Michael Bang Nielsen

Hierarchical RLE level set: A compact and versatile deformable surface representation

This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 × 3000 × 3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the H-RLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage.

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Level set methods [Osher and Sethian. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the “Dynamic Tubular Grid” or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 10243

Guide shapes for high resolution naturalistic liquid simulation

Art direction of high resolution naturalistic liquid simulations is notoriously hard, due to both the chaotic nature of the physics and the computational resources required. Resimulating a scene at higher resolution often produces very different results, and is too expensive to allow many design cycles. We present a method of constraining or guiding a high resolution liquid simulation to stay close to a finalized low resolution version (either simulated or directly animated), restricting the solve to a thin outer shell of liquid around a guide shape. Our method is generally faster than an unconstrained simulation and can be integrated with a standard fluid simulator. We demonstrate several applications, with both simulated and hand-animated inputs.

Effects of type 2 diabetes on the regulation of hepatic glucose metabolism.

Glucose production is inappropriately increased in people with type 2 diabetes both before and after food ingestion. Excessive postprandial glucose production occurs in the presence of decreased and delayed insulin secretion and lack of suppression of glucagon release. These abnormalities in hormone secretion, coupled with impaired insulin-induced suppression of glucose production and stimulation of splanchnic glucose uptake, likely account in large part for the excessive amounts of glucose that reach the systemic circulation for disposal by peripheral tissues following food ingestion. In contrast, when adequate basal insulin concentrations are present, neither glucagon-induced stimulation of glucose production nor glucose-induced suppression of glucose production differs in diabetic and nondiabetic subjects matched for gender, age, and degree of obesity. However, when insulin secretion is defective, lack of suppression of glucagon can cause substantial hyperglycemia by enhancing rates of glucose production. Therefore, normalization of hepatic glucose metabolism in people with type 2 diabetes mellitus likely will require normalization of insulin and glucagon secretion as well as hepatic insulin action.

Improved Variational Guiding of Smoke Animations

Smoke animations are hard to art‐direct because simple changes in parameters such as simulation resolution often lead to unpredictable changes in the final result. Previous work has addressed this problem with a guiding approach which couples low‐resolution simulations – that exhibit the desired flow and behaviour – to the final, high‐resolution simulation. This is done in such a way that the desired low frequency features are to some extent preserved in the high‐resolution simulation. However, the steady (i.e. constant) guiding used often leads to a lack of sufficiently high detail, and employing time‐dependent guiding is expensive because the matrix of the resulting set of equations needs to be recomputed at every iteration. We propose an improved mathematical model for Eulerian‐based simulations which is better suited for dynamic, time‐dependent guiding of smoke animations through a novel variational coupling of the low‐ and high‐resolution simulations. Our model results in a matrix that does not require re‐computation when the guiding changes over time, and hence we can employ time‐dependent guiding more efficiently both in terms of storage and computational requirements. We demonstrate that time‐dependent guiding allows for more high frequency detail to develop without losing correspondence to the low resolution simulation. Furthermore, we explore various artistic effects made possible by time‐dependent guiding.

Out-of-core and compressed level set methods

This article presents a generic framework for the representation and deformation of level set surfaces at extreme resolutions. The framework is composed of two modules that each utilize optimized and application specific algorithms: 1) A fast out-of-core data management scheme that allows for resolutions of the deforming geometry limited only by the available disk space as opposed to memory, and 2) compact and fast compression strategies that reduce both offline storage requirements and online memory footprints during simulation. Out-of-core and compression techniques have been applied to a wide range of computer graphics problems in recent years, but this article is the first to apply it in the context of level set and fluid simulations. Our framework is generic and flexible in the sense that the two modules can transparently be integrated, separately or in any combination, into existing level set and fluid simulation software based on recently proposed narrow band data structures like the DT-Grid of Nielsen and Museth [2006] and the H-RLE of Houston et al [2006]. The framework can be applied to narrow band signed distances, fluid velocities, scalar fields, particle properties as well as standard graphics attributes like colors, texture coordinates, normals, displacements etc. In fact, our framework is applicable to a large body of computer graphics problems that involve sequential or random access to very large co-dimension one (level set) and zero (e.g. fluid) data sets. We demonstrate this with several applications, including fluid simulations interacting with large boundaries (≈ 15003), surface deformations (≈ 20483), the solution of partial differential equations on large surfaces (≈ 40963) and mesh-to-level set scan conversions of resolutions up to ≈ 350003 (7 billion voxels in the narrow band). Our out-of-core framework is shown to be several times faster than current state-of-the-art level set data structures relying on OS paging. In particular we show sustained throughput (grid points/sec) for gigabyte sized level sets as high as 65% of state-of-the-art throughput for in-core simulations. We also demonstrate that our compression techniques out-perform state-of-the-art compression algorithms for narrow bands.

