Search results
Results from the WOW.Com Content Network
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]
It is available free of charge for non-commercial users. [6] License: open source under GPL license (free of charge) Languages: 55; Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines; Algebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points ...
The denominator of this expression is the distance between P 1 and P 2. The numerator is twice the area of the triangle with its vertices at the three points, (x 0,y 0), P 1 and P 2. See: Area of a triangle § Using coordinates.
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]
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Free-space diagram of the red and the blue curve. In contrast to the definition in the text, which uses the parameter interval [0,1] for both curves, the curves are parameterized by arc length in this example. An important tool for calculating the Fréchet distance of two curves is the free-space diagram, which was introduced by Alt and Godau. [4]
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 ...