Abstract. In this paper we present a GPU-accelerated implementation of the well-known freeform deformation algorithm to allow for deformable objects within fully interactive virtual environments. We furthermore outline how our real-time deformation approach can be integrated into the X3D standard for more accessibility of the proposed methods. The presented technique can be used to deform complex detailed geometries without pre-processing the mesh by simply generating a lattice around the model. The local deformation is then computed for this lattice instead of the complex geometry, which efficiently can be carried out on the GPU using CUDA. Keywords: Deformable objects, real-time simulation, FFD, CUDA, X3D. 1

The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C 1 splines on uniform tetrahedral partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octahedron is further split into a fixed number of disjunct tetrahedra. The Bernstein-Bézier coefficients of the piecewise polynomials are directly determined by appropriate combinations of the data values in a local neighborhood. As previously shown, the splines provide an approximation order two for smooth functions as well as their derivatives. We present the first visualizations using these splines and show that they are well-suited for GPU-based, interactive high-quality visualization of isosurfaces from discrete data.