Research Projects

scratched cutlery scene

Rendering Specular Microgeometry with Wave Optics

Simulation of light reflection from specular surfaces is a core problem of computer graphics. Most existing solutions either make the approximation of providing only a large-area average solution in terms of a fixed BRDF (ignoring spatial detail), or are based only on geometric optics (which is an approximation to more accurate wave optics), or both. We design the first rendering algorithm based on a wave optics model, but also able to compute spatially-varying specular highlights with high-resolution detail. We compute a wave optics reflection integral over the coherence area; our solution is based on approximating the phase-delay grating representation of a micron-resolution surface heightfield using Gabor kernels. Our results show both single-wavelength and spectral solution to reflection from common everyday objects, such as brushed, scratched and bumpy metals.

You can download the SIGGRAPH 2018 paper (PDF), video (MP4), supplemental material (Zip Archive) and more from Lingqi Yan's page.

brushed metal scene

Predicting Appearance from Measured Microgeometry of Metal Surfaces

The visual appearance of many materials is created by micro-scale details of their surface geometry. In this paper, we investigate a new approach to capturing the appearance of metal surfaces without reflectance measurements, by deriving microfacet distributions directly from measured surface topography. Modern profilometers are capable of measuring surfaces with sub-wavelength resolution at increasingly rapid rates. We consider both wave- and geometric-optics methods for predicting BRDFs of measured surfaces and compare the results to optical measurements from a gonioreflectometer for five rough metal samples. Surface measurements are also used to predict spatial variation, or texture, which is especially important for the appearance of our anisotropic brushed metal samples. Profilometer-based BRDF acquisition offers many potential advantages over traditional techniques, including speed and easy handling of anisotropic, highly directional materials. We also introduce a new generalized normal distribution function, the ellipsoidal NDF, to compactly represent non-symmetric features in our measured data and texture synthesis.

The project page has links to download the paper (ACM Transactions on Graphics 2015) and related materials, now updated with the measured data and ellipsoid importance sampling.

luminaire scene

Complex Luminaires: Illumination and Appearance Rendering

Simulating a complex luminaire, such as a chandelier, is expensive. Prior approaches cached information on an aperture surface that separates the luminaire from the scene, but many luminaires have large or ill-defined apertures leading to excessive data storage and inaccurate results. In this paper, we separate luminaire rendering into illumination and appearance components. A precomputation stage simulates the complex light flow inside the luminaire to generate two data structures: a set of anisotropic point lights (APLs) and a radiance volume. The APLs represent the light leaving the luminaire, allowing its near- and far-field illumination to be efficiently computed at render time. The luminaire's appearance consists of high- and low-frequency components which are both visually important. High-frequency components are computed dynamically at render time, while the more computationally expensive low-frequency components are approximated using the precomputed radiance volume.

You can download the paper (PDF, ACM Transactions on Graphics 2015) here.

luminaire scene

On the Appearance of Translucent Edges

This project investigated the visual appearance of edges on translucent objects: how they differ from opaque edges, what causes their unusual features, and how it relates to material properties.

The project page has links to download the paper (CVPR 2015) and related materials.

kitchen scene

Bidirectional Lightcuts

Scenes modeling the real-world combine a wide variety of phenomena including glossy materials, detailed heterogeneous anisotropic media, subsurface scattering, and complex illumination.  Predictive rendering of such scenes is difficult; unbiased algorithms are typically too slow or too noisy. Virtual point light (VPL) based algorithms produce low noise results across a wide range of performance/accuracy tradeoffs, from interactive rendering to high quality offline rendering, but their bias means that locally important illumination features may be missing. We introduce a bidirectional formulation and a set of weighting strategies to significantly reduce the bias in VPL-based rendering algorithms.  Our approach, bidirectional lightcuts, maintains the scalability and low noise global illumination advantages of prior VPL-based work, while significantly extending their generality to support a wider range of important materials and visual cues.  We demonstrate scalable, efficient, and low noise rendering  of scenes with highly complex materials including gloss, BSSRDFs, and anisotropic volumetric models. 

You can download a SIGGRAPH 2012 preprint paper (pdf)  here.
The SIGGRAPH presentation slides are available in keynote format or as exports to pdf and powerpoint.

scorpion in amber

Single Scattering in Refractive Media with Triangle Mesh Boundaries

Light scattering in refractive media is an important optical phenomenon for computer graphics.  While recent research has focused on multiple scattering, there has been less work on accurate solutions for single or low-order scattering.  Refraction through a complex boundary allows a single external source to be visible in multiple directions internally with different strengths; these are hard to find with existing techniques. This paper presents techniques to quickly find paths that connect points inside and outside a medium while obeying the laws of refraction. We introduce a half-vector based formulation to support the most common geometric representation, triangles with interpolated normals; hierarchical pruning to scale to triangular meshes, a solver with strong accuracy guarantees, and a faster method that is empirically accurate.  A GPU version achieves interactive frame rates in several examples.
You can download a SIGGRAPH 2009 preprint paper (pdf) and a quicktime movie here.
The presentation slides are available in keynote, pdf, or powerpoint + movies formats.

agglomerative clustering tree

Fast Agglomerative Clustering

This paper describes how to build binary trees using agglomerative (or bottom-up) construction quickly and evaluates the quality of the trees compared to divisive (or top-down) construction in two applications: BVH trees for ray tracing and light trees for Lightcuts.  We introduce a novel faster unordered agglomerative clustering algorithm for use when the clustering function is non-decreasing.  Our results indicate that the agglomerative-built trees generally have higher quality though the build times are a little slower than the fastest divisive approaches.

