Recursive subdivision using interval arithmetic allows us to render CSG combinations of implicit function surfaces with or without anti -aliasing, Related algorithms will solve the collision detection problem for dynamic simulation, and allow us to compute mass. center of gravity, angular moments and other integral properties required for Newtonian dynamics. Our hidden surface algorithms run in ‘constant time.’ Their running times are nearly independent of the number of primitives in a scene, for scenes in which the visible details are not much smaller than the pixels. The collision detection and integration algorithms are utterly robust — collisions are never missed due 10 numerical error and we can provide guaranteed bounds on the values of integrals. CR Categories and Subject Descriptors: G. 1.0 [Numerical Analysis ] Numerical Algorithms 1.3.3 [Picture and Image Generation ] Display algorithms, Viewing algorithms, 1.3.5 [Computational Geometry and Object Modeling] Curve, surface, solid and object representations, 1.3,5 [Computational Geometry and Object Modeling] Hierarchy and geometric transformations. 1.3.7 [Three-Dimensional Graphics and Realism] Visible line/surface algorithms, Animation