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Axiomatizability of Geometry without Points
Synthese, 1960The aim of this paper is to make more precise the well-known conviction that geometry may be built without speaking about points. In the first section we prepare some general syntactical theorems which are needed. In the second section we apply these theorems to a certain theory of topology without points.
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Mathematics Magazine, 1977
Finite sets with distinguished subsets called lines give examples of the theory of balanced incomplete block designs.
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Finite sets with distinguished subsets called lines give examples of the theory of balanced incomplete block designs.
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Detail-generating geometry completion for point-sampled geometry
Machine Vision and Applications, 2013In this paper, we present a novel method for detail-generating geometry completion over point-sampled geometry. The main idea consists of converting the context-based geometry completion into the detail-based texture completion on the surface. According to the influence region of boundary points surrounding a hole, a smooth patch covering the hole is ...
Ren-fang Wang +4 more
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2010
Point-line geometries are just rank two geometries, and so inherit the concepts of morphism and cover from the last chapter. The symmetry between the two types is broken by the concept of a subspace, which treats points differently from lines. A new graph, the point-collinearity graph, is useful in describing geometric properties.
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Point-line geometries are just rank two geometries, and so inherit the concepts of morphism and cover from the last chapter. The symmetry between the two types is broken by the concept of a subspace, which treats points differently from lines. A new graph, the point-collinearity graph, is useful in describing geometric properties.
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Drill Point Geometry and Optimization
Journal of Engineering for Industry, 1982The geometrical parameters of the drill point, i.e., relief angles, chisel form, web size, and errors of symmetry have a major influence on drill performance. This paper deals with geometrical aspects of the drill point and with the development of fundamental mathematical definitions for the design of improved drill point grinders.
E. Lenz, S. Kaldor
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Radiosity for point-sampled geometry
12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings., 2004In this paper, we propose a radiosity method for the point-sampled geometry to compute diffuse inter reflection of light. Most traditional radiosity methods subdivide the surfaces of objects into small elements such as quadrilaterals. However, the point-sampled geometry includes no explicit information about surfaces, presenting a difficulty in ...
Y. Dobashi, T. Yamamoto, T. Nishita
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Ray Tracing Point Sampled Geometry
2000We present a novel technique for ray tracing geometry represented by points. Our approach makes it possible to render high quality ray traced images with global illumination using unstructured point-sampled data thus avoiding the time-consuming process of reconstructing the underlying surface or any topological information. Compared with previous point
Gernot Schaufler, Henrik Wann Jensen
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Taxicab Geometry- a Non-Euclidean Geometry of Lattice Points
The Mathematics Teacher, 1971During the past decade, much im-portance has been placed on the structure of mathematical systems. Structure has been the byword in the construction of texts and courses. For this task the framework of geometry has been found to be quite acceptable at the secondary level.
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Point-Voting based Point Cloud Geometry Compression
2021 IEEE 23rd International Workshop on Multimedia Signal Processing (MMSP), 2021Chaofei Wang +4 more
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