Individual Polygons Research Articles

A new figure fracturing algorithm for variable-shaped EB exposure-data generation

This paper discusses a new figure fracturing algorithm to be used in input data generation for the variable-shaped EB (electron beam) exposure system. In the input data generation of this kind of system, processing is required in which the individual polygons composing the mask pattern are represented as a set of trapezoids (figure fracturing). The figure fracturing considered in this paper differs from those in the conventional methods, in that the generation of a narrow trapezoid as well as the partitioning of the critical part is suppressed, in order to improve the accuracy of LSI mask fabrication. In this paper, the problem is solved as the fracturing of the composite rectangle into a set of rectangles by removing slant edges from the polygon. The relation graph is introduced to represent the relation among the partitioning line candidates. A graph-based algorithm is presented that efficiently selects the adequate partition lines from all possible candidates. The proposed method is applied to the mask fabrication for 64 M and 256 M DRAM, and a satisfactory fractured result is obtained in a practical execution time. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 87–102, 2000

USING LANDSCAPE HIERARCHIES TO GUIDE RESTORATION OF DISTURBED ECOSYSTEMS

Reestablishing native plant communities is an important focus of ecosystem restoration. In complex landscapes containing a diversity of ecosystem types, restoration requires a set of reference vegetation conditions for the ecosystems of concern, and a predictive model to relate plant community composition to physical variables. Restoration also requires an approach for prioritizing efforts, to facilitate allocation of limited institutional resources. Hierarchy theory provides a conceptual approach for predicting plant communities of disturbed ecosystems and, ultimately, for prioritizing restoration efforts. We demonstrate this approach using a landscape in southwestern Georgia, USA. Specifically, we used an existing hierarchical ecosystem classification, based on geomorphology, soil, and vegetation, to identify reference plant communities for each type of ecosystem in the landscape. We demonstrate that ecosystem identity is highly predictable using: only geomorphic and soil variables, because these upper hierarchical levels control the development of vegetation, a lower hierarchical level. We mapped the potential distribution of reference ecosystems in the landscape and used GIS (geographic information systems) to determine relative abundance of each ecosystem, as a measure of its historical rarity. We joined the reference ecosystem map with a current cover map to determine current abundance of each reference ecosystem, and percentage conversion to different disturbance classes. We show that over half of the landscape supports something other than reference plant communities, but degree of rarity varies widely among ecosystems. Finally, we present an index that integrates information on historical and current rarity of ecosystems, and disturbance levels of individual polygons, to prioritize restoration efforts. The premise of the index is that highest priority be given to restoring (1) currently rare ecosystems that were also historically rare and (2) the least disturbed examples of these ecosystems, as these will require the least effort to restore. We found that 80% of high-priority sites occur within just three (of 21) ecosystems. Moreover, the high-priority ecosystems all occur within stream valleys. Our approach provides managers with a straightforward methodology for determining potential distribution of reference ecosystems and for allocating efforts and resources for restoration in complex landscapes. Development of a priority index for a specific landscape requires an understanding of the hierarchical relationships among geomorphology, soil characteristics, and plant communities, in addition to well-defined restoration objectives.

The influence of fuzzy set theory on the areal extent of thematic map classes

In thematic maps information is traditionally represented in a onepolygon-one class method which assumes each polygon in the map can be assigned unambiguously to a single class. Additionally, thematic map classes are assumed to be exhaustive and mutually exclusive. The introduction of fuzzy classifications overcomes the traditional limitations on the mutually exclusive nature of map classes assigning varying levels of class membership for individual map polygons. As a consequence, fuzzy set theory expands the conventional assumptions regarding the total areal extent of thematic map classes. Considering that a map polygon may simultaneously belong to more than one thematic map class, the total areal extent of all classes in a thematic map need not be equal to the geographical extent of the study area. Although this apparent paradox has already been noted in previous papers, as far as we know,an analytical formulation of the influence of fuzzy classifications on the areal extent of thematic map classes has never been provided. This Letter offers an analytical solution to evaluate the total areal extent of thematic map classes as a function of fuzzy class membership levels.

Strain accumulation rates in the San Francisco Bay area, 1972–1989

Maps of the strain accumulation rate in the San Francisco Bay area have been constructed from trilateration observations extending from about 1972 until the Loma Prieta earthquake in late 1989. The observations were corrected to remove offsets imposed by shallow fault creep and by four M ∼6 earthquakes that occurred in the Bay area during that time interval. The Bay area was divided into 32 contiguous polygons, and the uniform (in both space and time) strain rates that best explain the changes in the corrected (earthquake and shallow fault creep offsets removed) distances within each polygon were calculated. In a coordinate system with the 1 axis directed N58°E and the 2 axis N32°W (perpendicular and parallel to the local tangent to the small circle drawn about the Pacific‐Sierra Nevada pole of rotation) the averages of these 32 strain rates (each weighted by the area of the polygon) are ε11=9.2±7.4, ε12=−160.7±4.6, and ε22=8.2±6.2 nanostrain/yr, where extension is reckoned positive and quoted uncertainties are standard deviations. As expected from the Pacific‐Sierra Nevada relative plate motion, the overall strain rate is predominantly right‐lateral shear across a vertical plane striking N32°W. The net increase in the 12,225 km2 area of the trilateration network is only 212±110 m2/yr, which arises from almost equal extensions in the N32°W and N58°E directions. Within the network the strain rates vary from polygon to polygon. Significant areal dilatation rates are observed in almost ⅓ of the individual polygons and the N32°W extension rates tend to be negative to the west of the Hayward‐Rodgers Creek fault trend and positive east of it. The N58E extension rate is positive in 22 out of 32 polygons, a proportion that is significantly larger than would be expected by chance if the N58°E extension rate were zero or negative. The pre‐1989 strain accumulation across the eventual site of the Loma Prieta rupture involves fault normal contraction as well as right‐lateral shear, consistent with the rupture mechanism.

