Cage Based Deformations: A Survey

Abstract

Cage based deformation techniques aims to be an easy to use tool for graphics modeling, texturing and animation. In this paper we describe the most important methods, their foundations, and the desirable properties that they should satisfy. We also present a comparative to show the strong and weak points of each one, taking into account their distinctive utilities. Finally, we discuss some applications that exploit cage capabilities in order to create a more complex deformation system or to simplify other deformation techniques.

Appendix

First, we expose Green coordinates pseudocode, extracted from Lipman’s paper [22]. The 2D and 3D version for deforming object vertexes $\varLambda \subset C^{in}$. We have changed $\phi _{i}(v)$ from the original paper by $\omega _{i}(v)$ to keep coherence all over the document. We note that for exterior or boundary points one should add to these coordinates the $\{\alpha _{k}\}$ and $\beta$ as is introduced in Sect. 6.2, and explained in depth in Sect. 4 of Lipman’s paper. Note that $\alpha _{k}$ and $\beta$ also posses a simple closed-form formula employing the regular barycentric coordinates in triangles (3D) or edges (2D).

Harmonic Coordinates implementation is exposed in the corresponding Sect. 4.1, there is no pseudocode in the paper. Finally, Mean Value Coordinates pseudocode from Ju’s paper [18] is presented. It is written for value interpolation, but with some modifications could be adapted for mesh deformation.