Abstract: A method for use with a computer system includes assembling a group of volume units to represent at least a portion of a three-dimensional (3-D) object and compressing each volume unit onto a pixel plane to form an associated indication of the volume unit. The indications are used to form a first image of a view of the portion(s) of the 3-D object on a display of the computer system. The view of some of the volume units are changed leaving the view of the remaining volume units unchanged. The indications that are associated with the remaining volume units are used to form a second image of the portion(s) of the 3-D object on the display.

Abstract: A method of modeling and rendering a three-dimensional complex surface using a triangle mesh is disclosed. The method can reduce memory requirement and rendering time by using local height maps and by assigning neighborhood coordinates to any point on a surface near the triangle mesh assigned to that surface. Barycentric coordinates are used to identify points in a triangular polygon to work with height data in the local height map associated with that triangular polygon. The local height maps allow collision detection of a ray with the three-dimensional surface. Lipshitz constants associated with the three-dimensional surfaces are used to find a point on the next ray closest to the three-dimensional surface to jump to, making the search for such collision points efficient.