As-Rigid-As-Possible Surface Modeling

EUROGRAPHICS/ACM SIGGRAPH Symposium on Geometry Processing 2007
Olga Sorkine-Hornung, Marc Alexa
Test of Time Award, EUROGRAPHICS Symposium on Geometry Processing 2022

As-Rigid-As-Possible (ARAP) Surface Modeling

Bending the Cactus: the original model on the left is manipulated by translating handle vertices (yellow). The red vertices are constrained to stay put. Note that no explicit rotation constraints are provided by the user.


Modeling tasks, such as surface deformation and editing, can be analyzed by observing the local behavior of the surface. We argue that defining a modeling operation by asking for rigidity of the local transformations is useful in various settings. Such formulation leads to a non-linear, yet conceptually simple energy formulation, which is to be minimized by the deformed surface under particular modeling constraints. We devise a simple iterative mesh editing scheme based on this principle, that leads to detail-preserving and intuitive deformations. Our algorithm is effective and notably easy to implement, making it attractive for practical modeling applications.


The as-rigid-as-possible deformation algorithm is implemented as a CGAL package. Check the manual here.

video (interactive editing sessions)


We wish to thank Mario Botsch and Leif Kobbelt for insightful discussions and the anonymous reviewers for their valuable comments. This work was supported in part by the Alexander von Humboldt Foundation.