Hiroshi Toriya

Octree-Related Data Structures and Algorithms

The octree is not always a desirable data structure. Here, together with their formal definitions and related algorithms, are two data structures more suitable for graphics operations.

UNDO and REDO Operations for Solid Modeling

This article describes a method of representing a solid design procss using a tree structure. This representation supposrts UNDO and REDO operations for regenerating any solid in a previous stage of the design. The implementations of invertible set operations is also given in detail.

XVL: a compact and qualified 3D representation with lattice mesh and surface for the Internet

Computer graphics systems and CAD/CAM systems are widely used and an abundance of 3D-Data in various fields exists. However, based on the VRML technique, it is difficult to send such 3D-Data through the Internet, because of the large data size. Transmission of practical and highly detailed 3D-Data through the Internet becomes a primary requirement. Therefore, a compact and qualified 3D-Data representation method is greatly required. This paper describes XVL (eXtended VRML with Lattice), a new framework for compact 3D-Data representation with high quality surface shape. By utilizing a free-form surface technique, qualified surfaces are transferred with a limited amount of data size and rendered. Free-form surfaces transferred by an efficient data structure are called lattice structure. This data structure contains only vertices, topologies, and attributes, and can be converted to the original surface. Because the lattice structure is regarded as a polygon mesh, it can be easily integrated to a VRML file. These surfaces and lattice have the same topology and are thus interchangeable in the lattice structure. By using weighting attributes, a sophisticated surface shape can be represented. Some practical XVL applications, such as an intuitive surface design system, are also introduced.

A method to convert a Gregory patch and a rational boundary Gregory patch to a rational Be´zier patch and its applications

A Gregory patch and a rational boundary Gregory patch have characteristics such that any n-sided loop is interpolated smoothly and that many patches can be generated to connect smoothly with each other. However, since the mathematical form of these patches is different from conventional surface patches such as the Bezier patch, no algorithm was known to subdivide them. The subdivision algorithm that could be applied to other surface patches could not be applied to them.

Boolean operations for solids with free-form surfaces through polyhedral approximation

This paper describes a new implementation method for Boolean operations between solids with free-form surfaces. Boolean operations consist of two processes-topological modification and geometric modification-which are performed separately in our method. This separation makes the Boolean operation process simple and robust. Surfaces contained in the final solid are interpolated by the repatching facility using Gregory patches.

An enhanced rounding operation between curved surfaces in solid modeling

This paper introduces a method using the rolling ball technique to generate geometrical and topological information to blend two surfaces in B-reps-based solid modeling systems. At first, a ball is positioned so that it touches both surfaces to be blended, and the trajectories of the tangent points of the ball and the surfaces are computed. Edges are generated on the surfaces along the trajectories, and are then joined by arcs to create the blending surfaces. The created surface depends on the shape of the surrounding edges, and is interpolated using rational boundary Gregory(RBG) patches. By using this method, blending surfaces can be connected smoothly, even at the corner of a solid. This method can also be applied to surface blends other than those using the rolling ball technique. Variable-radius blends which are essential in free-form surface design can also be generated using this method.

Boolean Operations on Solids Bounded by a Variety of Surfaces

In the CAD/CAM/CAE field, it is important that solid modeling systems support and handle characteristics of many different types of surfaces. This paper describes a Boolean operations algorithm for such solid modeling systems. The algorithm works for solids with a wide range of surfaces. There are two main problems in Boolean operations on solids with various types of surface. The first problem is that the curves calculated by the intersection of two surfaces are given in a very complicated form, and therefore must be represented approximately. The algorithm avoids the accumulation of approximation errors by using the three-surface intersection calculation method. The second problem is the speed of intersection calculations and also the range of surfaces supported by the Boolean operation algorithm. The algorithm uses two intersection calculation methods depending on the type of surface. This means that Boolean operations can be applied to a wide range of surfaces, and also that the speed and reliability of the Boolean operations increase due to the selection of the most suitable algorithm.

Invertible Set Operations for Solid Modeling

The paper describes a method of representing the solid design process using a tree data structure. Previous stages in the development of a design can be quickly regenerated by specifying nodes of this tree. A detailed description of the implementation of invertible set operations is also presented.

Free-Form Surfaces

Surfaces have been studied as an expanded form of curves for a long time. As the pioneers of studies on surface representations, Coons and Bezier can be referred. In 1964, Coons proposed the Coons surface[44] for surface representation. It is used to define surface shapes interactively in computers. Bezier proposed the Bezier surf ace [11,13] in 1966, also for representing surfaces and it is used in the design of automobile bodies. Both the Coons and the Bezier surfaces, used for surface representations, create rectangular patches. Since the Coons and Bezier surfaces, a lot of research has been done to expand and generalize representations by these surfaces.

Functions in Aiding Design

In the initial stages of designing a product, there will be various requirement regarding the product’s appearance, quality, reliability, or cost. Often, it is difficult to satisfy all these requirements completely. Conventional CAD systems enable designers to model the required geometric shape, although this does not always meet with the desired requirements. If it does not, the shape has to be corrected. In addition, the changing requirements of a product means that the product shape has also to be modified sometimes. Because of this, the functions that easily modify the product shape once it is designed are indispensable to design flexibility and productivity. In conventional CAD systems, however, functions that aid design have not been fully supported, thus making the modification in product shape very difficult.