Being able to animate a human character in a way that does not require the expertise of a professional animator can be useful in many different applications: children would be able to animate stories, witnesses would be able to visually describe an accident to lawyers, football fans would be able to re-produce their favorite football plays. These applications and others like them have motivated this thesis: it focuses on the development of methods that given a sketch of the desired motion, can interactively create a physically realistic motion that matches that sketch.

This problem is very hard to solve in part because human-like characters are high-dimensional and therefore the space of their motions also appears to be highdimensional. However, the high dimensionality of the problem is an artifact of the problem representation because most dynamic human motions are intrinsically lowdimensional with legs and arms operating in a coordinated way. For example, six to eight dimensions are enough to represent a human jump that looks quite similar to the original high-dimensional version.

In this thesis, we experiment with two different approaches that use this observation to build a compact (reduced-space) representation of the motion based on available motion capture data. In the first part of the thesis we build a continuous low-dimensional representation of the desired motion. By confining the solution to a smaller search space, we are able to synthesize physically realistic motion for a human character that matches a rough sketch provided by the user.

In the second part of the thesis, we build a discrete reduced-space representation of the desired motion. This representation can be viewed as a combination of the motion graph and interpolation techniques. The final motion is an interpolation of k time-scaled paths through the motion graph. We assess its physical correctness using our analysis of the physical correctness of interpolated motions. The optimization in the discrete space supports interactive frame rates and allows for the synthesis of less dynamic motions and motions that are sequences of different behaviors. We also demonstrate how to search a motion graph of a reasonable size for an optimal (or nearly-optimal) solution.

For both, the continuous and discrete optimization approaches the synthesized motion is likely to contain natural coordination patterns because the solution is constrained to a much smaller search space computed based on motion capture data. This objective is difficult to describe mathematically and is often not achieved when optimizing in the full search space. In the last chapter of the thesis, we compare the two approaches and provide some intuition as to when one is more applicable than the another.

154 pages

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