What is the blog?

This blog is a re-interpretation of the tessendorf.org website I had for several years. At the moment I am putting up the papers and reports page. Eventually I will put up the other pages on frumple and old Arete Image Software materials. You can also find this information at my university page

Wednesday, March 4, 2015

Advection Solver Performance with Long Time Steps, and Strategies for Fast and Accurate Numerical Implementation

Jerry Tessendorf
February, 2015
Technical Note
A detailed look at solving advection equations by using a Characteristic Map. Three items in this note: (1) Using the CM as the tool for advection, substeps can be generated by efficiently, in fact logarithmically fast; (2) The exact solution for the CM is given, leading to an accurate numerical algorithm for using it. Because the solution involves exponentiated 3X3 matrices, the algorithm is relatively slow although very accurate. In fact, for rigid rotations the algorithm is exact. (3) Several standard tests of advection accuracy are evaluated and the error in several popular advection schemes are quantified by comparing them with the exact solution.

eWave: Using an Exponential Solver on the iWave Problem

Jerry Tessendorf
March 2014
Technical Note
The iWave approach to simulating surface waves is fast and efficient, but suffers stability and artifact problems. By rephrasing the algorithm to employ two first order diffential equations for the displacement and velocity potential, and using an exponential solver, much more accurate simulations result. Importantly, the solution is free of the stability and artifact issues of the previous approach, and maintains high efficiency and flexibility.