You can download a preprint of the IRT08 paper (pdf) here. 
The presentation slides are available in powerpoint and pdf formats. 
Several people asked if a divisive builder that tries splits on all three axes rather than just the longest one would make a significant difference.  I tried this and SAH estimated cost results (see figure 6) are shown in this table.  The quality improved at the cost of slower builds but still does not match the agglomerative quality.  The maximum depth of each BVH  is shown in paranthesis () with agglomerative trees tending to be a little deeper than the divisive ones.
Divisive - 1 axis
(32) 46.1
(31) 17.7
(35) 70.5
(42) 29.4
Divisive - 3 axis
(30) 43.5
(29) 17.4
(33) 62.7
(41) 28.2
(60) 36.1
(39) 15.5
(44) 54.0
(65) 22.6

etched globe

Microfacet Refraction

This work extends microfacet theory (eg, Cook-Torrance models) to handle refraction through rough surfaces such as etched glass globe shown. We also discuss the Smith shadowing-masking approximation for general microfacet distributions and good importance sampling strategies (which is essential when simulating transmitted light). Published at EGSR 2007. You can download the EGSR 2007 paper (pdf) here.

Erratum: Fixed typo in equation 40 (eta should be eta^2 inside the square root)

pretty picture

Multidimensional Lightcuts

This work extends the approach and concepts of Lightcuts to scalable rendering of complex effects such as motion blur, depth of field, and volume rendering. We achieve greater scalability by holistically considering complete pixel integrals and using an implicit hierarchy called the product graph.

You can download the SIGGRAPH 2006 paper (pdf) and a movie from the

The SIGGRAPH presentation slides are available in powerpoint or pdf formats, and a separate archive of clips on the movies page. (Note: the powerpoint file was created on a Macintosh computer and some of the graphs do not seem to display properly under Windows.)

pretty picture

Lightcuts: A Scalable Approach to Illumination

Computing the illumination from complex sources such as area lights, HDR environment maps, and indirect, can be very expensive.  Lightcuts introduces a new scalable algorithm for computing the illumination from thousands or millions of point lights.  Using a perceptual metric, a binary light tree of clusters, and conservative per-cluster error bounds, we show that we can accurately compute the illumination from hundreds of point lights using only hundreds of shadow rays.  A lightcut is cut through the global light tree that adaptively partitions the lights into clusters to locally control the cost vs. error tradeoff.  We also introduce a related technique called reconstruction cuts that uses the lightcut framework to further reduce shading costs by intelligently interpolating illumination while preserving high frequencies details like shadow boundaries and glossy highlights.

You can download the SIGGRAPH 2005 paper (pdf) (Note: several figures were printed incorrectly in the proceedings but are correct in the PDF) and a movie from the

The SIGGRAPH presenation slides are available in powerpoint or pdf formats. 

A related technical report discusses several important implementation issues for the Ward BRDF including the correct sampling weights that should be used when using it associated Monte Carlo sampling distribution.

user study

Perceptual Illumination Components

Different components of global illumination have widely varying costs, but may not provide the same benefits to image quality. We performed a user study to examine this issue. We divided the illumination into several components based on the BRDF (indirect diffuse, indirect gloss, indirect specular), rendered images with different subsets of the illumination. We then had people rank the images and studied the results. What we found is the components had differing affects on user-ranking (though indirect diffuse was usually the most important), but that we could predict their importances quite accurately using a simple model and some simple image/material statistics. We think this can provide insight for creating more efficient rendering systems in the future.

Published in SIGGRAPH 2004. More information can be found on the first author's page.

texture with edges

Feature-Based Textures

By adding explicit features (eg, discontinuity edges) to a standard raster-based textures, we can increase image quality, especially during magnification, with only minimal extra storage.  Features can be automatically extracted from vector format images, approximated for raster images, or hand annotated.

Published in EGSR 2004. More information can be found on this project page.

dragon image

Combining Edges and Points

By combining edges (explicit discontinuities) and points (shading samples), we are able to reconstruct high quality images from relatively sparse data. By computing the exact locations of discontinuities, we are able to interpolate the sparse data without smoothing out these sharp features and we also show that knowing the subpixel location of the edges allows to compute good quality anti-aliasing almost for free and without supersampling. Our software implementation runs at interactive rates on the CPU and future versions should be able to exploit the GPU for even faster framerates.

Published SIGGRAPH 2003. More information can be found on this project page.

