Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

S. Avvakumov; A. Sossinsky

doi:https://doi.org/10.1134/S0001434618030124

Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

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

Abstract

We define normal forms of regular closed polygonal curves in R², prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.

Original language	English
Pages (from-to)	466-473
Number of pages	8
Journal	Mathematical Notes
Volume	103
Issue number	3-4
DOIs	https://doi.org/10.1134/S0001434618030124
State	Published - 1 Mar 2018
Externally published	Yes

Keywords

Euler functional
gradient descent
local moves
normal form of a polygonal curve
regular closed polygonal curve
regular homotopy
winding number of a plane curve

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1134/S0001434618030124

Cite this

@article{f91450d7eea74aa8815e66e79b7226c1,

title = "Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves",

abstract = "We define normal forms of regular closed polygonal curves in R2, prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.",

keywords = "Euler functional, gradient descent, local moves, normal form of a polygonal curve, regular closed polygonal curve, regular homotopy, winding number of a plane curve",

author = "S. Avvakumov and A. Sossinsky",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = mar,

day = "1",

doi = "https://doi.org/10.1134/S0001434618030124",

language = "الإنجليزيّة",

volume = "103",

pages = "466--473",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "3-4",

}

TY - JOUR

T1 - Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

AU - Avvakumov, S.

AU - Sossinsky, A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We define normal forms of regular closed polygonal curves in R2, prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.

AB - We define normal forms of regular closed polygonal curves in R2, prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.

KW - Euler functional

KW - gradient descent

KW - local moves

KW - normal form of a polygonal curve

KW - regular closed polygonal curve

KW - regular homotopy

KW - winding number of a plane curve

UR - http://www.scopus.com/inward/record.url?scp=85046372543&partnerID=8YFLogxK

U2 - https://doi.org/10.1134/S0001434618030124

DO - https://doi.org/10.1134/S0001434618030124

M3 - مقالة

SN - 0001-4346

VL - 103

SP - 466

EP - 473

JO - Mathematical Notes

JF - Mathematical Notes

IS - 3-4

ER -

Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this