Tuesday, October 11, 2011

The Characteristic Map for Fast and Efficient VFX Fluid Simulations
Jerry Tessendorf and Brandon Pelfrey
June, 2011
Computer Graphics International Workshop on VFX, Computer Animation, and Stereo Movies
The Method of Characteristics is examined as a tool for making fluid simulation more efficient and effective in VFX production. A mathematical frame- work for a Characteristic Map is shown to be a general- ization of the previous methods called Gridless Advec- tion and Semi-Lagrangian Mapping. We demonstrate that the Characteristic Map can be used to modify a fluid flow post-simulation, including injecting higher resolution motion, and precise flow control from blend- ing Characteristic Maps.
Angular Smoothing and Spatial Diffusion from the Feynman Path Integral Representation of Radiative Transfer
Jerry Tessendorf
October, 2010
Journal of Quantitative Spectroscopy and Radiative Transfer
The propagation kernel for time dependent radiative transfer is represented by a Feynman Path Integral (FPI). The FPI is approximately evaluated in the spatial-Fourier domain. Spatial diffusion is exhibited in the kernel when the approximations lead to a gaussian dependence on the Fourier domain wave vector. The approximations provide an explicit expression for the diffusion matrix. They also provide an asymptotic criterion for the self-consistency of the diffusion approximation. The criterion is weakly violated in the limit of large numbers of scattering lengths. Additional expansion of higher-order terms may resolve whether this weak violation is significant.
I Love It When A Cloud Comes Together
Sho Hasegawa, Jason Iversen, Hideki Okano, and Jerry Tessendorf
July, 2010
Siggraph, Los Angeles
One of the action sequences in the film The A-Team takes place within a growing system of storm clouds. The story plot required the creation of a fully 3D environment of clouds covering tens of kilometers of evolving storm, modeled and simulated at high reso- lution because the camera and story elements are embedded within it. The cloud system covered approximately 20 kilometers, at a resolution as small at 0.1 meters. A variety of clouds types were modeled, corresponding to the different cloud taxonomies in differ- ent regions of a storm supercell. Individual cloud structure was controlled and directed down to arbitrarily fine spatial detail. This talk discusses the software tools developed to model, simulate, and render this complex, high resolution cloud system.
Resolution Independent Volumes
Jerry Tessendorf and Michael Kowalski
July, 2011
Siggraph, Los Angeles
Course notes for the 2011 Siggraph course "Production Volume Rendering 2". Emphasises script-based manipulation of volumetric data, illustrated with a scripting language called Felt.
Monocoupled 3D and 2D River Simulations
Sanjit Patel, Jerry Tessendorf, and Jeroen Molemaker
August, 2009
Symposium on Computer Animation, New Orleans
This is a poster presented at SCA in New Orleans. To achieve a high resolution simulation of a river, we employed two different simulation methods. A full Navier-Stokes 3D simulation at a medium resolution to get the overall motion, followed by a high resolution simulation of surface displacement waves. The dynamics of the surface displacements was driven in part by the motion of the 3D simulation.
Numerical Integration of the Feynman Path Integral for Radiative Transport
Jerry Tessendorf
May, 2009
International Conference on Mathematics, Computational Methods and Reactor Physics, Saratoga Springs, New York, May 3-7, 2009, American Nuclear Society.
The radiative transport problem is cast in integral form using a transport kernel. The transport kernel has an explicit representation in terms of a Feynman Path Integral over all paths between selected points in a volume. This representation is setup in detail. Numerical evaluation of this Path Integral is formulated with a Frenet-Serret based procedure for generating valid random paths, and with a numerical evaluation of the weight for each valid path. Very early sanity checks of a numerical implementation are reported. Approaches to optimization are identified.
Simulation of Interactive Surface Waves
Jerry Tessendorf
October, 2008
This is a set of notes for a very short course on water surface wave simulation via the iWave algorithm. I presented the course over two class sessions at the Clemson University, and at University of Pennsylvania. The notes are in two files: one that covers background and enough detail to execute the algorithm in code, and in the second pdf file there are technical details of the meaning of the square root of a derivative operator. Many thanks to Robert Geist, Don House, and Mike Westall for inviting me to Clemson and taking care of me while there, and to Norm Badler, Alla Safanova, Stephen Lane, and Jessica Marcus for inviting me to UPenn and taking care of me.
Production Volume Rendering
Jerry Tessendorf
November, 2008
This is a set of notes for a very short course on volume rendering. I presented the course over two class sessions at the University of Pennsylvania just before Thanksgiving. Despite the brevity of the class time, I was very pleased to hear afterward from several students in the class who had successfully written volume renderers from the notes (and from some rendering code they had previously built in the class). Some of the students have put up websites (http://www.alinenormoyle.com/projects/clouds/index.html, www.sunilkamat.com/files/ReadMe.pdf, and http://www.seas.upenn.edu/~tgorkin/VolumeRenderer/volumeRenderer.html). Many thanks to Norm Badler, Alla Safanova, Stephen Lane, and Jessica Marcus for inviting me to UPenn and taking care of me during my stay.
A Simple Improvement of Gas Simulation Quality
Victor Grant, Charles Anderson, Nathan Ortiz, Jerry Tessendorf
January, 2008
With some very simple additional processing, low-resolution fluid simulations can be rendered with fine detail. This is a sketch that was submitted to siggraph 2008, but unfortunately not accepted.
Golden Compass Auroras
Nathan Ortiz, Eric Horton, Michael Kowalski, Jerry Tessendorf
January, 2008
Talk, Siggraph 2008
Describes the many layers of volumetric elements constructed and animated for the Auroras at the end of Golden Compass.
Golden Compass Daemon Deaths
Scott Townsend, Eric Horton, Sanjit Patel, Jerry Tessendorf
January, 2008
Talk, Siggraph 2008
Describes the many layers of volumetric elements and fluid simulations for the daemon deaths in Golden Compass.
Multiple-Forward-Scattering in Volume Rendering of Participating Media
Jerry Tessendorf
January, 2006
Natural volumetric media have phase functions which typically are sharply peaked in the forward scattering direction, with backscatter accounting for only a few percent of the total angular redistribution from a single scattering event. This property has been exploited in the past in the small-angle approximation for radiative transfer, successfully for many engineering and science applications. The small-angle approximation also robustly describes the multiple-forward-scattered behavior of the light field many scattering lengths into the participating medium, including the asymptotic regime, in agreement with experimental measurements and computationally intensive simulations. Physically, the important missing ingredient not found in the small-angle approximation is occasional large angle scatters that reverse the propagation direction of some of the light. This paper introduces a quantitative model of multiple scattering which contains both the multiple-forward-scatter character and a few large-angle scattering events. The model is derived directly from the Green's function representation of radiative transfer, and path integrals are used to construct the appropriate form of the small angle approximation. The model is suitable for media that have internal structure.
Interactive Water Surfaces
Jerry Tessendorf
Game Programming Gems 4, Charles River Media
Chapter from Game Programming Gems 4 on the basic iWave algorithm for simulating water surface interaction with obstructions in the water.
Motion Blur Algorithm for Clipped Triangle Rendering
Jerry Tessendorf
December, 2004
Notes on a general algorithm from tracking the motion of vertices on an image plane as the 3D positions of the camera can vertices move.
Efficient Rendering of Atmospheric Phenomena
Kirk Riley, David S. Ebert, Martin Kraus, Jerry Tessendorf, and Charles Hansen
September, 2004
Eurographics Symposium on Rendering, H. W. Jensen and A. Keller (eds), 2004
Rendering of atmospheric bodies involves modeling the complex interaction of light throughout the highly scattering medium of water and air particles. Scattering by these particles creates many well-known atmospheric optical phenomena including rainbows, halos, the corona, and the glory. Unfortunately, most radiative transport approximations in computer graphics are ill-suited to render complex angularly dependent effects in the presence of multiple scattering at reasonable frame rates. Therefore, this paper introduces a multiple-model lighting system that efficiently captures these essential atmospheric effects. We have solved the rendering of fine angularly dependent effects in the presence of multiple scattering by designing a lighting approximation based upon multiple scattering phase functions. This model captures gradual blurring of chromatic atmospheric optical phenomena by handling the gradual angular spreading of the sunlight as it experiences multiple scattering events with anisotropic scattering particles. It has been designed to take advantage of modern graphics hardware; thus, it is capable of rendering these effects at near interactive frame rates.

