Showing papers on "Polygon published in 1973"

System of polygon sorting by dissection

Abstract: A polygon-dissection structure is disclosed incorporated in a system for processing geometric data, e.g. data representing three-dimensional polygons, as by subdividing such polygons to accomplish sorting of the data. The system operates to divide a working volume, e.g. a perspective pyramid, into successivelysmaller subvolumes. The separating planes are placed at arbitrary angles to coincide with the edges and surfaces of polygons that define objects to be represented. Polygons which straddle separating planes are dissected into two parts which are thereafter treated separately. Dissection by the system results in simplification in accounting for the polygons in relation to specific subvolumes. The system can be applied to the detection of those polygons which hide others thereby enabling a solution to the hidden-surface problem. Additionally, the system affords a simple mechanism for resolving shadowed portions of polygons as well as portions of polygons obstructed by semi-transparent surfaces and for explicitly computing and displaying implied lines of intersections existing between two inter-penetrating polygons. Alternatively, the system provides an efficient way of detecting if any or a multiplicity of polyhedra solids interpenetrate.

Structural system employing eight-sided polygonal units constructed of prefabricated elements

Abstract: A structural system for single or multiple story construction having one, two or more units arranged singly or in side-by-side relationship, each of the units having a floor member in the shape of an eight-sided polygon. A plurality of prefabricated side panels are secured to the floor member and extend vertically around the periphery of the floor member with at least one of the side panels being a common panel to an adjacent unit. Where at least four of the units are arranged such that each unit has two side panels common to two adjacent units, a square-shaped interstitial space is formed which can serve as a connecting passageway between the units or a semi-enclosed area.

The polygon-circle paradox and convergence in thin plate theory

Abstract: The solution for a simply supported many-sided polygonal plate does not agree with that for the corresponding circular plate. This paper describes the earlier work of Rao and Rajaiah on polygonal plates and then explains why best convergence of series solutions occurs when the boundary conditions are defined as

Learning priorities in a paired-associate task with polygons and numbers as a function of polygon-set variability

Abstract: Ss performed a paired-associate task with polygons and numbers, where polygon sets satisfied four different combinations of feature variability. Two groups of Ss working with two sets where forms were highly variable on the Jaggedness feature (HH, HL) consistently selected certain polygons for early pairing. These polygons were assumed to have high primacy, and their selection was independent of all feature measures of forms and their derivatives. Two groups of Ss working with two sets where forms were not highly variable on the Jaggedness feature (LL, LH) formed pairings at a slower rate. Within these groups, selection of individual polygons for early learning was dependent on several measures reflecting their extremity on both Jaggedness and Area measures. No such differences were obvious with groups differing in Area variability. Results are interpreted in terms of a hierarchy of response bases for early pairing where “Gestalts” are used in conditions of high Jaggedness variability and “extremes” in co...

On the compressive radical of semigroups

Abstract: A centered right -polygon (synonyms: -operand, -system) is called right compressive if and and left compressive if and . Here is the congruence on the semigroup called the kernel of the -polygon which is defined as follows: .The intersection of the kernels of all right (left) compressive -polygons is called the right (left) compressive radical of . In this paper we study compressively semisimple and compressively radical semigroups.

Generalization gradients for categorization of polygon patterns.

Abstract: Two polygons at each of 3 levels of association value (AV) were used to produce 72 variants with 2 different units of perturbation (dissimilarity to the original) and a varying number of perturbations (1 to 6) per form. More correct categorizations were observed for patterns with the smaller unit of perturbation and also for those with the highest level of AV (p < .01). Generalization gradients evaluating the frequency of correct categorizations against an increasing number of perturbations were sharpest for the larger unit of distortion (p < .01), and no systematic differences in gradient due to association value were evident. Results were interpreted as stressing the importance of association value and constraint metrics for categorization tasks.

Interactive Curve Fitting

Abstract: Interactive curve fitting is one of the main problems met when trying to fulfill the task of converting the description of the shape of a car body model into a computer compatible form. The solution proposed by Bezier has gained wide attention and acceptance mainly because of the idea of relating the shape of the curve to a polygon that mimics the curve itself. It is noted that the degree to which the polygon mimics the associated curve decreases as the number of points of inflexion, sharp bends or other odd behaviors require higher order polygons. Some solutions proposed by other authors to overcome this problem are briefly discussed and a contribution to the problem is given

Image contouring and comparing.

Abstract: A contour image representation is stated and an algorithm for converting a set of digital television images into this representation is explained. The algorithm consists of five steps: digital image thresholding, binary image contouring, polygon nesting, polygon smoothing, and polygon comparing. An implementation of the algorithm is the main routine of a program called CRE; auxiliary routines provide cart and turn table control, TV camera input, image display, and xerox printer output. A serendip application of CRE to type font construction is explained. Details about the intended application of CRE to the perception of physical objects will appear in sequels to this paper.

Codability of polygon patterns.

Abstract: Sz~mnary.-39 Ss were presented with a code containing 13 categories, e.g., Area, Associations, and instructed to provide S descriptive statements for each of 20 polygons. Statements were ranked in order of importance. Ss showed greater agreement in category choice for the description of some polygons, and such agreement as was present decreased as the importance of the statement in question decreased ( p < .OS). When descriptions produced by the firsr group of Ss were given to a second group (n = 1 7 ) , systematic differences in identification of polygons from the statements alone became obvious. Polygons associated with greater agreemenr in category choice for the mosr imporonr statement were also those identified more accurately by the second group ( 9 < .05) . Further relationships of category usage to physical measures of polygons, e.g., size, are also discussed.

A dual analogue model for πN andNN elastic scattering

Abstract: The model is an extension of the analogue model by Fairlie and Nielsen. In the case of πN scattering the conducting plate has the shape of a polygon of two circular arcs, whereas inNN scattering the shape is a polygon of four circular arcs. The boundary value problem is solved by constructing the conformal mapping of the are polygons onto the unit circle. The shifting of the Δ trajectory and the exotic trajectory with respect to the f trajectory is predicted to be −1/3 and −2/3 respectively. The residues of the f Regge pole in ππ, πN andNN scattering factorize. Some phenomenological consequences are discussed.