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Analogous to straight line segments above, one can also define arcs as segments of a curve. In one-dimensional space, a ball is a line segment. An oriented plane segment or bivector generalizes the directed line segment. Beyond Euclidean geometry, geodesic segments play the role of line segments.
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Intersection of two line segments. For two non-parallel line segments (,), (,) and (,), (,) there is not necessarily an intersection point (see diagram), because the intersection point (,) of the corresponding lines need not to be contained in the line segments. In order to check the situation one uses parametric representations of the lines:
The Fifth Avenue Line, also called the Fifth Avenue Elevated or Fifth Avenue–Bay Ridge Line, was an elevated rail line in Brooklyn, New York City, United States. It ran above Hudson Avenue, Flatbush Avenue , Fifth Avenue , 38th Street, and Third Avenue from Downtown Brooklyn south to Bay Ridge .
Given a line and any point A on it, we may consider A as decomposing this line into two parts. Each such part is called a ray and the point A is called its initial point. It is also known as half-line (sometimes, a half-axis if it plays a distinct role, e.g., as part of a coordinate axis). It is a one-dimensional half-space. The point A is ...
Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced. For example: 5 November 1605 (pronounced "the fifth of November ...
The first bus company in Manhattan was the Fifth Avenue Coach Company, which began operating the Fifth Avenue Line (now the M1 route) in 1886. When New York Railways began abandoning several streetcar lines in 1919, the replacement bus routes (including the current M21 and M22 routes) were picked up by the New York City Department of Plant and ...
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.