Keyframe animation is a common technique to generate animations of deformable characters and other soft bodies. With spline interpolation, however, it can be difficult to achieve secondary motion effects such as plausible dynamics when there are thousands of degrees of freedom to animate. Physical methods can provide more realism with less user effort, but it is challenging to apply them to quickly create specific animations that closely follow prescribed animator goals. We present a fast space-time optimization method to author physically based deformable object simulations that conform to animator-specified keyframes. We demonstrate our method with FEM deformable objects and mass-spring systems. Our method minimizes an objective function that penalizes the sum of keyframe deviations plus the deviation of the trajectory from physics. With existing methods, such minimizations operate in high dimensions, are slow, memory consuming, and prone to local minima. We demonstrate that significant computational speedups and robustness improvements can be achieved if the optimization problem is properly solved in a low-dimensional space. Selecting a low-dimensional space so that the intent of the animator is accommodated, and that at the same time space-time optimization is convergent and fast, is difficult. We present a method that generates a quality low-dimensional space using the given keyframes. It is then possible to find quality solutions to difficult space-time optimization problems robustly and in a manner of minutes.

Controllers are necessary for physically-based synthesis of character animation. However, creating controllers requires either manual tuning or expensive computer optimization. We introduce linear Bellman combination as a method for reusing existing controllers. Given a set of controllers for related tasks, this combination creates a controller that performs a new task. It naturally weights the contribution of each component controller by its relevance to the current state and goal of the system. We demonstrate that linear Bellman combination outperforms naive combination often succeeding where naive combination fails. Furthermore, this combination is provably optimal for a new task if the component controllers are also optimal for related tasks. We demonstrate the applicability of linear Bellman combination to interactive character control of stepping motions and acrobatic maneuvers.

Abstract Many data‐driven animation techniques are capable of producing high quality motions of human characters. Few techniques, however, are capable of generating motions that are consistent with physically simulated environments. Physically simulated characters, in contrast, are automatically consistent with the environment, but their motions are often unnatural because they are difficult to control. We present a model‐predictive controller that yields natural motions by guiding simulated humans toward real motion data. During simulation, the predictive component of the controller solves a quadratic program to compute the forces for a short window of time into the future. These forces are then applied by a low‐gain proportional‐derivative component, which makes minor adjustments until the next planning cycle. The controller is fast enough for interactive systems such as games and training simulations. It requires no precomputation and little manual tuning. The controller is resilient to mismatches between the character dynamics and the input motion, which allows it to track motion capture data even where the real dynamics are not known precisely. The same principled formulation can generate natural walks, runs, and jumps in a number of different physically simulated surroundings.

Animating natural human motion in dynamic environments is difficult because of complex geometric and physical interactions. Simulation provides an automatic solution to parts of this problem, but it needs control systems to produce lifelike motions. This paper describes the systematic computation of controllers that can reproduce a range of locomotion styles in interactive simulations. Given a reference motion that describes the desired style, a derived control system can reproduce that style in simulation and in new environments. Because it produces high-quality motions that are both geometrically and physically consistent with simulated surroundings, interactive animation systems could begin to use this approach along with more established kinematic methods.

We present results from a user study that compared six visualization methods for two-dimensional vector data. Users performed three simple but representative tasks using visualizations from each method: 1) locating all critical points in an image, 2) identifying critical point types, and 3) advecting a particle. Visualization methods included two that used different spatial distributions of short arrow icons, two that used different distributions of integral curves, one that used wedges located to suggest flow lines, and line-integral convolution (LIC). Results show different strengths and weaknesses for each method. We found that users performed these tasks better with methods that: 1) showed the sign of vectors within the vector field, 2) visually represented integral curves, and 3) visually represented the locations of critical points. Expert user performance was not statistically different from nonexpert user performance. We used several methods to analyze the data including omnibus analysis of variance, pairwise t-tests, and graphical analysis using inferential confidence intervals. We concluded that using the inferential confidence intervals for displaying the overall pattern of results for each task measure and for performing subsequent pairwise comparisons of the condition means was the best method for analyzing the data in this study. These results provide quantitative support for some of the anecdotal evidence concerning visualization methods. The tasks and testing framework also provide a basis for comparing other visualization methods, for creating more effective methods and for defining additional tasks to further understand the tradeoffs among the methods. In the future, we also envision extending this work to more ambitious comparisons, such as evaluating two-dimensional vectors on two-dimensional surfaces embedded in three-dimensional space and defining analogous tasks for three-dimensional visualization methods.

Presents results from a user study that compared six visualization methods for 2D vector data. Two methods used different distributions of short arrows, two used different distributions of integral curves, one used wedges located to suggest flow lines, and the final one was line-integral convolution (LIC). We defined three simple but representative tasks for users to perform using visualizations from each method: (1) locating all critical points in an image, (2) identifying critical point types, and (3) advecting a particle. The results show different strengths and weaknesses for each method. We found that users performed better with methods that: (1) showed the sign of vectors within the vector field, (2) visually represented integral curves, and (3) visually represented the locations of critical points. These results provide quantitative support for some of the anecdotal evidence concerning visualization methods. The tasks and testing framework also provide a basis for comparing other visualization methods, for creating more effective methods and for defining additional tasks to further understand tradeoffs among methods. They may also be useful for evaluating 2D vectors on 2D surfaces embedded in 3D and for defining analogous tasks for 3D visualization methods.