Abstract In this paper, we present a general, systematic and consistent treatment of time and events for computer animation. We first formalize the concepts of events and create a time primitive called an event unit. We then present a succession of organization schemes to compose event units for generating complex motion sequences. We present a directed graph representation for the organization of time and events that suggests the form of an event‐based time programming language. Details of implementation of a general event simulation system are given. Our approach provides a clean partitioning for the problem of motion design, a hierarchical scheme to compose motion behaviors from time primitives and a programming model for organizing animation. Traditional methods of kinematic controls and key frame interpolation are special cases of our general scheme. In addition, our treatment of events can be combined with kinematics, dynamics or constraint‐based systems to generate powerful motion modeling systems.

In this paper, we describe a new kind of constraint-based figure-maker for parametrically defined curves. Figures are made by defining objects and imposing constraints on their geometric behavior. We present a formulation of constraints as three ways in which two scalar real valued functions may be compared. This lets us specify equality, optimality and inequality constraints. We also introduce the mechanism of connectors. Connectors are used to connect various geometric entities through constraints. Behavior of connectors depends only on the local properties of curves. Connectors remove the need for an object to know about the kinds of constraints or the kinds of other objects it is connected to in order to act to satisfy a constraint. This makes for a very manageable and scalable program as the number of objects and constraints grows. An objects is modified in response to deviation of its state from the desired state specified through constraints. We have implemented some general low-level methods of specifying and satisfying constraints. These basic mechanisms can be used as an assembly language and combined hierarchically to define very general constraints.

In this paper, we present a robust and mathematically sound ray-intersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine tuning or human choice of interactive parameters. Instead, it requires two upper bounds: "L" that limits the net rate of change of the implicit surface function f(x,y,z) and "G" that limits the rate of change of the gradient. We refer to an implicit surface with these rate limits as an "LG-implicit surface."Existing schemes to intersect a ray with an implicit surface have typically been guaranteed to work only for a limited set of implicit functions, such as quadric surfaces or polynomials, or else have been ad-hoc and have not been guaranteed to work. Our technique significantly extends the ability to intersect rays with implicit surfaces in a guaranteed fashion.