Mark Meyer, John Anderson
May 2007
Many applications in Computer Graphics contain computationally expensive calculations. These calculations are often performed at many points to produce a full solution, even though the subspace of reasonable solutions may be of a relatively low dimension. The calculation of facial articulation and rendering of scenes with global illumination are two example applications that require these sort of computations. In this paper, we present Key Point Subspace Acceleration and Soft Caching, a technique for accelerating these types of computations.
Key Point Subspace Acceleration (KPSA) is a statistical acceleration
scheme that uses examples to compute a statistical subspace and a set
of characteristic key points. The full calculation is then computed
only at these key points and these points are used to provide a
subspace based estimate of the entire calculation. The soft caching
process is an extension to the KPSA technique where the key points are
also used to provide a confidence estimate for the KPSA result. In
cases with high anticipated error the calculation will then ``fail
through'' to a full evaluation of all points (a cache miss), while
frames with low error can use the accelerated statistical evaluation
(a cache hit).
Additional materials: [SiggraphSlides.pdf], [softCaching.mov]
Available in the proceedings of Siggraph 2007
Available as Pixar Technical Memo #06-04b
Other versions:
Mark Meyer, John Anderson
January 2006
Global illumination provides important visual cues to an animation, however its computational expense limits its use in practice. In this paper, we present an easy to implement technique for accelerating the computation of indirect illumination for an animated sequence using stochastic ray tracing. We begin by computing a quick but noisy solution using a small number of sample rays at each sample location. The variation of these noisy solutions over time is then used to create a smooth basis. Finally, the noisy solutions are projected onto the smooth basis to produce the final solution. The resulting animation has greatly reduced spatial and temporal noise, and a computational cost roughly equivalent to the noisy, low sample computation.
Additional materials: [ShotRender.mov]
To appear in SIGGRAPH 2006
Available as Pixar Technical Memo #06-03
Michael Kass, John Anderson
January 2006
The Spacetime Constraints formulation attempts to marry the realism of physical simulation with the controllability of keyframe animation, but the resulting nonlinear optimization problems are generally extremely complicated and slow to solve. Here we explore the range of Spacetime Constraints problems that give rise to quadratic optimization functions solvable with linear systems of equations. We find that they generalize traditional splines to encompass oscillatory solutions. These problems can be solved at full frame rates, giving animators a keyframe animation tool with built in knowledge of a physical model. In addition to the splines themselves, we also introduce a new analysis method to extract oscillatory behavior from physical simulations in a way that can be connected naturally to the splines. It turns out that in order to have sufficient control of the frequency response of splines, we solve the Spacetime Constraints problems over the domain of complex numbers. As a consequence, our solutions have an imaginary part in addition to the real part. The imaginary part defines a phase angle that we show is very useful for controlling and generalizing oscillatory behavior whether extracted from simulation data or authored by hand.
Additional materials: [WigglySplines.mov]
Available as Pixar Technical Memo #06-06
Lena Petrovic, Mark Henne, John Anderson
January 2005
Hair is one of the crucial elements in representing believable digital humans. It is one of the most challenging elements, too, due to the large number of hairs on a human head, their length, and their complex interactions. Hair appearance, in rendering and simulation, is dominated by collective properties, yet most of the current approaches model individual hairs. In this paper we build on the existing approaches to illumination and simulation by introducing a volumetric representation of hair which allows us to efficiently model collective properties of hair. We use this volumetric representation of hair to describe hair response to illumination, hair to hair collisions, and to subtly direct simulations of hair. Our method produces realistic results for different types of hair colors and styles and has been used in a production environment.
Additional materials: [clip1.mp4], [clip2.mp4], [clip3.mp4], [clip4.mp4], [clip5.mp4], [clip6.mp4]
Available as Pixar Technical Memo #06-08