Light Deformation Tool: Rigid Elements Method

@inproceedings{RUNKJRM14,
 abstract = { 3D structural modeling requires adapted tools for editing and deforming geological objects. For example, the geometry of stratigraphic horizons or fault surfaces may have to be manipulated either to produce a satisfying initial shape or to update it when new elements or data are introduced into the model or modified.
When accuracy is the main concern, deformation methods discretizing the mechanical behavior laws, such as finite elements methods, are generally preferred. However, in certain applications, the need for simplicity, efficiency and robustness may be more important than physical accuracy. Therefore, we propose to extend a computer graphics algorithm [Botsch et al., 2007] togeological models. This hybrid method takes advantages of both mechanical and geometrical approaches. The displacement is discretized using rigid cubic elements linked together by a non-linear quadratic energy. The rigidity brings the robustness to this algorithm because elements cannot degenerate during the process. Furthermore, rigid body motion simplifies the description of the displacement. The linear system to solve for minimizing the global energy is sparse symmetric positive definite, allowing very efficient direct or iterative solvers.
We present the mathematical background of our adaptation of this algorithm to geological objects deformations. },
 author = { Laurent, Gautier AND Caumon, Guillaume },
 booktitle = { Proc. 31st Gocad Meeting },
 location = { Nancy },
 title = { Light Deformation Tool: Rigid Elements Method },
 year = { 2011 }
}