Super Space Clothoids - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ACM Transactions on Graphics Year : 2013

Super Space Clothoids

Abstract

Thin elastic filaments in real world such as vine tendrils, hair ringlets or curled ribbons often depict a very smooth, curved shape that low-order rod models -- e.g., segment-based rods -- fail to reproduce accurately and compactly. In this paper, we push forward the investigation of high-order models for thin, inextensible elastic rods by building the dynamics of a G2-continuous piecewise 3D clothoid: a smooth space curve with piecewise affine curvature. With the aim of precisely integrating the rod kinematic problem, for which no closed-form solution exists, we introduce a dedicated integration scheme based on power series expansions. It turns out that our algorithm reaches machine precision orders of magnitude faster compared to classical numerical integrators. This property, nicely preserved under simple algebraic and differential operations, allows us to compute all spatial terms of the rod kinematics and dynamics in both an efficient and accurate way. Combined with a semi-implicit time-stepping scheme, our method leads to the efficient and robust simulation of arbitrary curly filaments that exhibit rich, visually pleasing configurations and motion. Our approach was successfully applied to generate various scenarios such as the unwinding of a curled ribbon as well as the aesthetic animation of spiral-like hair or the fascinating growth of twining plants.
Fichier principal
Vignette du fichier
Siggraph2013_Super_Space_Clothoids_Casati_Bertails-Descoubes.pdf (7.27 Mo) Télécharger le fichier
Vignette du fichier
Super-Space-Clothoids_Representative_Image.jpg (235.79 Ko) Télécharger le fichier
Siggraph2013_Super_Space_Clothoids_Casati_Bertails-Descoubes.mp4 (139.85 Mo) Télécharger le fichier
Siggraph2013_Super_Space_Clothoids_Supplemental_Casati_Bertails-Descoubes.pdf (75.74 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive
Format Figure, Image
Format Video
Format Other
Loading...

Dates and versions

hal-00840335 , version 1 (02-07-2013)
hal-00840335 , version 2 (03-07-2013)
hal-00840335 , version 3 (16-01-2014)

Identifiers

Cite

Romain Casati, Florence Bertails-Descoubes. Super Space Clothoids. ACM Transactions on Graphics, 2013, Proceedings of SIGGRAPH 2013, 32 (4), pp.Article No. 48. ⟨10.1145/2461912.2461962⟩. ⟨hal-00840335v3⟩
486 View
1648 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More