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Another way to generalize it is (even in 2D) to consider a variable distance, e.g. parametrized by another curve. [22] One can for example stroke (envelope) with an ellipse instead of circle [22] as it is possible for example in METAFONT. [26] An envelope of ellipses forming two general offset curves above and below a given curve
The function has positive values at points x inside Ω, it decreases in value as x approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω. [1] However, the alternative convention is also sometimes taken instead (i.e., negative inside Ω and positive outside). [2]
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable [1] (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points (,,, …
The classical measure of dependence, the Pearson correlation coefficient, [1] is mainly sensitive to a linear relationship between two variables. Distance correlation was introduced in 2005 by Gábor J. Székely in several lectures to address this deficiency of Pearson's correlation, namely that it can easily be zero for dependent variables.
Exact algorithms for computing the graph edit distance between a pair of graphs typically transform the problem into one of finding the minimum cost edit path between the two graphs. The computation of the optimal edit path is cast as a pathfinding search or shortest path problem , often implemented as an A* search algorithm .
The enumeration formulas for unit distance graphs generalize to higher dimensions, and shows that in dimensions four or more the number of strict unit distance graphs is much larger than the number of subgraphs of unit distance graphs. [2] Any finite graph may be embedded as a unit distance graph in a sufficiently high dimension.