Outside-in: an alternative approach to forest map digitizing

ABSTRACT Abstract. This paper examines the problem of polygon digitizing, and suggests an inversion of the traditional approach for polygons of the environmental type, where each individual polygon, rather than its boundaries, is of primary interest. Many workers in geology, forestry, soil science, etc. have found the tedious specification of boundary arcs and their topological linkage and editing to be a major block to productivity. An alternative digitizing approach is described using Thiessen/Voronoi polygons to generate topology automatically and to reduce map digitizing times significantly. The digitizing of representative points within each polygon is performed using the GIS. The stand-alone Voronoi polygon building and boundary extraction module then generates linked arcs that are returned to the GIS for further analysis. Examples of the productivity enhancement in a production environment are given, along with the algorithms used.

Exploration Applications Through Remote Sensing of Ice-Wedge Polygons: ABSTRACT

Petroleum exploration is facilitated through remote-sensing techniques such as Landsat digital data processing and aerial photointerpretation. These techniques were applied to reconstruct past geologic environments and to analyze the present geomorphic setting of the Colville delta on the North Slope of Alaska. By examining differences in the distribution of selected characteristics of ice-wedge polygons, the positions of former fluvial channels and lake beds and the relative age of the surface could be determined. Characteristics of ice-wedge polygons such as size, shape, central relief, and rim condition were delineated using aerial photography of various scales and dates. Maps of selected characteristics assisted in identifying outcrops of the Pleistocene Gubik Formation, frequently flooded areas, and the locations of former distributary channels and lake beds. Although Landsat digital data were not as effective as aerial photography in geologic mapping, primarily due to pixel resolution being one order of magnitude larger than an individual polygon, major surface features and outcrops could be identified from variations in vegetation and the surface water content of ice-wedge polygons. In addition, tundra surface with ice-wedge polygons could be differentiated from that without. An understanding of ice-wedge polygon characteristics, which infer geologic environment and evolution, and the application of similar remote-sensing techniques can assist exploration geologist in determining past and present geologic environments in inaccessible periglacial regions. End_of_Article - Last_Page 290------------

A Triangulation Data Structure for Choropleth Base Maps

Abstract Most early methods for encoding choropleth maps have used the region or individual data zone as the organisational unit for storing the locational and topological properties of the map. This paper presents an alternative approach to encoding choropleth maps where the neighbourhood relationships are encoded using the node as the organisational unit. The direct relationship between choropleth base maps and a Thiessen diagram enables the same triangular data structures developed to store a Delauney triangulation to be used to store a choropleth map. Individual polygons are retrieved by enumerating the sequence of nodes that comprise their outline in a clockwise manner. The commonality among the data structures for storing different types of maps should permit the development of general purpose display algorithms.

Spatial distribution of lemming mats in the Canadian High Arctic

Spatial distributions of lemming mats on exposed beach ridges on Bathurst and Devon islands, N. W.T., in the Canadian High Arctic were recorded by triangulation. The collared lemming Dicrostonyx groenlandicus is the only microtine in this region, which eliminates interspecific influences. In addition, vegetation is sparse, making centres of activity easy to identify. Mats were relatively permanent structures with a mean diameter of 3.88 m and an average of 13.0 burrows. The mean nearest neighbour distance ranged from 40 to 45 m and the average mat polygon area (interpreted as territory or home range) was 0.34 ha. Individual mat polygons were contiguous with an average of 5.3 other polygons and the distribution of the mats over the environment was nonrandom. The data support the conclusion that lemming mats represent core areas within lemming territories or home ranges which are distributed regularly over the environment because of social processes which influence social interaction. The data are discussed as they apply to current theories on microtine demography and population dynamics.

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

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 conditions of low Jaggedness variability.

Construction de mosaïques pour l'analyse des textures subpolyédriques

Packing polyhedra into geometric models is a useful approach to the description of sub-polyhedric rock textures. When a packed aggregate of polyhedra is cut, a mosaic of individual polygons is obtained. Crystallographic concepts, enabling to predict what kinds of mosaics are obtained along any section plane in the polyhedral aggregate, are introduced. Thus, the shape (regular or irregular), the number of sides of the polygons in a given mosaic and likewise, the pattern of a mosaic — whether the mosaics made up of polygons of one type only, or a mixture of several types — can be determined by crystallographic operations. A few mosaics, obtained when packed aggregates of tetrakaidecahedra, rhombododecahedra, and cube-rhombododecahedra are cut along preferred planes of orientation, are presented. Geometric models are compared to the textural pattern of a few rocks, ceramics and metals. The frequency distribution of the mosaic types obtained by cutting across packed aggregates of tetrakaidecahedra is looked into it. Lastly, the spatial random distribution of two, and also the three mineral phases in the aggregate is graphically illustrated.

Thermal Contraction Cracks in an Arctic Tundra Environment

Field observations in the Mackenzie Delta area largely substantiate Lachenbruch's theoretical considerations of thermal contraction crack development. Frost crack patterns, representing the incipient stage of tundra polygons, were observed on both bare and vegetated surfaces of low alluvial flats and sandspits of three islands. Individual polygons, where developed, ranged in size from 20 to 30 metres diameter on bare surfaces to 2 to 3 metres on sedge-covered areas, and 80% of the angular intersections measured were of orthogonal type. Most cracks exhibited random orientations, except in close proximity to water bodies where tendencies toward normal and subparallel orientations occurred.