Search results
Results from the WOW.Com Content Network
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry.
A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules: The distance between an object and itself is always zero. The distance between distinct objects is always positive. Distance is symmetric: the distance from x to y is always the same as the distance from y to x.
The Euclidean distance is the prototypical example of the distance in a metric space, [11] and obeys all the defining properties of a metric space: [12] It is symmetric, meaning that for all points and , (,) = (,). That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is ...
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.
The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the lengths of all paths from the first point to the second. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space.
In physics, a vector field (,,) is a function that returns a vector and is defined for each point (with coordinates ,,) in a region of space. The idea of sources and sinks applies to b {\displaystyle \mathbf {b} } if it follows a continuity equation of the form
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance.
Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [1] [2] [3] More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a subject within ...