Motion control and surface modeling of articulated figures in computer animation

Motion control and surface modelling remain the two major challenges in the creation of articulated figures for computer animation. This thesis addresses motion control with an interactive figure manipulation tool encorporating dynamic analysis with kinematic constraints, and surface modelling with a new approach to surface representation using tensor-product splines. Kinematic control in computer animation is time-consuming, because the manipulation of an articulated figure requires the positioning of large number of interdependent degrees-of-freedom. Dynamic analysis (simulation through the Newtonian equations of motion) has been proposed as an aid in this process, but algorithms incorporating kinematic constraints are too slow to be used in an interactive system. Recursive dynamic formulations run at interactive rates on current hardware but do not directly accommodate kinematic constraints. Manikin is an interactive animation system unifying both kinematic procedures and dynamic analysis for motion control in the positioning of articulated figures for key-frame animation. A novel method of incorporating kinematic constraints into a recursive dynamic formulation is presented. Modelling the skin of an articulated figure requires a smoothly flowing surface covering the limbs and deforming realistically around the joints as the underlying skeleton changes position. With polygonal models, additional polygons are easily created where they are needed, but a prohibitively large number of data points are required to represent a smooth surface. Tensor product spline surfaces are smooth; however, patches cannot be added locally but must be created by splitting an entire row or column of patches. This non-local refinement adds significantly to the number of patches required to represent a surface and makes manipulation, especially in the design and animation of computer characters, difficult. A hierarchical free-form surface is a new, general, space efficient approach to the representation of tensor-product spline surfaces that offers greater editing flexibility than is found with traditional representations. This representation is a data structuring technique allowing local refinement of a tensor-product spline surface, so that the number of patches in a given region can be increased without affecting the rest of the surface. The hierarchical form is applicable to any spline with a refinement procedure and locally supported basis functions. Applications include spline curves and volumes as well as surfaces, and a method using the hierarchical form in fitting tensor-product surfaces to gridded data is also presented. The hierarchical form, coupled with a reference plus offset representation of the hierarchy, allows surface manipulation independent of refinement and allows broad scale changes in surface shape that maintains fine scale surface details. These properties greatly ease the task of creating a realistic animated figure with a single tensor-product spline surface and are useful in free-form surface design in general.