Search results
Results from the WOW.Com Content Network
For the simplest version of Theta*, the main loop is much the same as that of A*. The only difference is the update _ vertex ( ) {\displaystyle {\text{update}}\_{\text{vertex}}()} function. Compared to A*, the parent of a node in Theta* does not have to be a neighbor of the node as long as there is a line-of-sight between the two nodes.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
In computational geometry, the Theta graph, or -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction involves partitioning the space around each vertex into a set of cones , which themselves partition the remaining vertices of the graph.
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).
In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by (), using a script form of the Greek letter theta to contrast with the upright theta used for Shannon capacity.
There are a number of notational systems for the Jacobi theta functions.The notations given in the Wikipedia article define the original function (;) = = (+)which is equivalent to
In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface , it is therefore L such that L 2 is the canonical bundle , here also equivalently the holomorphic cotangent bundle .
In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as = ((+)) for real values of t.Here the argument is chosen in such a way that a continuous function is obtained and () = holds, i.e., in the same way that the principal branch of the log-gamma function is defined.