The author proposes replacing the conventional Euclidean Processing with Homogeneous Processing, which is free from the ill effects of division and has the desirable properties of duality and projective invariance. The division operation negatively affects such properties as exaclness, robustness, and generality in computer-aided design systems. He mainly discusses two types of geometric processing in the homogenized geometric paradigm, i.e., subdivision method in surface design and set operations in solid modeling.

In order to achieve space-shared communication, it is essential to develop a truly 3D information space. Therefore, we aimed to construct a unified 3D CG space, that is, a unified 3D geometric modeling system. As for the basic coding method, "Extended Geometry Scheme" is proposed. By using this scheme, we have realized the 3D CG space with unified structure. Another important aspect of the space-shared communication is the development of teleoperation using robots on networks. It is important that 3D images are displayed naturally without wrong feeling in such real operation space. We have developed a 3D image display method using the parallax and focus function of human's eyes simultaneously. The proposed 3D display method is a combination of real image generation by Fresnel lens and parallax display with stereoscopic glasses. By using this method, it is possible to display realistic 3D images.

Introduces a model of a simple geometric processor on which geometric computation packages for solid modeling and computer graphics can be based. An exact integer representation and an adaptive determinant sign detection method are built into a geometric library to give a solution to the problem of accuracy and efficiency in 3D geometric programs. The computational core of this geometric library is designed so that it can be readily replaced with a simple hardware processor. The geometric computations are based on signed Plucker coordinates and the 4/spl times/4 determinant method. A method for classifying degenerate configurations of points using parallel sign detections of the Plucker coordinates of points, lines and planes using the processor is developed. A geometric computation library designed in this way has many advantages when compared to conventional geometric approaches.

Abstract The technique of solid modeling is essential in CAD/CAM applications, and is currently well established. However, problems remain, such as the lack of uniformity in geometric computations and the lack of stability of Boolean operations of two solids. In this paper, we introduce a theoretical solid modeling system that operates on boundary representations of polyhedral objects and is based on a new paradigm. The characteristics of the system are the following: (I) in Boolean Operations and modeling transformations, all geometric computations are performed by the 4 × 4 determinant method or the 4 × 4 matrix method in homogeneous space, which allows the system to avoid division operations, (2) all geometric computations are performed by the exact integer arithmetic, which makes the geometric algorithms stable and simple, and (3) primitive solids are constructed consistently in the integer domain, and the consistency is assured throughout Boolean operations and transformations.

An intersection detection method for solid modeling which is invariant under projective transformations is presented. We redefine the fundamental geometric figures necessary to describe solid models and their dual figures in a homogeneous coordinate representation. Then we derive conditions, which are projectively invariant, for intersections between these primitives. We will show that a geometric processor based on the 4 x 4 determinant method is applicable to a wide range of problems with little modification. This method has applications in intersection detections of rational parametric curves and surfaces and hidden-line/surface removal algorithms.

Abstract A new paradigm for geometric processing is proposed. The paradigm can be featured by the four key phrases: (1) Totally Four Dimensional Homogeneous Processing, (2) 4 × 4 Matrix Method and 4 × 4 Determinant Method, (3) Integer Arithmetic with Adaptive Data‐Length Control Technique, (4) Systematic Paradigm Structures Based on the Duality.

Triangulation is an efficient way to simplify and unify interference problems, such as hidden line and surface elimination and Boolean shape operations in solid modeling. Almost all of the processing relevant to a triangle can be performed by computing some 4 x 4 determinants. The author proposes a hardware processor (TRIANGLE PROCESSOR) that quickly intersects a triangle with a point, a line segment, or another triangle. Various applications of the TRIANGLE PROCESSOR are explained in this paper, including applications to face and volume triangulations.The author stresses that the triangulation approach and the TRIANGLE PROCESSOR simplify, speed up and unify various types of processing relating to interference.