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The set of geometric primitives is based on the dimension of the region being represented: [1]. Point (0-dimensional), a single location with no height, width, or depth.; Line or curve (1-dimensional), having length but no width, although a linear feature may curve through a higher-dimensional space.
In mathematics and its applications, the signed distance function or signed distance field (SDF) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space (such as the surface of a geometric shape), with the sign determined by whether or not x is in the interior of Ω.
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
The fundamental geometric primitives are: A single point. A line segment, defined by two end points, allowing for a simple linear interpolation of the intervening line. A polygonal chain or polyline, a connected set of line segments, defined by an ordered list of points.
Geometric graph theory is a branch of graph theory. It concerns straight-line embeddings of graphs in geometric spaces and graphs defined from configurations in a ...
Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing. The non-orientable genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n cross-caps (i.e. a non-orientable surface of (non-orientable) genus n). (This number is also called the demigenus.)
The concept of line is often considered in geometry as a primitive notion in axiomatic systems, [1]: 95 meaning it is not being defined by other concepts. [9] In those situations where a line is a defined concept, as in coordinate geometry, some other fundamental ideas are taken as primitives.
The first number in this sequence, 7, is the degree of the Hoffman–Singleton graph, and the McKay–Miller–Širáň graph of degree seven is the Hoffman–Singleton graph. [2] The same construction can also be applied to degrees d {\displaystyle d} for which ( 2 d + 1 ) / 3 {\displaystyle (2d+1)/3} is a prime power but is 0 or −1 mod 4.
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