Search results
Results From The WOW.Com Content Network
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
Line arrangements. In discrete geometry, an arrangement is the decomposition of the d-dimensional linear, affine, or projective space into connected cells of different dimensions, induced by a finite collection of geometric objects, which are usually of dimension one less than the dimension of the space, and often of the same type as each other, such as hyperplanes or spheres.
Although the most popular version is for arrangements of lines in the plane, there exist some generalizations of the zone theorem. For instance, in dimension , considering arrangements of hyperplanes, the complexity of the zone of a hyperplane is the number of facets (- dimensional faces) bounding the set of cells (-dimensional faces) intersected by .
Euclidean line and Euclidean geometry are terms introduced to avoid confusion with generalizations introduced ... this partition is known as an arrangement of lines.
Here, an arrangement is simple when no two of its lines are parallel and no three lines pass through the same point. A face is one of the polygons formed by the arrangement, not crossed by any of its lines. Faces may be bounded or infinite, but only the bounded faces with exactly three sides count as triangles for the purposes of the theorem. [1]
Constructing an arrangement means, given as input a list of the lines in the arrangement, computing a representation of the vertices, edges, and cells of the arrangement together with the adjacencies between these objects, for instance as a doubly connected edge list. - Might be easier to parse if separated into two sentences.
Amazon on Thursday reported better-than-expected revenue and profits for the holiday shopping period, but its stocks dipped in after-hours trading due to disappointing guidance for the current ...
In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S.Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space.