Martin Wicke

Non-rigid registration under isometric deformations

We present a robust and efficient algorithm for the pairwise non‐rigid registration of partially overlapping 3D surfaces. Our approach treats non‐rigid registration as an optimization problem and solves it by alternating between correspondence and deformation optimization. Assuming approximately isometric deformations, robust correspondences are generated using a pruning mechanism based on geodesic consistency. We iteratively learn an appropriate deformation discretization from the current set of correspondences and use it to update the correspondences in the next iteration. Our algorithm is able to register partially similar point clouds that undergo large deformations, in just a few seconds. We demonstrate the potential of our algorithm in various applications such as example based articulated segmentation, and shape interpolation.

Adaptive space deformations based on rigid cells

We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thin‐shell and solid deformations of 2D and 3D objects, and is applicable to arbitrary sample‐based representations, such as meshes, triangle soups, or point clouds.

A Finite Element Method on Convex Polyhedra

We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping.

Polyhedral finite elements using harmonic basis functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.

Modular bases for fluid dynamics

We present a new approach to fluid simulation that balances the speed of model reduction with the flexibility of grid-based methods. We construct a set of composable reduced models, or tiles, which capture spatially localized fluid behavior. We then precompute coupling terms so that these models can be rearranged at runtime. To enforce consistency between tiles, we introduce constraint reduction. This technique modifies a reduced model so that a given set of linear constraints can be fulfilled. Because dynamics and constraints can be solved entirely in the reduced space, our method is extremely fast and scales to large domains.

Shape Decomposition Using Modal Analysis

We introduce a novel algorithm that decomposes a deformable shape into meaningful parts requiring only a single input pose. Using modal analysis, we are able to identify parts of the shape that tend to move rigidly. We define a deformation energy on the shape, enabling modal analysis to find the typical deformations of the shape. We then find a decomposition of the shape such that the typical deformations can be well approximated with deformation fields that are rigid in each part of the decomposition. We optimize for the best decomposition, which captures how the shape deforms. A hierarchical refinement scheme makes it possible to compute more detailed decompositions for some parts of the shape.

Localization of mobile users using trajectory matching

We present an algorithm enabling localization of moving wireless devices in an indoor setting. The method uses only RF signal strength and can be implemented without specialized hardware. The mobility of the users is modeled by learning a function mapping a short history of signal strength values to a 2D position. We use radial basis function (RBF) fitting to learn a reliable estimate of a mobile nodes position given its past signal strength measurements. Even though we deal with extremely noisy measurements in a cluttered indoor setting, nodes are not required to be stationary during measurement or learning. We evaluate our algorithm in a real indoor setting using MicaZ motes, achieving an average localization accuracy of 1.3 m. In our experiments, using historical data improves the localization accuracy by almost a factor of two compared to using only the most current measurements.

Efficient Animation of Point‐Sampled Thin Shells

We present a novel framework for the efficient simulation and animation of discrete thin shells. Our method takes a point sampled surface as input and performs all necessary computations without intermediate triangulation. We discretize the thin shell functional using so-called fibers. Such fibers are locally embedded parametric curves crisscrossing individual point samples. In combination, they create a dense mesh representing the surface structure and connectivity for the shell computations. In particular, we utilize the fibers to approximate the differential surface operators of the thin shell functional. The polynomials underlying the fiber representation allow for a robust and fast simulation of thin shell behavior. Our method supports both elastic and plastic deformations as well as fracturing and tearing of the material. To compute surfaces with rich surface detail, we designed a multiresolution representation which maps a high-resolution surface onto a fiber network of lower resolution. This makes it possible to animate densely sampled models of very high surface complexity. While being tuned for point sampled objects, the presented framework is versatile and can also take triangle meshes or triangle soups as input.

Interactive 3D painting on point-sampled objects

We present a novel painting system for 3D objects. In order to overcome parameterization problems of existing applications, we propose a unified sample-based approach to represent geometry and appearance of the 3D object as well as the brush surface. The generalization of 2D pixel-based paint models to point samples allows us to elegantly simulate paint transfer for 3D objects. In contrast to mesh-based painting systems, an efficient dynamic resampling scheme permits arbitrary levels of painted detail. Our system provides intuitive user interaction with a six degree-of-freedom (DOF) input device. As opposed to other 3D painting systems, real brushes are simulated including their dynamics and collision handling.

CSG tree rendering for point-sampled objects

This paper presents an algorithm for rendering of point-sampled CSG models. The approach works with arbitrary CSG trees of surfel models with arbitrary sampling densities. Edges and corners are rendered by reconstructing the involved surfaces separately. The reconstructed surfaces are clipped at intersections. This way, blurring at any magnification is avoided. As opposed to existing methods, which resample surfaces close to object intersections, the proposed approach preserves the original object representation. Since no resampling is needed, dynamic scenes can be handled very flexible. Complex intersections involving any number of objects can be rendered.