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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.
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.
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.)
Graph drawing (3 C, 36 P) M. ... Geometric modeling; Geometric primitive; Geometric spanner; Gilbert–Johnson–Keerthi distance algorithm; Gilbert–Pollak conjecture;
Variations include geometric spanners, graphs whose vertices are points in a geometric space; tree spanners, spanning trees of a graph whose distances approximate the graph distances, and graph spanners, sparse subgraphs of a dense graph whose distances approximate the original graph's distances. A greedy spanner is a graph spanner constructed ...
The smallest Paley graph, with q = 5, is the 5-cycle (above). Self-complementary arc-transitive graphs are strongly regular. A strongly regular graph is called primitive if both the graph and its complement are connected. All the above graphs are primitive, as otherwise μ = 0 or λ = k.
In Euclidean geometry, uniform scaling (isotropic scaling, [3] homogeneous dilation, homothety) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is ...