Showing papers on "Polygon published in 1984"

Growth and mortality of individual plants as a function of "available area".

Abstract: We looked at the relationship between "available area", as defined by Thiessen polygons around individual plants, and plant size and mortality in even-aged green-house populations of Lapsana communis L. Polygon area was a good predictor of plant weight in these populations. After nine weeks growth, just prior to the onset of self-thinning, the dry weight of plants was directly proportional to the square root of polygon area. After the onset of selfthinning, plant weight appeared to be directly related to polygon area to the 3/2 power. Plants in small polygons were much more likely to die than those in larger areas. Thinning changed the frequency distribution of polygon sizes from highly skewed and unequal to normal and more equal, while inequality in surviving plant sizes did not appear to be affected by thinning.

Triangulation and shape-complexity

Abstract: This paper describes a new method for triangulating a simple n-sided polygon. The algorithm runs in time O(n log s), with s _< n. The quantity s measures the sinuosity of the polygon, that is, the number of times the boundary alternates between complete spirals of opposite orientation. The value of s is in practice a very small constant, even for extremely winding polygons. Our algorithm is the first method whose performance is linear in the number of vertices, up to within a factor that depends only on the shape-complexity of the polygon. Informally, this notion of shape-complexity measures how entangled a polygon is, and is thus highly independent of the number of vertices. A practical advantage of the algorithm is that it does not require sorting or the use of any balanced tree structure. Aside from the notion of sinuosity, we are also able to characterize a large class of polygons for which the algorithm can be proven to run in O(n log log n) time. The algorithm has been implemented, tested, and empirical evidence has confirmed its theoretical claim to efficiency.

Pipelined, line buffered real-time color graphics display system

Abstract: A color graphics system for displaying a plurality of polygons, based upon polygon commands supplied by a host computer. The system accepts the commands from the host and circulates them in a circular queue past a polygon processor or "painter's station" which examines each to see if it is on the line currently being processed. If the polygon is on the line, a line command or "micropainter" is generated and placed in a pipeline comprising a plurality of microprocessors, one for each picture element ("pixel") in the video scan line. The micropainters are passed from processor to processor down the pipeline, in synchronization with the video scan. Each pixel processor examines the micropainter and stores its color if the painter affects the pixel on the scan line which is assigned to that processor, and, in one embodiment, if the micropainter is painting a polygon which is higher (less in depth) than the last polygon whose color was stored in the processor. A special command, called a "microinspector" is introduced into the pipeline once each scan, and causes each pixel processor in turn to output its stored video information to a video refresh processor, which drives the display.

On k-hulls and related problems

Abstract: For any set X of points (in any dimension) and any k = 1,2, ..., we introduce the concept of the k-hull of X. This unifies the well-known notion of 'convex hulls' with the notion of 'centers' recently introduced by F.F. Yao. The concept is intimately related to some other concepts (k-belts, k-sets) studied by Edelsbrunner, Welzl, Lovasz, Erdos and others. Several computational problems related to k-hulls are studied here. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, the 'parametric' searching technique of Megiddo is used in a nontrivial way. We will also extend Megiddo's technique to Las Vegas algorithms. Our results have applications to a variety of problems in computational geometry: efficient computation of the 'cut' guaranteed by the classical 'Ham Sandwich theorem', faster preprocessing time for polygon retrieval, and theoretical improvements to a problem of intersecting lines and points posed by Hopcroft.

Multiprocessor computer system for forming a color picture from object elements defined in a hierarchic data structure

Abstract: A multiprocessor system for forming a color picture from object elements defined in a hierarchic data structure. The object elements are Bezier polygons each of the sides of which forms a Bezier curve. There is provided an array of parallel connected point processors which perform three functions. First of all, from the highest level of the data structure they determine the relevance of each object element to a point in question until either irrelevance is detected or one or more elementary object elements remain. Furthermore, for each point and each relevant elementary object element a binary inside/outside determination is made. Finally, the color is implemented by a priority determination of the elementary object elements determined to be "inside". The inside/outside decision is made in that during successive steps the relevant polygon sides are divided and in that the contribution to the inside/outside determination by the parallelogram diagonalized by the current side portion is decided. The number of intersections of a semi-infinite straight line with respect to the sides of the polygon in question ultimately decides the inside/outside determination.

An analytic visible surface algorithm for independent pixel processing

Abstract: An algorithm is presented that solves the visible surface problem at each pixel independently. This allows motion blur and depth of field blurring to be integrated into the algorithm. It also allows parallel processing. The algorithm works on large numbers of polygons. An analytic Gaussian filter is used. The filter can be elongated or scaled differently for each polygon to adjust for its speed or distance from the focal plane. This is achieved by shrinking or scaling the polygon prior to solving the hidden surface problem so that blurring is correctly presented when objects obscure each other.