Friday, October 7, 2011

Practical Rendering of Multiple Scattering Effects in Participating Media
Simon Premoze, Michael Ashikhmin, Jerry Tessendorf, Ravi Ramamoorthi, and Shree Nayar
September, 2004
Eurographics Symposium on Rendering, H. W. Jensen and A. Keller (eds), 2004
Volumetric light transport effects are significant for many materials like skin, smoke, clouds, snow or water. In particular, one must consider the multiple scattering of light within the volume. While it is possible to simulate such media using volumetric Monte Carlo or finite element techniques, those methods are very computationally expensive. On the other hand, simple analytic models have so far been limited to homogeneous and/or optically dense media and cannot be easily extended to include strongly directional effects and visibility in spatially varying volumes. We present a practical method for rendering volumetric effects that include multiple scattering. We show an expression for the point spread function that captures blurring of radiance due to multiple scattering. We develop a general framework for incorporating this point spread function, while considering inhomogeneous media¿this framework could also be used with other analytic multiple scattering models.
Simulating Ocean Surface
Jerry Tessendorf
January, 2004
Siggraph course notes, 1999-2004
Notes and slides from a course given at Siggraph from 1999 to 2004.
Notes 2004
Slides 2004
Notes 2002
Slides 2002
Slides 2001
Tetrad Volume and Particle Rendering in X2
Bill La Barge, Jerry Tessendorf, and Vijoy Gaddipati
August, 2003
Siggraph Sketch
In the movie X2 XMen United, Cerebro is a large spherical cavity that extends mutant mental capabilities. To depict its large, cavernous, dynamic nature, and the connnection between the machine and the characters, the atmospheric element of the scene was built based on a fully 3D volumetric rendering technology developed at Cinesite. In addition, this volumetric technique was also used to connect floating vinnettes in the space with the land masses on the borders of Cerebro. The teleportation effect of the character Nightcrawler is accompanied by a dynamic smokey filament effect using turbulent particle dynamics and particle rendering.
Concepts for Volume Rendering
Jerry Tessendorf
August, 2003
Notes on the path integral mathematics for doing volume rendering. Written to be succinct, not as a tutorial or explanatory. Suggests a full algorithm for doing multiple scattering.
Efficiently Rendering Gobs and Gobs of Particles
Jerry Tessendorf
May, 2002
Software has been developed and deployed which is able to render unlimited numbers of particles in very low amounts of RAM. This approach also generates volumetric lighting and opacity, including self-shadowing, making the particle renderer an efficient volume renderer. The algorithms combine several channels of alpha and depth data with techniques to transform the hiding and shadow map problems to a compositing operation.
Deforming Geometric Volumes: Kinematics, Dynamics, Constraints, and Collisions
Jerry Tessendorf
February, 2002
These notes are intended as an outline of some geometric techniques that may be applicable to modeling and dynamics problems that include volumetric objects. Of particular interest are objects consisting of an enclosed volume, with the volume undergoing deformations while subjected to external forces, collisions, and boundary constraints
that combine to reshape the volume dynamically.
Algorithm for Capturing a 3D Model from Multiple Camera Views
Jerry Tessendorf
March, 2000
Neat and clean theory for taking rotoscope outlines from multiple images and reconstructing the 3D object in the view. Underwent very limited testing at the time, with success.
Fast Wake Algorithm Derivation
Jerry Tessendorf
March, 2000
One pager on creating boat wakes in the FFT water surface method.
The Map of a Sphere to and from the Image Plane
Jerry Tessendorf
November, 1999
A brief note laying the map of projecting a sphere to the image, and back.
Implementation of Curved Strands I: Frenet-Serret Framework
J Tessendorf and D D Weston
January, 1999
Implements a representation of curved hair strands in terms of a Frenet-Serret geometric framework. This paper lays out the framework and implements a numerical scheme.

