Publications

Volumetric scalar datasets are common in many scientific, engineering, and medical applications where they originate from measurements or simulations. Furthermore, they can represent geometric scene content, e.g. as distance or density fields. Often isosurfaces are extracted, either for indirect volume visualization in the former category, or to simply obtain a polygonal representation in case of the latter. However, even moderately sized volume datasets can result in complex isosurfaces which are challenging to recompute in real-time, e.g. when the user modifies the isovalue or when the data itself is dynamic. In this paper, we present a GPU-friendly algorithm for the extraction of isosurfaces, which provides adaptive level of detail rendering with view-dependent tessellation. It is based on a longest edge bisection scheme where the resulting tetrahedral cells are subdivided into four hexahedra, which then form the domain for the subsequent isosurface extraction step. Our algorithm generates meshes with good triangle quality even for highly nonlinear scalar data. In contrast to previous methods, it does not require any stitching between regions of different levels of detail. As all computation is performed at run-time and no preprocessing is required, the algorithm naturally supports dynamic data and allows us to change isovalues at any time.

The physically-based simulation of mechanical effects has been an important research topic in computer graphics for more than two decades. Classical methods in this field discretize Newton's second law and determine different forces to simulate various effects like stretching, shearing, and bending of deformable bodies or pressure and viscosity of fluids, to mention just a few. Given these forces, velocities and finally positions are determined by a numerical integration of the resulting accelerations.

In the last years position-based simulation methods have become popular in the graphics community. In contrast to classical simulation approaches these methods compute the position changes in each simulation step directly, based on the solution of a quasi-static problem. Therefore, position-based approaches are fast, stable and controllable which make them well-suited for use in interactive environments. However, these methods are generally not as accurate as force-based methods but still provide visual plausibility. Hence, the main application areas of position-based simulation are virtual reality, computer games and special effects in movies and commercials.

In this tutorial we first introduce the basic concept of position-based dynamics. Then we present different solvers and compare them with the classical implicit Euler method. We discuss approaches to improve the convergence of these solvers. Moreover, we show how position-based methods are applied to simulate hair, cloth, volumetric deformable bodies, rigid body systems and fluids. We also demonstrate how complex effects like anisotropy or plasticity can be simulated and introduce approaches to improve the performance. Finally, we give an outlook and discuss open problems.

In this paper we introduce an efficient and stable implicit SPH method for the physically-based simulation of incompressible fluids. In the area of computer graphics the most efficient SPH approaches focus solely on the correction of the density error to prevent volume compression. However, the continuity equation for incompressible flow also demands a divergence-free velocity field which is neglected by most methods. Although a few methods consider velocity divergence, they are either slow or have a perceivable density fluctuation.

Our novel method uses an efficient combination of two pressure solvers which enforce low volume compression (below 0.01%) and a divergence-free velocity field. This can be seen as enforcing incompressibility both on position level and velocity level. The first part is essential for realistic physical behavior while the divergence-free state increases the stability significantly and reduces the number of solver iterations. Moreover, it allows larger time steps which yields a considerable performance gain since particle neighborhoods have to be updated less frequently. Therefore, our divergence-free SPH (DFSPH) approach is significantly faster and more stable than current state-of-the-art SPH methods for incompressible fluids. We demonstrate this in simulations with millions of fast moving particles.