Showing papers on "Polygon published in 1974"

Reentrant polygon clipping

Abstract: A new family of clipping algorithms is described. These algorithms are able to clip polygons against irregular convex plane-faced volumes in three dimensions, removing the parts of the polygon which lie outside the volume. In two dimensions the algorithms permit clipping against irregular convex windows.Polygons to be clipped are represented as an ordered sequence of vertices without repetition of first and last, in marked contrast to representation as a collection of edges as was heretofore the common procedure. Output polygons have an identical format, with new vertices introduced in sequence to describe any newly-cut edge or edges. The algorithms easily handle the particularly difficult problem of detecting that a new vertex may be required at a corner of the clipping window.The algorithms described achieve considerable simplicity by clipping separately against each clipping plane or window boundary. Code capable of clipping the polygon against a single boundary is reentered to clip against subsequent boundaries. Each such reentrant stage of clipping need store only two vertex values and may begin its processing as soon as the first output vertex from the preceeding stage is ready. Because the same code is reentered for clipping against subsequent boundaries, clipping against very complex window shapes is practical.For perspective applications in three dimensions, a six-plane truncated pyramid is chosen as the clipping volume. The two additional planes parallel to the projection screen serve to limit the range of depth preserved through the projection. A perspective projection method which provides for arbitrary view angles and depth of field in spite of simple fixed clipping planes is described. This method is ideal for subsequent hidden-surface computations.

Higher order compatible triangular finite elements

Abstract: For a triangulated polygon Ω, classes of piecewise rational functions are defined which are inC p?1 (Ω). A basis of these functions which contains all polynomials of degree 2p?1 or less is considerably smaller than a similar basis of piecewise polynomial functions.

Enumerating Dissectible Polyhedra by Their Automorphism Groups

Abstract: A dissectible polyhedron is a natural extension of a concept whose history dates back to at least 1758 and Euler [7]—the concept of a dissection of a polygon. An interesting historical survey of dissections of a polygon is given by Brown [4]. Some approaches to the classical problem have been given by Moon and Moser [9] and by Guy [8] ; the latter provides an approach which is the basis of the work in this paper. A summary of enumeration results on dissections of polygons and polyhedra by automorphism groups has been given by the authors [2].Recent extensions of the problem have been investigated in a series of papers by Brown and Tutte [3; 5; 14; 15] and b y Takeo [10; 11; 12; 13].

Computer graphics for half-tone three-dimentional object images

Abstract: A system is described for displaying studio-quality television images of objects described by a set of closed polyhedra. The objects are defined by a series of opaque planar surfaces which may obscure and intersect each other. The image description lists are passed through a scan-conversion, hidden surface removal and shading process and are converted to a real-time television signal. Display occurs through a normal T.V.system.Resolution is 512 lines by 512 dots with a color definition of 15 bits (over 32,000 colors). Generation of the display list is through an interactive language based on a tablet input and three-dimensional rotation of the boundary polygon. Color definition is through an electronic "palatte," also interactively. The system incorporates shading of the surfaces based upon the angle of the normal to the surface to the observer.The system is resident on an 8K 16-bit minicomputer which accesses a hybrid rotation array.

The MAPEDIT system for automatic map digitization

Abstract: A system for the automatic digitization of polygon boundaries is described. Digitized map files are created from a driver tape containing identification codes and approximate centroids of polygonal boundaries (e.g., census tracts), and a film image of the map. The digitizer scans on the film plane in an automatic line-following mode, producing the first stage of the map file for the editing system. The MAPEDIT system, which can be used either interactively or in batch mode, reads maps in several standard formats and provides for combining and selecting maps by census (or other) geocodes or by longitude and latitude. This system provides several stages of data compression, analysis, and verification, including algorithms for detecting straight lines, finding corners, fitting insets of maps together and matching boundaries common to a pair of polygons. Auxiliary programs (1) provide a very high resolution (1 part in 25,000) C.R.T. plot of the map, (2) allow a detailed examination and editing of the map and (3) supply missing geocodes using auxiliary tapes such as the Medlist tapes.

Screw press - with polygon cross-section mixing zone and angled faces

Abstract: Designed for the mixing and plasticising of thermoplastic or rubber materials, the mixing zone located in the screw comprises a section with a polygon cross-section and rectangular surfaces supporting angled faces. The purpose is to ensure an intensive mixing action to give a fully homogeneous product.

Method and apparatus for fan folding sheet material

Abstract: A method and apparatus for fan folding a web including a folding section and a guiding section upstream of the folding section. The folding and guiding sections are formed from a flat sheet of metal. The guiding section merges into the folding section on a line which is a portion of a polygon whose sides are the bases of triangles forming a plurality of sections which constitute the folding section. The guiding section is defined by portions of polygons of the same perimeter dimension as the portion of the first polygon and each of which has fewer sides than the adjacent downstream polygon.

Electronic control systems for internal combustion engines

Abstract: An electronic control system for internal combustion engines wherein the duration of injection is proportional to a regulating voltage controlled by at least one operative parameter of the engine. To this end an input voltage defined by a succession of sides of a polygon is subjected to a plurality of transistorized circuits adapted to adjust each the slope of one section of the polygon in accordance with a predetermined parameter.