Designing interactively with elastic splines

David Brander; Jakob Andreas Bærentzen; Ann-Sofie Fisker; Jens Gravesen

doi:10.1016/j.cagd.2018.03.007

Designing interactively with elastic splines

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

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-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 language	English
Journal	Computer-Aided Geometric Design
Volume	62
Pages (from-to)	181-191
Number of pages	11
ISSN	0167-8396
DOIs	https://doi.org/10.1016/j.cagd.2018.03.007
Publication status	Published - 2018

Keywords

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

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10.1016/j.cagd.2018.03.007

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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.",

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author = "David Brander and B{\ae}rentzen, \{Jakob Andreas\} and Ann-Sofie Fisker and Jens Gravesen",

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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

SN - 0167-8396

VL - 62

SP - 181

EP - 191

JO - Computer-Aided Geometric Design

JF - Computer-Aided Geometric Design

ER -

Designing interactively with elastic splines

Abstract

Keywords

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