been generated by physical simulation. The motion is generated by solving a system of differential equations approximately at each time step, and numerical methods are employed for this purpose. In practice, evaluation of the differential equations can be very time consuming, especially if physical constraints on the system are required. Common algorithms, such as Runge-Kutta, achieve their stability by approximating higher-order derivatives through multiple evaluations of the differential equations over a single time-step.1 However, for computer animation we can usually tolerate a "visually acceptable" sacrifice in accuracy for faster evaluation of the equations of motion. In order to achieve interactive simulation rates, it is necessary to find explicit methods that meet the accuracy requirements and maintain stability while only requiring a single evaluation of the forces acting on the system per time step.
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