Physically Based Modeling and Control of Turning

Turning plays an important role in activities such as skiing and bicycling. The act of turning requires steering, which performs two functions: changing the direction of motion and ensuring that balance is maintained. We analyze and control turning motions for a simple physical model. The physically based motion of the simple model is then used as a basis for the motion of more complex display models. A phase-diagram description of periodic turning motions (as in slalom skiing) is presented. The phase diagram is used to construct a control algorithm parameterized in terms of the frequency, sharpness, and heading of the turns. A second method of control allows an animator to draw an arbitrary path for the turning figure to follow while avoiding obstacles. A finite-time optimization is used to find the best physically feasible motion that closely follows the desired path. Examples of alpine skiing, snowboarding, bicycling, and telemark skiing are given.