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Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
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.
Green line has two intersections. Yellow line lies tangent to the cylinder, so has infinitely many points of intersection. Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all.
For example, the first Napoleon point is the point of concurrency of the three lines each from a vertex to the centroid of the equilateral triangle drawn on the exterior of the opposite side from the vertex. A generalization of this notion is the Jacobi point. The de Longchamps point is the point of concurrence of several lines with the Euler line.
a) different tangent lines (transversal intersection, after transversality), or b) the tangent line in common and they are crossing each other ( touching intersection , after tangency ). If both the curves have a point S and the tangent line there in common but do not cross each other, they are just touching at point S .
It is an easy task to determine the intersection points of a line with a quadric (i.e. line-sphere); one only has to solve a quadratic equation. So, any intersection curve of a cone or a cylinder (they are generated by lines) with a quadric consists of intersection points of lines and the quadric (see pictures).
where is the dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.. The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its ...
The speed at which the data is generated and processed to meet the demands and challenges that lie in the path of growth and development. Big data is often available in real-time. Compared to small data, big data is produced more continually. Two kinds of velocity related to big data are the frequency of generation and the frequency of handling ...