A two-continua approach to Eulerian simulation of water spray

Physics based simulation of the dynamics of water spray - water droplets dispersed in air - is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry and often challenge state of the art methods. Current spray simulation pipelines typically employ a combination of Lagrangian (particle) and Eulerian (volumetric) methods - the Eulerian methods being used for parts of the spray where individual droplets are not apparent. However, existing Eulerian methods in computer graphics are based on gas solvers that will for example exhibit hydrostatic equilibrium in certain scenarios where the air is expected to rise and the water droplets fall. To overcome this problem, we propose to simulate spray in the Eulerian domain as a two-way coupled two-continua of air and water phases co-existing at each point in space. The fundamental equations originate in applied physics and we present a number of contributions that make Eulerian two-continua spray simulation feasible for computer graphics applications. The contributions include a Poisson equation that fits into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods.

Synthesizing waves from animated height fields

Computer animated ocean waves for feature films are typically carefully choreographed to match the vision of the director and to support the telling of the story. The rough shape of these waves is established in the previsualization (previs) stage, where artists use a variety of modeling tools with fast feedback to obtain the desired look. This poses a challenge to the effects artists who must subsequently match the locked-down look of the previs waves with high-quality simulated or synthesized waves, adding the detail necessary for the final shot. We propose a set of automated techniques for synthesizing Fourier-based ocean waves that match a previs input, allowing artists to quickly enhance the input wave animation with additional higher-frequency detail that moves consistently with the coarse waves, tweak the wave shapes to flatten troughs and sharpen peaks if desired (as is characteristic of deep water waves), and compute a physically reasonable velocity field of the water analytically. These properties are demonstrated with several examples, including a previs scene from a visual effects production environment.

Finite Element Methods on Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces

The simulation of physical processes on interfaces and a variety of applications in geometry processing and geometric modeling are based on the solution of partial differential equations on curved and evolving surfaces. Frequently, an implicit level set type representation of these surfaces is the most effective and computationally advantageous approach. This paper addresses the computational problem of how to solve partial differential equations on highly resolved level sets with an underlying very high-resolution discrete grid. These high-resolution grids are represented in a very efficient dynamic tubular grid encoding format for a narrow band. A reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach, by isotropic or truly anisotropic curvature motion, are investigated as characteristic model problems. The proposed methods are based on semi-implicit finite element discretizations directly on these narrow bands, require only standard numerical quadrature, and allow for large time steps. To combine large time steps with a very thin and thus storage inexpensive narrow band, suitable transparent boundary conditions on the boundary of the narrow band and a nested iteration scheme in each time step are investigated. This nested iteration scheme enables the discrete interfaces to move in a single time step significantly beyond the domain of the narrow band of the previous time step. Furthermore, algorithmic tools are provided to assemble finite element matrices and to apply matrix vector operators via fast, cache-coherent access to the dynamic tubular grid encoded data structure. The consistency of the presented approach is evaluated, and various numerical examples show its application potential.

Microsensor measurements of hydrogen gas dynamics in cyanobacterial microbial mats.

We used a novel amperometric microsensor for measuring hydrogen gas production and consumption at high spatio-temporal resolution in cyanobacterial biofilms and mats dominated by non-heterocystous filamentous cyanobacteria (Microcoleus chtonoplastes and Oscillatoria sp.). The new microsensor is based on the use of an organic electrolyte and a stable internal reference system and can be equipped with a chemical sulfide trap in the measuring tip; it exhibits very stable and sulfide-insensitive measuring signals and a high sensitivity (1.5–5 pA per μmol L-1 H2). Hydrogen gas measurements were done in combination with microsensor measurements of scalar irradiance, O2, pH, and H2S and showed a pronounced H2 accumulation (of up to 8–10% H2 saturation) within the upper mm of cyanobacterial mats after onset of darkness and O2 depletion. The peak concentration of H2 increased with the irradiance level prior to darkening. After an initial build-up over the first 1–2 h in darkness, H2 was depleted over several hours due to efflux to the overlaying water, and due to biogeochemical processes in the uppermost oxic layers and the anoxic layers of the mats. Depletion could be prevented by addition of molybdate pointing to sulfate reduction as a major sink for H2. Immediately after onset of illumination, a short burst of presumably photo-produced H2 due to direct biophotolysis was observed in the illuminated but anoxic mat layers. As soon as O2 from photosynthesis started to accumulate, the H2 was consumed rapidly and production ceased. Our data give detailed insights into the microscale distribution and dynamics of H2 in cyanobacterial biofilms and mats, and further support that cyanobacterial H2 production can play a significant role in fueling anaerobic processes like e.g., sulfate reduction or anoxygenic photosynthesis in microbial mats.