Analysis and design of polygonal resistors by conformal mapping

Abstract: To compute the electrical resistance (≈ conformal modulus) of a polygonally shaped resistor cut from a sheet of uniform resistivity, it suffices to find a conformal map of the polygon onto a rectangle. Constructing such a map requires the solution of a Schwarz-Christoffel parameter problem. First we show by examples that this is practical numerically. Then we consider an inverse “resistor trimming” problem in which the aim is to cut a slit in a given polygon just long enough to increase its resistance to a prescribed value. We show that here the solution can be obtained by solving a “generalized parameter problem.” The idea of a generalized parameter problem is applicable also in many other Schwarz-Christoffel computations.

High-speed video graphics system and method for generating solid polygons on a raster display

Abstract: A real-time video graphics system for generating solid polygons on a raster display screen from X-Y vertex coordinates of the polygons. Solid objects are defined in a host processor system as three-dimensional polygons. The host processor calculates the X-Y vertex coordinates for each polygon and deposits them, along with a corresponding instruction and pixel video data, in a shared RAM. The video graphics system obtains the instruction and data from the shared RAM and calculates from the X-Y vertex coordinates the X coordinates of the left and right edges of each solid polygon for each horizontal line of the display. The system writes pixel data for a horizontal stripe of 32 pixels into a frame buffer in one frame buffer memory write cycle of approximately 320 nanoseconds. Pixel data is periodically read out of the frame buffer, one complete stripe at a time, and shifted out serially to refresh the display screen.

Efficient nesting of congruent convex figures

Abstract: Optimal nesting is the arrangement of two- dimensional polygons within a rectangular board so that waste is minimized. Our approach follows a top-down, stepwise refinement of the original problem into simpler subproblems; the combined solution of all of the problems permits the solution of the original problem. We first show that the original problem can be decomposed into two subproblems--one consisting of finding all convex paver polygons and the other of optimal (minimal waste) circumscription of the original figure in the most appropriate paver polygon.

An algorithm for constructing regions with rectangles: Independence and minimum generating sets for collections of intervals

Abstract: We provide an algorithm which solves the following problem: given a polygon with edges parallel to the x and y axes, which is convex in the y direction, find a minimum size collection of rectangles, which cover the polygon and are contained within it. The algorithm is quadratic in the number of vertices of the polygon. Our method also yields a new proof of a recent duality theorem equating minimum size rectangle covers to maximum size sets of independent points in the polygon.

A Polynomial Solution For Potato-Peeling And Other Polygon Inclusion And Enclosure Problems

Abstract: We give a finiteness criteria for the potato-peeling problem that asks for the largest convex Polygon ('Potato') contained inside a given simple polygon, answering a question of J. Goodman. This leads to a polynomial-time, solution of O(n/sup 9/log n). The techniques used turn out to be useful for other cases of what we call the polygon inclusion and enclosure problem. For instance, the largest perimeter potato can be found in O(n/sup 6/) time and finding the smallest k-gon enclosing a given polygon can be done in O(n/sup 3/log k) steps.

Complexity, convexity, and unimodality

Abstract: A class of polygons termedunimodal is introduced. LetP = P1,p 2,...,p n be a simplen-vertex polygon. Given a fixed vertex or edge, several definitions of the distance between the fixed vertex or edge and any other vertex or edge are considered. For a fixed vertex (edge), a distance measure defines a distance function as the remaining vertices (edges) are traversed in order. If for every vertex (edge) ofP a specified distance function is unimodal thenP is a unimodal polygon in the corresponding sense. Relationships between unimodal polygons, in several senses, andconvex polygons are established. Several properties are derived for unimodal polygons when the distance measure is the euclidean distance between vertices of the polygons. These properties lead to very simple 0(n) algorithms for solving a variety of problems that occur in computational geometry and pattern recognition. Furthermore, these algorithms establish that convexity is not the key factor in obtaining linear-time-complexity for solving these problems. The paper closes with several open questions in this area.

Bounds on the Length of Convex Partitions of Polygons

Abstract: A heuristic for partitioning rectilinear polygons into rectangles, and polygons into convex parts by drawing lines of minimum total length is proposed. For the input polygon with n vertices, k concave vertices and the perimeter of length p, the heuristic draws partitioning lines of total length O(plogk) and runs in time O(nlogn). To demonstrate that the heuristic comes close to optimal in the worst case, a uniform family of rectilinear polygons Qk with k concave vertices, k=1, 2, ... and a uniform family of polygons Pk with k concave vertices, k=1, 2, ... are constructed such that any rectangular partition of Qk has (total line) length Ω(plogk), and any convex partition of Pk has length Ω(plogk/loglogk). Finally, a generalization of the heuristic for minimum length of convex partition of simple polygons to include polygons with polygonal holes is given.

