Michael Kass, Aaron Lefohn, John Owens
January 2006
Accurate computation of depth-of-field effects in computer graphics rendering is generally very time consuming, creating a problematic workflow for film authoring. The computation is particularly challenging because it depends on large-scale spatially-varying filtering that must accurately respect complex boundaries. Here we introduce an approximate depth-of-field computation that is good enough for film preview, yet can be computed interactively on a GPU. The method makes use of separable recursive filters to create efficient large-kernel convolutions. The individual recursive filters are derived from a minimum principle that produces spatially varying coefficients in the course of solving a tri-diagonal linear system. A straightforward GPU implementation of recursive filters would have poor performance, but using the well-established method of cyclic reduction, we are able to vectorize the computation and achieve interactive frame rates.
Additional materials: [movie.avi]
Available as Pixar Technical Memo #06-01
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
David Baraff, Andrew Witkin, Michael Kass
August 2003
Deficient cloth-to-cloth collision response is the most serious shortcoming of most cloth simulation systems. Past approaches to cloth-cloth collision have used history to decide wheter nearby cloth regions have interpenetrated. The biggest pitfall of history-based methods is that an error anywhere along the way can give rise to persistent tangles...This paper describes a history-free cloth collision response algorithm based on global intersection analysis of cloth meshes at each simulation step...
Available in the Proceedings of SIGGRAPH 2003
Tony DeRose, Michael Kass, Tien Truong
August 1998
The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological restrictions that NURBS impose. In order to move beyond these restrictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in high-end CG production has been limited.
Here we describe a series of developments that were required in
order for subdivision surfaces to meet the demands of high-end
production. First, we devised a practical technique for
constructing provably smooth variable-radius fillets and blends.
Second, we developed methods for using subdivision surfaces in
clothing simulation including a new algorithm for efficient
collision detection. Third, we developed a method for
constructing smooth scalar fields on subdivision surfaces, thereby
enabling the use of a wider class of programmable shaders. These
developments, which were used extensively in our recently
completed short film Geri's game, have become a highly
valued feature of our production environment.
Available in the Proceedings of SIGGRAPH 1998.