The PADL-1.0/2 system for defining and displaying solid objects

A Direct Minimization Approach for Obtaining the Distance between Convex Polyhedra

Computational methods used for the automatic generation of robot paths must be fully developed if truly automated manu facturing systems are to become a reality. An important requirement for determining feasible robot paths is the ability to compute the distance between the various elements of the robot and the workspace fixtures, jigs, and machinery. In this research, it is assumed that the robot and workspace solid geometry are represented as a collection of convex polyhe drons, and an efficient numerical algorithm for determining the minimum distance between two such polyhedrons is presented. In addition to determining the minimum distance between solids, the algorithm can also be used to efficiently ascertain whether a collision has occurred.

The numerical technique presented uses a sequence of constrained minimizations to obtain the closest three-dimen sional points on any two solid objects. Computational effi ciency is achieved with the algorithm presented because only the collection of planes (points and normals) which define the solids are used for the analysis. The bounding lines and vertices do not need to be explicitly calculated during the minimization procedure. The algorithm uses a direct ap proach for minimizing the nonlinear distance function which generates a sequence of search directions along the surfaces of the objects to obtain the global minimum. An extensive set of numerical tests are used to demonstrate the performance of the algorithm.

Optical implementation of a feature-based neural network with application to automatic target recognition

An optical neural network based on the neocognitron paradigm [IEEE Trans. Syst. Man Cybern. SMC-13, 826-834 (1983)] is introduced. A novel aspect of the architectural design is shift-invariant multichannel Fourier optical correlation within each processing layer. Multilayer processing is achieved by feeding back the output of the feature correlator iteratively to the input spatial light modulator and by updating the Fourier filters. By training the neural net with characteristic features extracted from the target images, successful pattern recognition with intraclass fault tolerance and interclass discrimination is achieved. A detailed system description is provided. Experimental demonstrations of a two-layer neural network for space-object discrimination is also presented.

An efficient algorithm for finding the CSG representation of a simple polygon

We consider the problem of converting boundary representations of polyhedral objects into constructive-solid-geometry (CSG) representations. The CSG representations for a polyhedron P are based on the half-spaces supporting the faces of P . For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practical O(n log n ) algorithm for doing this boundary-to-CSG conversion for a simple polygon of n sides. We also prove that such nice formulæ do not always exist for general polyhedra in three dimensions.

Model-based knowledge-based optical processors

An efficient 3-D object-centered knowledge base is described. The ability to on-line generate a 2-D image projection or range image for any object/viewer orientation from this knowledge base is addressed. Applications of this knowledge base in associative processors and symbolic correlators are then discussed. Initial test results are presented for a multiple degree of freedom object recognition problem. These include new techniques to achieve object orientation information and two new associative memory matrix formulations.