Plastic protecting cap for a polygon nut

Abstract: A plastic protecting cap for the clamping on a polygon nut, with a cylinder casing, which overlaps the polygon nut. The technical problem of the present invention is the provision of a plastic protecting cap, which, by a turning movement, can be clamped safely and firmly on the polygon nut and can be released therefrom by turning in opposite direction again. On the internal face of the casing, at least, two axial profile webs are arranged at places corresponding to polygonal corners, each web comprises a groove profile, open against the axis, with a vertex angle equal to the polygon angle, the radial distance of the vertex of each groove profile from the profile axis being slightly smaller than the radial distance of each corner of the polygon nut profile from the profile axis, and one flange surface of the groove profile is longer, in circumferential direction, than the other flange surface.

Invisibility coherence for faster scan-line hidden surface algorithms

Abstract: Invisibility coherence is a new technique developed to decrease the time necessary to render shaded images by existing scan-line hidden surface algorithms. Invisibility coherence is a technique for removing portions of a scene that are not likely to be visible. If a large portion of the scene is invisible, as is often the case in three-dimensional computer graphics, the processing time eliminated may be substantial. Invisibility coherence takes advantage of the observation that a minimal amount of processing needs to be done on objects (polygons, patches, or surfaces) that will be hidden by other objects closer to the viewer. This fact can be used to increase the efficiency of current scan-line algorithms, including both polygon-based and parametrically curved surface-based algorithms.Invisibility coherence was implemented and tested with the polygon hidden surface algorithm for constructive solid geometry developed by Peter Atherton [1]. The use of invisibility coherence substantially increases the efficiency of this scan-line algorithm. Invisibility coherence should work as well or even better with other scan-line hidden surface algorithms, such as the Lane-Carpenter, Whitted, and Blinn algorithms for parametrically curved surfaces [2]., or the Watkins, Romney, and Bouknight algorithms for polygons [3, 4, 5].

Multidimensional Data Structures

Abstract: Chapter III was devoted to searching problems in one-dimensional space. In this chapter we will reconsider these problems in higher dimensional space and also treat a number of problems which only become interesting in higher dimensions. Let U be some ordered set and let S ⊆ Ud for some d. An element x ∈ S is a d-tuple (x, …, xd-1). The simplest searching problem is to specify a point y ∈ Ud and to ask whether y ∈ S; this is called an exact match query and can in principle be solved by the methods of chapter III. Order Ud by lexicographic order and use a balanced search tree. A very general form of query is to specify a region R ⊆ Ud and to ask for all points in R ∩ S. General region queries can only be solved by exhaustive search of set S. Special and more tractable cases are obtained by restricting the query region R to some subclass of regions. Restricting R to polygons gives us polygon searching, restricting it further to rectangles with sides parallel to the axis gives us range searching, and finally restricting the class of rectangles even further gives us partial match retrieval. In one-dimensional space balanced trees solve all these problems efficiently. In higher dimensions we will need different data structures for different types of queries; d-dimensional trees, range trees and polygon trees are therefore treated in VII.2.. There is one other major difference to one-dimensional space. It seems to be very difficult to deal with insertions and deletions; i.e. the data structures described in VII.2. are mainly useful for static sets. No efficient algorithms are known as of today to balance these structures after insertions and deletions. However, there is a general approach to dynamization which we treat in VII.1.. It is applicable to a wide class of problems and yields reasonably efficient dynamic data structures.

Polygon signature correction

Abstract: A circuit for correcting the data rate to compensate for polygon facet irregularities in a flying spot scanner is described. A crystal controlled oscillator is used to generate the system clock. As each facet becomes the current facet, a number of pulses appropriate for that facet are subtracted from the bit clock stream so that there will always be a constant ratio between data speed and scan speed regardless of the scan speed variations between individual facets.

Clipping to the boundary of a circular-arc polygon

Abstract: This paper presents an algorithm for partitioning line segments and circular arcs according to a circular-arc polygon boundary. That is, given a line or circular arc and a boundary made up of line segments and circular arcs, partition the given line or circular arc into the pieces that lie inside and those that lie outside the boundary. The algorithm works on nonself-intersecting polygonal boundaries. This problem arises in computer graphics, when a circular-arc polygon boundary is used as a window on a scene. It is also related to geometrical problems that arise in integrated circuit design.

Method for ascertaining and filling of bounded areas of a colored raster display

Abstract: A method for use in a bit-mapped presentation display system for ascertaining the boundary of an arbitrarily-shaped closed polygon filled with a first color-coded pel pattern and then filling the ascertained polygon with a second color-coded pel pattern. The method steps comprise identifying the first color-coded pattern; determining all unique raster runs of said identified first pattern, and creating a counterpart data representation thereof; and filling in at least a portion of the raster color-coded domain with the second pattern as controlled by the data representation.

