*, Chao Yang, Weiyin Ma^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

Abstract This paper discusses the coincidence condition of two Bézier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two Bézier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable Bézier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a Bézier curve can be reparameterized into a non-reparameterizable one of a lower degree.

Original language	English
Article number	2625
Pages (from-to)	121-126
Journal	Computers and Graphics (Pergamon)
Volume	54
DOIs	https://doi.org/10.1016/j.cag.2015.07.013
Publication status	Published - 1 Feb 2016

Research Keywords

Bézier curve
Coincidence detection
Conjecture
Degeneration

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title = "Coincidence condition of two B{\'e}zier curves of an arbitrary degree",

abstract = "Abstract This paper discusses the coincidence condition of two B{\'e}zier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two B{\'e}zier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable B{\'e}zier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a B{\'e}zier curve can be reparameterized into a non-reparameterizable one of a lower degree.",

keywords = "B{\'e}zier curve, Coincidence detection, Conjecture, Degeneration",

author = "Xiao-Diao Chen and Chao Yang and Weiyin Ma",

year = "2016",

month = feb,

day = "1",

doi = "10.1016/j.cag.2015.07.013",

language = "English",

volume = "54",

pages = "121--126",

journal = "Computers and Graphics (Pergamon)",

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TY - JOUR

T1 - Coincidence condition of two Bézier curves of an arbitrary degree

AU - Chen, Xiao-Diao

AU - Yang, Chao

AU - Ma, Weiyin

PY - 2016/2/1

Y1 - 2016/2/1

N2 - Abstract This paper discusses the coincidence condition of two Bézier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two Bézier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable Bézier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a Bézier curve can be reparameterized into a non-reparameterizable one of a lower degree.

AB - Abstract This paper discusses the coincidence condition of two Bézier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two Bézier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable Bézier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a Bézier curve can be reparameterized into a non-reparameterizable one of a lower degree.

KW - Bézier curve

KW - Coincidence detection

KW - Conjecture

KW - Degeneration

UR - http://www.scopus.com/inward/record.url?scp=84939492239&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84939492239&origin=recordpage

U2 - 10.1016/j.cag.2015.07.013

DO - 10.1016/j.cag.2015.07.013

M3 - RGC 21 - Publication in refereed journal

SN - 0097-8493

VL - 54

SP - 121

EP - 126

JO - Computers and Graphics (Pergamon)

JF - Computers and Graphics (Pergamon)

M1 - 2625

ER -

Coincidence condition of two Bézier curves of an arbitrary degree

Abstract

Research Keywords

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