Technical Report MSC-2006-21

Title: Exploiting the Free Form Deformation Function as a Geometric Modeling Tool
Authors: Guy Sela
Supervisors: Gershon Elber
Abstract: Free Form Deformations (FFDs) are highly versatile tools, used mainly in the field of physical modeling, but also in animation, 2D and 3D registration, etc. FFDs deform one spatial domain into another, allowing deformation of objects embedded in the original volume. In this work, we demonstrate the versatility of FFDs by exploring two new applications. The first application uses FFDs in order to simulate a general soft tissue incision process. The FFDs are encoded with results of an off-line Finite Element (FE) incision simulation, emulating the response of tissue under incision, over time and in a canonical setting. In order to achieve the desired effect, this work uses an existing modeling tool, a deformation function that is a variant of FFD, called Discontinuous Free Form Deformation (DFFD). DFFD is able to introduce discontinuities into the deformed domain by inserting multiple knots into the B-spline knot vector. This discontinuity becomes the cut in the 3D model. At each time step, the volume around the active end of the scalpel path is mapped to the canonical volume in which the simulation was conducted, the deformation is applied, and the deformed geometry in the canonical volume is mapped back to the Euclidean domain. This mapping allows us to use a single off-line FE simulation, conducted on a volumetric model inside a canonical domain, for simulating general incision paths. The second application uses FFDs for artistically oriented modeling, trying to mimic works of artists such as Shigeo Fukuda and Markus Raetz. Here, two input models are combined to create one synergetic model that resembles the first input model from one viewing direction, and the second input model from a different, orthogonal to the first, viewing direction. In order to accomplish this, we use a two-dimensional FFD that is calculated by solving a surface fairing problem, using a Lagrange operator. The optimization problem maps one model’s silhouette into the other’s, and uses the surface thin plate (or bending) energy functional as the optimization functional. For each of the two applications, we provide examples and discuss possible future extensions.

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