Raster scanner variable-frequency clock circuit

Abstract: A circuit for correcting for polygon drive motor velocity irregularities in a flying spot scanner is described A crystal controlled oscillator is used to generate the system clock As the motor speeds up, or slows down, pulses are subtracted, or added, to the stream of clock pulses so that the data bit stream will always occupy the same line length on the page regardless of polygon velocity variations

Method and device for the continuous rectification of the rails of a railway track

Abstract: One displaces along the railway track at least one assembly of grinding units (13,14,15), angularly displaced the ones with respect to the others. One controls the pressure with which each grinding unit (13,14,15) is applied against the rail (12) in function of at least one parameter of a polygon (6) cirrcumscribing to a reference profile and the sides of which are parallel to the active surfaces of the corresponding grinding wheels (14) of the grinding units. The apparatus comprises grinding (13,14,15) angularly displacable on a carriage (11) guided along a rail (12). For each unit (13,14,15) it comprises at least one control circuit (19,20,21) defining, in function of a parameter of a polygon (6) circumscribing to a reference profile and the sides of which are parallel to the active surfaces of the grinding wheels (14) of the corresponding unit, the inclination of the unit and at least one control circuit (23,24,25) defining in function of at least one parameter of the polygon (6) the applying force with which the grinding wheel (14) is applied against the rail 12.

Wobble correction by two reflectors on an internally reflecting facet without bow

Abstract: An internally reflecting rotating polygon system for correcting wobble by double reflection from the active facet without bow is disclosed. Instead of the impinging light source being transverse to the axis of rotation of a rotating polygon, this rotating polygon 52 having internally reflecting facets 54 at a draft angle to the axis of rotation, a collimated light source impinges upon a rotating polygon 52 with the facets 54 having the predetermined draft angle D. A., and angles of incidence at the first and second reflections. By two further reflections, 56, 58, the light is then reimpinged upon the same facet 54; wobble is similarly corrected, but with no effects of bow.

Rotary polygon mirror and its manufacture

Abstract: PURPOSE:To form the rotary polygon mirror easily at low manufacturing cost by providing a metallic film which has a reflecting mirror surface on flanks of polygonal shape parts of a base material made of resin or principally of resin. CONSTITUTION:The base material which is in the same of, for example, a regular hexagonal prism and has a through hole 4 for installing a rotary polygon mirror coaxial with the center axis of a regular hexagon onto a rotary driving shaft in its center is formed of a composite resin consisting of or principally of resin. A metallic film 2 whose surface is cut into a reflecting mirror surface 2a is provided on >=1 flank that the polygonal shape part of the base material 1 has. A film 3 which functions as a reflection enhancing film and/or protection film is provided on the reflecting surface 2a.

Field effect transistor of the vertical MOS type

Abstract: A vertical MOS transistor comprises a first well region on an upper side of a semiconductor substrate, a second well region of a conductivity opposite to that of the first well region, which is provided within the first well region. Both well regions are formed by a double diffusion through the same diffusion window designed so that each angle formed by two adjacent sides is 150° or more. For instance, a 12-sided polygon 18- sided polygon or a circle is used for the diffusion window. Thus, it is easily possible to a vertical MOS transistor having low on-voltage and on-resistance, and high switching capability.

Light beam scanner

Abstract: PURPOSE:To prevent the entry of dust in external air providing a cover which covers a rotary polygon mirror, forming an air intake and an outlet in this cover, and forming an air flow from the air intake to the air outlet by utilzing a rotating polygon mirror. CONSTITUTION:The polygon mirror cover 11 covering the rotary polygon mirror 1 is provided. This cover 11 provided with nonreflection-treated glass 12 in an incidence and projection window 13 where a light beam is transmitted i.e. at a light beam entry and exit surface, and the air intake 14 are sucking the air in a dust-proof case is formed at the upper part. The polygon mirror cover 11 is fixed on a lower polygon mirrror cover 26 fixed to an optical system attachment base 21 and a rotating mechanism attachment base 50 for holding a turntable 2 rotatably is fixed to the cover 26.

Mixed Random Mosaics

Abstract: Cowan [2] has defined random mosaics processes RMP in R2 and has given some basic properties of them. In particular Cowan introduces the fundamental parameters α, βk, γk of the process and, in terms of them, he computes the mean values of the area α, perimeter h, number of ares w and number of vertices v of a typical polygon of the RMP. Our purpose is to consider the RMP obtained by superposition of two independent random mosaics. Then, the characteristics a12, h12, w12, v12 of the resulting process are computed in terms of the characteristics ai, hi, wi, vi, of each process. The case of non random tessellations mixed with random mosaics is also considered.