Computer Geometric Modeling Research Articles

A unified architecture for the computation of B-spline curves and surfaces

B-Splines, in general, and Non-Uniform Rational B-Splines (NURBS), in particular, have become indispensable modeling primitives in computer graphics and geometric modeling applications. In this paper, a novel high-performance architecture for the computation of uniform, nonuniform, rational, and nonrational B-Spline curves and surfaces is presented. This architecture has been derived through a sequence of steps. First, a systolic architecture for the computation of the basis function values, the basis function evaluation array (the BFEA), is developed. Using the BFEA as its core, an architecture for the computation of NURBS curves is constructed. This architecture is then extended to compute NURBS surfaces. Finally, this architecture is augmented to compute the surface normals, so that the output from this architecture can be directly used for rendering the NURBS surface.

Elimination and resultants.2. Multivariate resultants

In part 1 we explained how resultants apply to problems in computer graphics and geometric modeling. This tutorial concerns methods for constructing multivariate resultants, including methods for bidegree and equal-degree polynomial equations. It also describes u-resultants, a powerful use of standard resultants.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Automatic Finite Element Mesh Generation Over Intersecting Rigid Body-Movable Subdomains for the Automation of Parametric Conceptual Design

An approach for the automatic generation and refinement of three-dimensional finite element meshes subdivided by multiply connected, rigid body movable subdomains has been developed. A combination of computational geometry and geometric modeling techniques have been employed to implement parametric computer-aided design based on the finite element method. Nonconvexity of an overall three-dimensional domain has been handled by combining convex geometric primitives as subdomains for the construction of a three-dimensional domain. A clipping technique is employed for determining intersection points between subdomains bounded by traingulated surface, following their rigid body movements. To demonstrate the utility of this approach to parametric redesign, a series of meshes that model a hip joint prosthesis and a reciprocating internal combustion engine, as assemblies of parametrically-defined geometric primitives, has been developed.

The role of geometric modeling in computer integrated manufacturing

This paper briefly describes the theories behind the different geometric modelling techniques. Through an examination of some of the important applications such as Numerical Control Machining, Computer Aided Design, Computer Aided Assembly, and Robot Programming and Simulation, we conclude the need for the integration of two or more modeling techniques in one system. This paper also addresses the problem of interfacing geometric modelers with other components of Computer Integrated Manufacturing. This discussion involves the problems of standardization. Finally some of the major challenges facing computer geometric modeling are defined as future areas for research such as the representation of both form and size tolerance in the model and the predicted interface with expert systems.

多面体の内外判定の新しい方法

In computer graphics and geometric modeling, polyhedron's inside test, a determination whether a given point lies inside or outside a polyhedron, plays an important role. However, this cannot be realized easily. Since former methods have some difficulties, a yew method of design is introduced in this papaer.When all polygons of polyhedron's faces are projected ont.o a sphere whose center lies on the given point with radius of 1, the sum of area becomes 4π i f the point lies inside the polyhedron. Otherwise, this becomes 0. Though it is difficult to calculate an area of the polygon on the sphere, it can be calculated by dividing the polygon into triangles.This new algorithm of inside test was programmed and applied to two kinds of object, one, a cube and the other an octagonal prism. As a result, the errors of area's calculation for 4π was under 0.03%. These figures confirms that the test can be applied to rather complex objects.