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Whited B.,Walt Disney Animation Studios | Rossignac J.,Georgia Institute of Technology
IEEE Transactions on Visualization and Computer Graphics | Year: 2011

We define b-compatibility for planar curves and propose three ball morphing techniques between pairs of b-compatible curves. Ball-morphs use the automatic ball-map correspondence, proposed by Chazal et al. [1], from which we derive different vertex trajectories (linear, circular, and parabolic). All three morphs are symmetric, meeting both curves with the same angle, which is a right angle for the circular and parabolic. We provide simple constructions for these ball-morphs and compare them to each other and other simple morphs (linear-interpolation, closest-projection, curvature-interpolation, Laplace-blending, and heat-propagation) using six cost measures (travel-distance, distortion, stretch, local acceleration, average squared mean curvature, and maximum squared mean curvature). The results depend heavily on the input curves. Nevertheless, we found that the linear ball-morph has consistently the shortest travel-distance and the circular ball-morph has the least amount of distortion. © 2011 IEEE.

Handy Turner T.,Walt Disney Animation Studios
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2010

From the earliest stages of the Beauty and the Beast 3D conversion project, the advantages of accurate desk-side 3D viewing was evident. While designing and testing the 2D to 3D conversion process, the engineering team at Walt Disney Animation Studios proposed a 3D viewing configuration that not only allowed artists to "compose" stereoscopic 3D but also improved efficiency by allowing artists to instantly detect which image features were essential to the stereoscopic appeal of a shot and which features had minimal or even negative impact. At a time when few commercial 3D monitors were available and few software packages provided 3D desk-side output, the team designed their own prototype devices and collaborated with vendors to create a "3D composing" workstation. This paper outlines the display technologies explored, final choices made for Beauty and the Beast 3D, wish-lists for future development and a few rules of thumb for composing compelling 2D to 3D conversions. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Harmon D.,New York University | Harmon D.,Columbia University | Vouga E.,Columbia University | Smith B.,Columbia University | And 2 more authors.
Communications of the ACM | Year: 2012

The advent of computers has allowed users to implement these models as software in a computational environment, launching the field of physical simulation. One particularly difficult aspect of simulation is the modeling of complex collisions. A collision occurs when two objects attempt to occupy the same point in space at the same time. Because elements advance at their own pace, those not entangled in collisions can proceed at large time steps. Asynchronous variational integrators (AVIs) belong to a larger class of integrators that exactly conserve both momentum and symplecticity. A more complete analysis leading to the geometric and conservation properties of AVIs invokes ideas from discrete mechanics and variational integration. Dissipation and friction are critical for expressing the widest possible range of scenarios in physical simulation.

Vouga E.,Columbia University | Harmon D.,Columbia University | Tamstorf R.,Walt Disney Animation Studios | Grinspun E.,Columbia University
Computer Methods in Applied Mechanics and Engineering | Year: 2011

An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous variational integrators [1] (AVIs) are extended to handle contact forces by associating different time steps to forces instead of to spatial elements. By discretizing a barrier potential by an infinite sum of nested quadratic potentials, these extended AVIs are used to resolve contact while obeying momentum- and energy-conservation laws. A series of two- and three-dimensional examples illustrate the robustness and good energy behavior of the method. © 2011 Elsevier B.V.

Tamstorf R.,Walt Disney Animation Studios | Grinspun E.,Columbia University
Graphical Models | Year: 2013

Computation of bending forces on triangle meshes is required for numerous simulation and geometry processing applications. In particular it is a key component in cloth simulation. A common quantity in many bending models is the hinge angle between two adjacent triangles. This angle is straightforward to compute, and its gradient with respect to vertex positions (required for the forces) is easily found in the literature. However, the Hessian of the bend angle, which is required to compute the associated force Jacobians is not documented in the literature. Force Jacobians are required for efficient numerics (e.g., implicit time stepping, Newton-based energy minimization) and are thus highly desirable. Readily available computations of the force Jacobian, such as those produced by symbolic algebra systems, or by autodifferentiation codes, are expensive to compute and therefore less useful. We present compact, easily reproducible, closed form expressions for the Hessian of the bend angle. Compared to automatic differentiation, we measure up to 7× speedup for the evaluation of the bending forces and their Jacobians. © 2013 Elsevier Inc. All rights reserved.

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