A speedy voxel-tracing method for cutting solid display of 3-D images

Abstract

This paper describes a high-speed image-generation method which arbitrarily cuts out a three-dimensional (3-D) digital object (3-D image) in a 3-D frame memory and three-dimensionally displays its internal shape realistically. The idea of ray-tracing is applied to a 3-D memory space so that a high-speed ray-tracing is carried out in it by using a 3-D digital differential analyzer (DDA) called the reversible step type. To obtain cross points of a ray (straight line) and an object in a 3-D frame memory, an algorithm indicating address orders of all the voxels through which the ray passes is shown. A viewpoint of obtaining a realistic 3-D representation with a smooth surface from an irregular digital surface, calculation method of normal vector is important. A new factor, “existential density,” which can be obtained by a simple calculation around the surface of the digital object, is introduced; and a method to obtain a normal vector from this factor using the distribution of density gradient also is described. Since this calculation requires 3 × 3 × 3 operators, addition/ subtraction of integers and shift operations, the operation is high speed and suitable for hardware. The proposed algorithm is confirmed by a computer simulation which produces 3-D images with smooth shading.