Thursday, October 6, 2011

Implementation of Curved Strands II: Dynamics
J Tessendorf and D D Weston
December, 1998
Sets up the dynamics of strands under the Frenet-Serret framework.
Impact of Multiple Scattering on Simulated Infrared Cloud Scene Images
Jerry Tessendorf and David Wasson
April, 1994
Characterization and Propagation of Sources and Backgrounds, SPIE Proceedings, vol 2223, 462-473, (1994)
The three-dimensional volumetric character of clouds is a critically important factor in determining cloud structure as seen in infrared imagery. Using a longwave cloud scene simulator which images a three-dimensional cloud volume, the 3D structure has been shown to be particularly important when viewing at low grazing angles. In order to conduct analyses of cloud scene structure in MW and visible bands as well, the longwave simulator has been significantly upgraded to perform imaging of clouds with multiple scattering included. The multiple scattering algorithm is based on a WKB approximation method for the exact radiative transfer problem, and comprehends the spatial variations in optical properties within the cloud volume. As a first analysis, we have generated a cloud scene which is backlit by the sun, and systematically assess the contributions of the thermal, solar, and multiple scattering mechanisms within the imagery. As might be expected, multiple scattering has its greatest impact at the cloud edges in the MW band, where the "silver lining" is formed. In the MW band, scattering can also play a role at cloud edges and create additional clutter by scattering earthshine into the field of view of the low grazing angle camera. In principle, this simulator is capable of operating throughout the visible and infrared bands, for realistically size clouds.
Scattering in the 3D Cloud Scene Simulator
Jerry Tessendorf and David Wasson
February, 1994
Arete Associates Technical Report
One of two documents describing early approaches to multiple scattering in a rendering system.
3D Cloud Scene Simulator V2 Algorithm for Scattering
Jerry Tessendorf and David Wasson
February, 1994
Arete Associates Technical Report
One of two documents describing early approaches to multiple scattering in a rendering system.
Measures of Temporal Pulse Stretching
Jerry Tessendorf
July, 1992
Ocean Optics XI, SPIE Publication, vol 1750, 407-418, (1992)
Temporal pulse stretching is a consequence of the multiple scatter by ocean water of a laser pulse. Although the physical process behind pulse stretching is intuitively clear, there is no widely held quantitative definition of it. Here temporal pulse stretching is defined in terms of temporal moments of the radiance at a fixed position and orientation with respect to the initial pulse axis. This definition has been chosen because it is directly measurable from the waveform output of a radiometer. The first temporal moment is a measure of the apparent delay of the pulse, and the variance from the second moment describes the increasing width. Using a WKB approach, an expression is obtained for the first two temporal moments for waveforms measured at positions along the initial pulse axis. Quantitative predictions of the temporal delay and width are made for a pulse with is initially a collimated point. To within an error of no more than 12%, the delay and width are proportional. Stretching effects on waveforms are shown graphically in plots at various distances from the source.
Structure and Spatial Spectra of Simulated Cloud Scenes at Infrared Wavelengths
Jerry Tessendorf, Daniel Weston, and Lisa Taylor
April, 1992
Characterization, Propagation, and Simulation of Sources and Backgrounds II, SPIE Publication, vol 1687, 499-508, (1992)
Longwave infrared imagery of cloud fields are examined in terms of their power spectral density (PSD). In order to systematically investigate the dependence of the PSD on viewing conditions, a cloud scene simulator is employed to generate images of a simulated cloud field. The cloud field is fully three dimensional and is described by its fluctuating temperature and liquid/ice water content fields. The image process accurately calculates the spatially varying attentuation of blackbody emission. Several views of a single cloud field are examined to study the effect of viewing angle on the image PSD. Zenith views produce isotropic PSDs, while nearly horizontal views contain a large amount of foreshortening and a correspondingly anisotropic PSD. One possible component of the foreshortening is simply geometric and can be estimated and compared to simulation output. We find that geometrically induced foreshortening does not describe the PSD effects observed in the simulation for the relatively thin cirrus-like cloud simulated here. Possibly this indicates that the three-dimensional cloud structure is more important in some views than in others when there are large fluctuations in the cloud optical properties. We are pursuing a more quantitative description of this behavior.
The Underwater Solar Light Field: Analytical Model from a WKB Evaluation
Jerry Tessendorf
July, 1991
Underwater Imaging, Photography, and Visibility, SPIE Publication, vol 1537, 10-20, (1991)
