Generalized implicit functions for computer graphics

We describe a method of generalizing implicit functions by use of modal deformations and displacement maps. Modal deformations, also known as free vibration modes, are used to describe the overall shape of a solid, while displacement maps provide local and fine surface detail by offsetting the surface of the solid along its surface normals. The advantage of this approach to geometric description is that collision detection and dynamic simulation become simple and inexpensive even for complex shapes. In addition, we outline an efficient method for fitting such models to three dimensional point data.