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The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functions.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.
The solutions in both cases are non-trivial but yield to straightforward application of trigonometry, analytical geometry or integral calculus. Both problems are intrinsically transcendental – they do not have closed-form analytical solutions in the Euclidean plane. The numerical answers must be obtained by an iterative approximation procedure.
This is a special case of the generalization of a geometric series of real or complex numbers to a geometric series of operators. The generalized initial term of the series is the identity operator T 0 = I {\displaystyle T^{0}=I} and the generalized common ratio of the series is the operator T . {\displaystyle T.}
Boost.Geometry support Douglas–Peucker simplification algorithm; Implementation of Ramer–Douglas–Peucker and many other simplification algorithms with open source licence in C++; XSLT implementation of the algorithm for use with KML data. You can see the algorithm applied to a GPS log from a bike ride at the bottom of this page
The rotating calipers technique for designing geometric algorithms may also be interpreted as a form of the plane sweep, in the projective dual of the input plane: a form of projective duality transforms the slope of a line in one plane into the x-coordinate of a point in the dual plane, so the progression through lines in sorted order by their ...