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  2. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2). The intersection P′ of two lines is then simply given by [4]

  3. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the lineline intersection between two distinct lines , which either is one point (sometimes called a vertex ) or does not exist (if the lines are parallel ).

  4. Intersection - Wikipedia

    en.wikipedia.org/wiki/Intersection

    In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the lineline intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...

  5. Incidence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Incidence_(geometry)

    The computation of the intersection of two lines shows that the entire pencil of lines centered at a point is determined by any two of the lines that intersect at that point. It immediately follows that the algebraic condition for three lines, [a 1, b 1, c 1], [a 2, b 2, c 2], [a 3, b 3, c 3] to be concurrent is that the determinant,

  6. Desargues configuration - Wikipedia

    en.wikipedia.org/wiki/Desargues_configuration

    Although it may be embedded in two dimensions, the Desargues configuration has a very simple construction in three dimensions: for any configuration of five planes in general position in Euclidean space, the ten points where three planes meet and the ten lines formed by the intersection of two of the planes together form an instance of the configuration. [2]

  7. Bentley–Ottmann algorithm - Wikipedia

    en.wikipedia.org/wiki/Bentley–Ottmann_algorithm

    Therefore, two line segments that share an endpoint, or a line segment that contains an endpoint of another segment, both count as an intersection of two line segments. When multiple line segments intersect at the same point, create and process a single event point for that intersection.

  8. Intersection curve - Wikipedia

    en.wikipedia.org/wiki/Intersection_curve

    The intersection of two planes. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms ...

  9. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    Lines A, B and C are concurrent in Y. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil.