O Control of Motion Path and Speed in a Spline - Animation

Various graphical models for the visualization of pharmacologically-active proteins have been developed to help recognize a three-dimensional structure of molecules; these models have been principally aimed at visualizing the static images of molecules. This work is an extension of such computer representations to animated display of molecular activities such as the folding of protein molecules. This dissertation describes a new graphical model suitable for the animation of protein folding. During animation, the motion path of individual atoms forming a molecule may exhibit an undesirable wiggle or inflection under certain conditions. The G ^1 class of splines can be used to eliminate these artifacts, but a mathematical representation of the G^1^lines has not been developed to date. We develop an analytic expression for the G ^1^lines. Moreover, we extend and apply the G^1 splines for the generation of more diversified motion path in an interactive animation environment. This dissertation develops a method termed the incremental knot spacing to control the motion speed by an approximation in the discrete parameter domain so that control of motion speed is achieved. We separate temporal aspect from spatial aspect of animation while providing a means of hitting key frames. Based on these major tools for the control of motion path and speed, we develop a molecular animation model termed the solid backbone model, in which a molecular backbone is depicted as a combination of shaded cylindrical surfaces. Most importantly, the inbetweening technique was incorporated into the model to smooth the motion transition.