Michael B. Nielsen

Postdoc, PhD

Graphics Group

Department of Computer Science

Aarhus University, Denmark

CV

Funded by the Danish Agency for Science, Technology and Innovation

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Contact

Email: bang@cs.au.dk

Phone: +45 29699756

Web: http://www.cs.au.dk/~bang

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The Dynamic Tubular Grid (DT-Grid) was used to create fluid effects in Pirates of the Caribbean 3.

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Source Code

DT-Grid source code is available here.

Current release v.0.91 (October 23, 2009).

Relevant papers including my dissertation can be found below.

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Recent Publications

Google Scholar Entry

	Abstract: 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.
	Paper					Improved Variational Guiding of Smoke Animations
						Michael B. Nielsen and Brian B. Christensen
						Eurographics 2010, to appear
	Video					Coming soon
	Abstract: We propose a novel approach to guiding of Eulerian-based smoke animations through coupling of simulations at different grid resolutions. Specifically we present a variational formulation that allows smoke animations to adopt the low-frequency features from a lower resolution simulation (or non-physical synthesis), while simultaneously developing higher frequencies. The overall motivation for this work is to address the fact that art-direction of smoke animations is notoriously tedious. Particularly a change in grid resolution can result in dramatic changes in the behavior of smoke animations, and existing methods for guiding either significantly lack high frequency detail or may result in undesired features developing over time. Provided that the bulk movement can be represented satisfactorily at low resolution, our technique effectively allows artists to prototype simulations at low resolution (where computations are fast) and subsequently add extra details without altering the overall “look and feel”. Our implementation is based on a customized multi-grid solver with memory-efficient data structures.
	Paper			Guiding of Smoke Animations Through Variational Coupling of Simulations at Different Resolutions
				Michael B. Nielsen, Brian B. Christensen, Nafees Bin Zafar, Doug Roble and Ken Museth
				ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2009, pp. 217-226.
	Video			Submitted Video in Quicktime
	Abstract: 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.
	Paper				Finite Element Methods on Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces
					Oliver Nemitz, Michael Bang Nielsen, Martin Rumpf and Ross Whitaker
					SIAM Journal of Scientific Computing, Vol. 31, No. 3. pp. 2258-2281.
	Abstract: Physical simulation on surfaces and various applications in geometry processing are based on partial differential equations on surfaces. The implicit representation of these eventually evolving surfaces in terms of level set methods leads to effective and flexible numerical tools. This paper addresses the computational problem of how to solve partial differential equations on level sets with an underlying very high-resolution discrete grid.  These high-resolution grids are represented in a very efficient format, which stores only grid points in a thin narrow band.  Reaction diffusion equations on a fixed surface and the evolution of a surface under curvature motion are considered as model problems. The proposed methods are based on a semi implicit finite element discretization directly on these thin narrow bands and allow for large time steps. To ensure this, suitable transparent boundary conditions are introduced on the boundary of the narrow band and the time discretization is based on a nested iteration scheme. Methods are provided to assemble finite element matrices and to apply matrix vector operators in a manner that do not incur additional overhead and give fast, cache-coherent access to very large data sets.
	Paper				Narrow Band Methods for PDEs on Very Large Implicit Surfaces
					Oliver Nemitz, Michael Bang Nielsen, Martin Rumpf and Ross Whitaker
					Proc. VMV 2007
	Dissertation						Efficient and High Resolution Level Set Simulations - Data Structures, Algorithms and Applications
							Supplementary note 1
	Abstract: This paper 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 paper 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 (1500^3), surface deformations (2048^3), the solution of partial differential equations on large surfaces (4096^3) and mesh-to-level set scan conversions of resolutions up to 35000^3 (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 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.
	Paper		Out-Of-Core and Compressed Level Set Methods
			Michael Bang Nielsen, Ola Nilsson, Andreas Söderström and Ken Museth
			ACM Transactions on Graphics 26(4) (Presented at SIGGRAPH 2008, Partial Differential Equations paper session), October 2007. (Accepted August 2, 2007. Conditionally accepted November 20, 2006).
	Technical Sketch		Virtually Infinite Resolution Deformable Surfaces
			Michael Bang Nielsen, Ola Nilsson, Andreas Söderström and Ken Museth
			ACM SIGGRAPH 2006 (August 1 2006)
	Video		Bunny Morph Statue Fountain
	Abstract: This paper 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 non-narrow band regions while the dimensionally recursive encoding along each axis efficiently compacts non-narrow band planes and volumes.  Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 x 3000 x 3000 (45 billion voxels) on commodity PCs with only 1GB of memory.  This paper, 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 narrow band sequential access speed and overall memory usage.
	Paper							Hierarchical RLE Level Set: A Compact and Versatile Deformable Surface Representation
								Ben Houston Michael Bang Nielsen, Christopher Batty, Ola Nilsson and Ken Museth
								ACM Transactions on Graphics 25(1), January 2006. Pages 151-175. (Accepted October 22, 2005. Conditionally accepted for SIGGRAPH, April 4, 2005).
	Technical sketch							Gigantic Deformable Surfaces.
								Ben Houston, Michael Bang Nielsen, Christopher Batty, Ola Nilsson and Ken Museth
								ACM SIGGRAPH 2005.(July 31 2005)
	Video							Submitted Video Bunny-Enright Test in Resolution 100^3 Bunny-Enright Test in Resolution 1024^3
	Abstract: Level set methods [Osher88] 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 1024^3.
	Paper	Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets.
		Michael Bang Nielsen and Ken Museth
		Journal of Scientific Computing 26(3). March 2006. Pages 261-299. ISSN: 0885-7474 (Paper) 1573-7691 (Online) (Submitted November 12, 2004. Accepted January 26, 2005. Published Online January 6, 2006).
	Video	Enright test in resolution 1024^3
	Technical Report	Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets.
		Michael Bang Nielsen and Ken Museth
		Linköping Electronic Articles in Computer and Information Science, Vol. 9(001), 2004, ISSN 1401-9841. (November 11, 2004).
	Technical sketch	An Optimized, Grid Independent, Narrow Band Data Structure for High Resolution Level Sets
		Michael Bang Nielsen and Ken Museth
		SIGRAD 2004. (November 24, 2004).