Showing papers on "Geometric data analysis published in 1988"

Efficient Structures for Geometric Data Management

Abstract: Operators and representation schemes for geometric data.- Polyhedral chains.- A dual approach to detect polyhedral intersections in arbitrary dimensions.- The cell tree: An index for geometric databases.- The arc tree: An approximation scheme to represent arbitrary curved shapes.- Conclusions.

Geometric modeling and computer vision

Abstract: Geometric matching algorithms and geometric representations are examined for point sets, curves, surfaces, volumes, and their space-time trajectories. The author focuses mainly on general-purpose techniques. Geometric matching benefits greatly from taking advantage of symmetries and special features, e.g. dihedral edges and circles or any three reliably identifiable feature points. Volume matching and representation techniques are also presented. Texture and fractal representations are briefly described. >

System for providing three dimensional object descriptions

Abstract: A system for producing human readable physical data in text form from geometric data in mathematical form that partially describes a three dimensional object A first database is provided that contains geometric data in mathematical form representative of the shape of the object A second database contains physical data in text form At least a portion of the data in the first database can be extracted and used as the basis for calculations of physical data in mathematical form, which can be converted into human readable physical data in text form The resulting physical data can be merged with data from the second database to produce a complete geometric description in text of the object The present invention also contemplates a mechanism for using empirical data with a knowledge based system The knowledge based system can be used to modify the physical data to adapt geometric properties to a manufacturing process

Model generation and modification for dynamic systems from geometric data

Abstract: We are experimenting with a prototype implementation of a simulation system for rigid body motion where the objects to be simulated are specified by a geometric description and a few symbolic data, such as object density, the type of hinge between certain bodies, and environmental factors. In our approach, the system automatically generates the appropriate mathematical model describing the current system dynamics, and revises the model so as to account for unanticipated changes in the system’s topology. For example, when simulating impact behavior, the system will not know in advance what objects might collide at which points, thus invalidating the usual approach of defining constraint forces between point pairs that are negligible except when the points are in close proximity. We describe the overall organization of the system, and give a general method to effect this self-modification. Focusing on characteristic cases such as gaining or losing contact and low-velocity collision, we discuss our experience with the system, its flexibilities, and its limitations.

Estimating convex shapes from support line measurements using prior geometric information

Abstract: In this paper we present several algorithms for reconstructing 2-D convex sets given support line measurements for which the angles are known precisely but the lateral displacements are noisy. We extend the algorithms given in [5] by explicitly incorporating prior information about the shape of the objects to be reconstructed. In particular, the prior shape information is contained in a prior probability on support vectors, where a support vector is a vector formed from the lateral displacements of a particular set of support lines of an object. In order to relate the support vector prior to the expected shape of an object we develop a vector decomposition called the Size/Shape/Shift decomposition which helps to provide insight into the detailed geometric relationship between support vectors and 2-D convex objects. We then use the maximum a posteriori (MAP) criterion to determine the specific form of the support vector estimator. The computations involve a quadratic programming optimization stage, which is used to determine one component of the decomposition, and either a line search or conjugate gradient stage, which is used to determine the remaining components. The performance of the algorithms is demonstrated using simulated support line measurements of an ellipse.

Geometric modeling of smooth surfaces

Abstract: The methods of Computer Aided Geometric Design have arisen from the need of efficient computer representation of practical curves and surfaces used in engineering design. The generation of smooth surfaces from a set of three-dimensional data points is a key problem in this field. The purpose of this paper is to present algorithms for designing and testing smooth free-form surfaces.

Geometric easoning an rganized timizatisn for Automated Process Planning

Abstract: In order to contribute toward the realization of a practical computer-automated process planning system, this paper discusses two essential subjects: geometric reasoning and optimization capabilities. ESPER provides a solution for these two problems. Geometric reasoning mediates between symbolic reasoning and geometric modeling. It implies recognizing various features in geometric data as well as manipulation of these geometries. Optimization requires effective problem solving strategy and, in addition, cooperation between system inference and users’ interaction. For problem solving, knowledge is defined so as to avoid divergent search by pruning. Furthermore, users’ interactions can be incorporated into the optimization process to obtain a better solution. Through developing the system, it is shown that the methodology proposed here is effective for realizing practical process planning systems.