A GPU-based version was published at Graphics Interface 2006.

Render Cache for Interactive Rendering

priority sampling

During an interactive session it is not necessary (and perhaps not even desirable) to render every pixel of every frame.  Especially when using more expensive rendering methods such as global illumination.  In most cases, there is considerable coherence from one frame to the next which we can exploit to reduce our computational expense.  Also, in an interactive session, small visual artifacts are acceptable as long as they are small, fixed quickly, and do not distract the user.  In rendering methods such as ray tracing or global illlumination, the cost of renderering a pixel various greatly depending on various factors such as material, local geometry, and complexity of the local lighting.  Thus rerendering every pixel would make the framerate either highly variable which is far more objectionable in an interactive session than having some minor visual artifacts would be.

The render cache enables interactive display by caching rendered results as colored 3D points, reprojecting them to estimate the current image, and automatically deciding which subset of pixels should be (re)rendered for future frames.  Because the image generation and pixel (or ray) rendering happen asynchronously, we can guarantee a fast consistent framerate regardless of rendering cost (though renderering cost does affect visual quality).  In our experiments we have found that we get very good visual quality when only one tenth the pixels are rendered per frame and acceptable quality when only one hundreth of the pixels are renderered per frame (the rest of the pixels are estimated by reprojecting older results).

This work was begun while I was a post-doc at the iMAGIS lab in Grenoble, France and continued at Cornell.
You can view a project page here (including a link to the Eurographics Rendering Workshop '99 paper ).  (Powerpoint presentation)
A followup paper, Enhancing and Optimizing the Render Cache, appeared in EGRW 2002.  (Powerpoint presentation)
A GPU-based version was published at Graphics Interface 2006.

There is also a web-downloadable binary so that you can try it out for yourself or download the C++ source code under GPL license and compile it yourself.

Using Perceptual Texture Masking for Efficient Image Synthesis

masking in a texture

This work described a simple and fast way to precompute the perceptual masking ability of textures (stored as threshold elevation factors) and store them with the texture.  This allows them to be used during interactive computations to allow higher error thresholds in textured regions with almost no runtime overhead.

Published at Eurographics 2002.  You can get the paper here.

Density Estimation for Global Illumination

light through glass blocks

I investigated particle tracing and density estimation as a method to compute radiosity solutions on large environments. Traditional radiosity methods have been limited by their large memory requirements. The density estimation method uses much less memory because it can efficiently use secondary storage (e.g. disk) for most its storage needs. It can handle all transport paths (arbitrary BRDF) and it nicely decomposes the global illumination problem into three pieces: particle tracing, density estimation, and mesh decimation.

You can get my thesis here .
You can get our Transactions on Graphics 1997 paper here .
You can get our Eurographics Rendering Workshop '95 paper here .

Fitting Virtual Lights for Non-Diffuse Walkthroughs

with and without virtual lights

The essence of this work is to find ways to encode non-diffuse illumination solutions for rapid display using standard 3D graphics interfaces (e.g. OpenGL) and hardware.  We want to be able to use a sophisticated lighting algorithm such as global illumination with arbitrary material properties, but we also want to be able to display the results quickly enough for interactive walkthrough.  Current realtime graphics interfaces and hardware only implemented a relatively primitive local shading model.  Phong shading and perhaps some shadows are about the limit of their abilities.  We investigate the us of these basic primitives as a set of "appearance basis" functions that can be used to approximate the appearance computed by some more accurate, complete, and general model.

You can get our SIGGRAPH '97 paper here .


The path-buffer is a modified z-buffer with two z values per pixel. The extra z value allows us to use the the path-buffer and scan conversion to trace rays in a path tracing style algorithm. This reformulated algorithm is designed to be easy to accelerate using scan conversion and z-buffer type hardware. More details can be found in:

"The Path-Buffer" - Technical Report PCG-95-4
Bruce Walter and Jed Lengyel
Here are pdf versions of the technical report and figures.

I implemented the path-buffer on the simulator for UNC's PixelFlow machine as proof of concept with the goal of interactive path tracing in simple environments.  But then I got distracted by working on my dissertation and have not worked on the path buffer since.

Other projects

Iterative Adaptive Sampling

"Accurate Direct Illumination Using Iterative Adaptive Sampling" - IEEE TVCG June 2006
Michael Donikian, Bruce Walter, Kavita Bala, Sebastian Fernandez, and Donald P. Greenberg

Analyzing Ray Casting and Particle Tracing

Rays are used as a primitive in many different rendering algorithms, but unfortunately the costs of ray casting are not very well understood. In order to better understand the costs of the particle tracing phase of our density estimation radiosity algorithm, we are working on analyzing the costs of ray casting and the variance of particle tracing.
"Cost Analysis of a Monte Carlo Radiosity Algorithm" - Technical Report PCG-95-3
Bruce Walter and Peter Shirley
I don't have the source for the original report anymore, but here is a pdf version of an updated, though not quite finished, version of this technical report.
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