An analytical expression for the underwater radiance distribution due to a purely "delta function" sun is discussed.
Radiative Transfer on Curved Surfaces
J. Tessendorf
April, 1990
Journal of Mathematical Physics, vol 31, no. 4, 1010-1019, (1990)
After a review of appropriate concepts in local surface geometry, a formally exact solution of the radiative transfer equation is constructed, for transfer from one surface of arbitrary shape to another.
Downwelling Irradiance Fluctuations in the Small-Angle Approximation
Jerry Tessendorf
April, 1990
Ocean Optics X, SPIE Publication, vol 1302, 454-463, (1990)
Mean and rms fluctuations of downwelling irradiance below a rough ocean surface have been modelled using the small-angle approximation for the in-water radiance distribution.
Time-Dependent Radiative Transfer and Pulse Evolution
J. Tessendorf
February, 1989
Journal of the Optical Society of America A, vol 6, no 2, 280-297, (1989)
The time dependent radiative transfer equation in an absorbing and scattering medium is recast as an evolution equation that is similar to the global formulation of Preisendorfer.
Approximate Parametric Receiver Operating Characteristics for Poisson Distributed Noise
Jerry Tessendorf
January, 1989
Applied Optics, vol 28, 214-216, (1989)
ROC curves for poisson distributed noise.
Comparison Between Data and Small-Angle Approximations for the In-Water Solar Radiance Distribution
J. Tessendorf
September, 1988
Journal of the Optical Society of America A, vol 5, no 9, 1410-1418, (1988)
Qualitative and quantitative properties of the in-water distribution of solar radiance, as predicted by the radiative transfer equation, are examined.
Finite-Difference Evolution of a Scattered Laser Pulse in Ocean Water
J. Tessendorf, C. Piotrowski, R.L. Kelly
July, 1988
Ocean Optics IX, SPIE Publication, vol 925, 22-35, (1988)
The propagation of a finite-sized laser pulse through ocean water is simulated.
Radiative Transfer as a Sum over Paths
J. Tessendorf
January, 1987
Physical Review A, vol 35, no. 2, 872-878 (1987)
The radiative-transfer equation describes the collection of path taken by an element of radiation as it travels from one location to another. When backscatter can be ignored, the exact solution is constructed as a formal sum (path integral) over all such paths. In the appropriate limit the usual (diffusive) small-angle solution and the multiple scattering solution can be obtained. Another small-angle solution has also been found which includes some of the nonlinear and large-angle behavior not present in the diffusive solution. After several attenuation lengths, length scales are characterized by a parameter constructed our of the absorption and scattering coefficients, and the rms scattering angle per scattering event. The two solutions are compared i n the case of a point beam.
Green's Functions at Zero Viscosity
H. M. Fried and J. Tessendorf
April, 1984
Journal of Mathematical Physics, vol 25, 1144-1154 (1984)
Fradkin-type propagator representations are written for solutions to Navier-Stokes and related equations, for arbitrary dimension D and arbitrary source geometry. In the limit of very small viscosity, velocity/vorticity solutions are given in terms of Cauchy position coordinates q of a particle advected by the velocity flow v, using a set of coupled equations for q and v. For localized point vortices in two dimensions, the vectors q become the time-dependent position coordinates of interacting vortices, and our equations reduce to those of the familiar, coupled vortex problem. The formalism is, however, able to discuss three-dimensional vortex motion, discrete or continuous, including the effects of vortex stretching. The mathematical structure of vortex stretching in a D-dimensional fluid without boundaries is conveniently described in terms of an SU(D) representation of these equations. Several simple examples are given in two dimensions, to anchor the method in the context of previoiusly known, exact solutions. In three dimensions, vortex stretching effects are approximated using a previous "strong coupling" technique of particle physics, enabling one to build a crude model of the intermittent growth of enstrophy, which may signal the onset of turbulence. For isotropic turbulence, the possibility of a singularity in the inviscid enstrophy af a finite time is related to the behavior of a single function characterizing the intermittency.
Mean-Field Burgers' Model of Turbulence
J. Tessendorf
October, 1983
Brown University Dept of Physics Report BROWN-HET-516
A mean-field expansion of the Martin, Siggia, and Rose functional formalism for turbulence is proposed as a "strong-coupling" approximation. To carry out the expansion, the volume of the wavenumber space must be truncated to a large but finite amount. Burgers' model with homogeneous average flow is examined in detail to several orders of approximation. The two point cumulant is calculated. The mean-field expansion is described as a perturbation expansion, with its small parameter inversely proportional to the truncated volume of wavenumber space. Renormalization and some features of the expansion are explored.