Designing interactively with elastic splines

David Brander, Jakob Andreas Bærentzen, Ann-Sofie Fisker*, Jens Gravesen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline.
Original languageEnglish
JournalComputer-Aided Geometric Design
Volume62
Pages (from-to)181-191
Number of pages11
ISSN0167-8396
DOIs
Publication statusPublished - 2018

Keywords

  • Elastic curves
  • Cubic splines
  • Computer-aided design
  • Hot-blade cutting

Cite this

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title = "Designing interactively with elastic splines",
abstract = "We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes negligible. Using a database of cubic B{\'e}zier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline.",
keywords = "Elastic curves, Cubic splines, Computer-aided design, Hot-blade cutting",
author = "David Brander and B{\ae}rentzen, {Jakob Andreas} and Ann-Sofie Fisker and Jens Gravesen",
year = "2018",
doi = "10.1016/j.cagd.2018.03.007",
language = "English",
volume = "62",
pages = "181--191",
journal = "Computer-Aided Geometric Design",
issn = "0167-8396",
publisher = "Elsevier",

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Designing interactively with elastic splines. / Brander, David; Bærentzen, Jakob Andreas; Fisker, Ann-Sofie; Gravesen, Jens.

In: Computer-Aided Geometric Design, Vol. 62, 2018, p. 181-191.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Designing interactively with elastic splines

AU - Brander, David

AU - Bærentzen, Jakob Andreas

AU - Fisker, Ann-Sofie

AU - Gravesen, Jens

PY - 2018

Y1 - 2018

N2 - We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline.

AB - We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline.

KW - Elastic curves

KW - Cubic splines

KW - Computer-aided design

KW - Hot-blade cutting

U2 - 10.1016/j.cagd.2018.03.007

DO - 10.1016/j.cagd.2018.03.007

M3 - Journal article

VL - 62

SP - 181

EP - 191

JO - Computer-Aided Geometric Design

JF - Computer-Aided Geometric Design

SN - 0167-8396

ER -