Abstract: A method for determining a distance between a first node and a second node that share a root node within a structured program. A first node path between the first node and the root node is determined, and a first node depth is counted. A second node path between the second node and the root node is also determined, and a second node depth is likewise counted. One of the node paths that has a highest count is designated as the deepest path, and the other is designated as the shallowest path. The deepest path is descended to a depth that is equal to that of the shallowest path, and a distance count is increased by one count for each node that was descended on the deepest path to reach a depth that is equal to the shallowest path. Both the deepest path and the shallowest path are descended to the root node, and the distance count is increased by two counts for each node that was descended. The distance count is provided as the distance between the first node and the second node.

Abstract: A computer display system for real time display of digital movie frames, derived from 24 bit, bit mapped graphic images formed of pixels and 32 bit floating point z values, and sprites which can interact with the movie frames. The system displays movies comprised of a compressed image frame, and a value limited, posterized, and compressed z frame. The incorporation of the novel z frame allows for 24 different levels of interactive, real time clipping of the sprites with the background image frame. The apparatus of an image frame associated with the z frame can also allow for two separate movies comprised of image frames and z frames to be superimposed with precedence clipping between the two independent movies in real time.

Abstract: A method and apparatus for the production of digital movies of modeled elements within a virtual environment using a virtual camera which renders image frames. A mapper indicates those positions within the environment onto which the camera can and cannot go. A script writer determines the camera positions of the image frames needed for all the possible individual movies required to navigate the environment, and writes at least some of the positions into a script. A camera controller moves the camera to the positions called for in the script, operates the camera to render image frames, and names the image frames rendered by the camera. A movie builder builds at least some of the image frames rendered by the camera into individual movies, each movie having a predetermined series of image frames such that the sequential display of the series provides the illusion of motion. A movie unifier unifies all the individual movies into a single unified movie.