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A standard chord length is used: in the UK this is conventionally 30 metres, or sometimes 20 metres. Half chords, i.e. 15 metre or 10 metre intervals, are marked on the datum rail using chalk. The string, which is one full chord long, is then held taut with one end on two marks at each end of a chord, and the offset at the half chord mark measured.
If the vehicle can also travel in reverse, then the path follows the Reeds–Shepp curve. [1] Lester Eli Dubins (1920–2010) [2] proved using tools from analysis [3] that any such path will consist of maximum curvature and/or straight line segments. In other words, the shortest path will be made by joining circular arcs of maximum curvature ...
This line has only one length. On the surface of a sphere, this is replaced by the geodesic length (also called the great circle length), which is measured along the surface curve that exists in the plane containing both endpoints and the center of the sphere. The length of basic curves is more complicated but can also be calculated. Measuring ...
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
Rankine's method or tangential angle method is an angular technique for laying out circular curves by a combination of chaining and angles at circumference, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods. This method requires access to only one road/path of communication ...
As ship design evolved from craft to science, designers learned various ways to produce long curves on a flat surface. Generating and drawing such curves became a part of ship lofting; "lofting" means drawing full-sized patterns, so-called because it was often done in large, lightly constructed mezzanines or lofts above the factory floor.
Lévy flights are, by construction, Markov processes.For general distributions of the step-size, satisfying the power-like condition, the distance from the origin of the random walk tends, after a large number of steps, to a stable distribution due to the generalized central limit theorem, enabling many processes to be modeled using Lévy flights.
A complete Fermat's spiral (both branches) is a smooth double point free curve, in contrast with the Archimedean and hyperbolic spiral. Like a line or circle or parabola, it divides the plane into two connected regions. Definition of sector (light blue) and polar slope angle α