Interactive spacetime control for animation

This paper describes new techniques to design physically based, goal directed motion of synthetic creatures. More specifically, it concentrates on developing an interactive framework for specifying constraints and objectives for the motion, and for guiding the numericrd solution of the optimization problem thus defined. The ability to define, modify and guide constrained spacetime problems is provided through an interactive user interface. Innovations that are introduced include, (1) the subdivision of spacetime into discrete pieces, or Spacetime Windows, over which subproblems can be formulated and solved, (2) the use of cubic B-spline approximation techniques to define a C2 function for the creature’s time dependent degrees of freedom, (3) the use of both symbolic and numerical processes to construct and solve the constrained optimization problem, and (4) the ability to specify inequality and conditional constraints. Creatures, in the context of this work, consist of rigid links connected by joints defining a set of generalized degrees of freedom. Hybrid symbolic and numeric techniques to solve the resulting complex constrained optimization problems are made possible by the special structure of physically based models of such creatures, and by the recent development of symbolic algebraic languages. A graphical user interface process handles communication between the user and two other processes; one devoted to symbolic differentiation and manipulation of the constraints and objectives, and one that performs the iterative numerical solution of the optimization problem. The user interface itself provides both high and low level definition of, interaction with, and inspection of, the optimization process and the resulting animation. Implementation issues and experiments with the Spacetime Windows system are discussed,

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