Physically based rigging for deformable characters
Introduction
Believable computer animation requires that virtual characters such as humans and animals be produced with a high degree of realism. Faces should express emotions through mouth and eyebrow movements, limbs should bend at joints, muscles should bulge when in use, and soft tissue such as fat should bounce and vibrate when the character walks.
To create such realism, the traditional animation pipeline requires that each character be rigged, a process that is analogous to setting up a puppet to be controlled by strings. After having been rigged, a character’s shape can be controlled through a set of abstract parameters with meaningful names, like “lift left eyebrow” or “bend right knee.” For each keyframe, instead of having to position each vertex of the surface mesh, the animator need only set the values of the control parameters. To include fleshy bounces and vibrations, the animator must either create them by hand or tack a physical simulation onto the geometrically crafted deformations. In interactive settings, such as video games, these additional motions are not always possible to anticipate, necessitating some form of physical simulation.
Elastic simulation has proved to be a powerful method both for automatically creating plausible skeleton-dependent deformations and for introducing secondary motions. These simulations can be performed quickly with techniques like the finite element method for linearized elastic dynamics, allowing for real-time simulation suitable for interactive video games and rapid prototyping for film production.
A significant shortcoming of these approaches is that the simulations do not provide a way for the animator to control the shape, other than by posing the skeleton. In this paper we address this limitation by introducing force-based rigging. In our system, deformations are created indirectly through the use of forces.
Section 3 describes our physical and numeric framework. Our system is built on a new method of pose-dependent linearization of elasticity, which ensures a correspondence between deformations and forces, while producing plausible results (both static and dynamic equilibria) at the speed of linear dynamics (Section 3.3). To increase realism, we introduce a new technique for handling collisions near creases (Section 3.4). Section 4 describes our rigging framework, which includes interactive optimization-based rig configuration (Section 4.2), computing rig forces from sculpted or measured surface deformations (Section 4.3), transferring rigging between characters (Section 4.4), and adaptive rigging (Section 4.5).
Section snippets
Background
Many methods have been devised for the geometric deformation of surfaces, including free-form deformation [26], [17], shape interpolation [16], [29], [2], and wire deformation [28]. Such methods form the building blocks for rigging in modern animation programs such as Maya. These methods are not based on physical simulation, so the animator must hand craft physically realistic motions. The work of Kry et al. uses simulated input deformations to produce very realistic (but not dynamic)
Deformable character formulation
Our modeling and simulation of deformable characters builds on the framework of Capell et al. [10], augmented with rigging forces, a new pose-dependent linearization scheme, and collision handling near creases.
The basic data defining a deformable character are: (i) an elastic domain (the interior of a triangular mesh Γ), with specified mass density, Poisson ratio, and Young’s modulus, (ii) an embedded cell complex (or control lattice) containing Ω, (iii) a skeleton S ⊂ Ω consisting of
Rigging—shape control using forces
Shape control is important because it enables the animator to create more realistic deformations and express the emotion and intent of a character. For example, skeletal controls will not effectively help the animator to make a character appear to breathe, produce a muscle bulge, or smile. To address this shortcoming, we introduce an additional control mechanism.
Since our framework is based on physical simulation, two natural mechanisms exist for influencing the shape: hard constraints and
Results
Some of the results of our rigging system have already been shown in Fig. 3, Fig. 4, Fig. 6, Fig. 7. We tested the system on two additional input surfaces: “Ganesh” (a rotund humanoid figure with an elephant’s head) designed using geometric modeling software, and a scan of a human. The Ganesh character was instrumented with three rigs which were then transferred to the human character. One of the rigs was derived from a third model, the arm scan demonstrated in Fig. 6, Fig. 7. Another rig,
Conclusion
Our system gives animators control over the shapes of elastic deformable characters by introducing force fields as the building blocks of rigging. The resulting simulations combine the guidance of the animator with other influences such as gravity, physical constraints, and user interaction. A key component is a new method of approximating non-linear elasticity via a pose-dependent linear system, which enables efficient dynamic simulation, computation of static equilibria, and optimization; our
Acknowledgments
Thanks to Brett Allen, Keith Grochow, Daichi Sasaki, Supriyo, Ernest Wu, and Yeuhi Abe. This research was supported by NSF Grants EIA-0121326, CCR-0092970, IIS-0113007, and CCR-0098005, and by UW Animation Research Labs, an Alfred P. Sloan Fellowship, Electronic Arts, Sony, Microsoft Research, Alias, and Washington Research Foundation.
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This work was done while the first author was at the University of Washington.