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Any Newton iteration needs convenient starting values, which can be derived by a visualization of both the curves.
Description
A parametrically or explicitly given curve can easily be visualized, because to any parameter t or x respectively it is easy to calculate the corresponding point. For implicitly given curves this task is not as easy. In this case one has to determine a curve point with help of starting values and an iteration. If one wants to determine the intersection points of two polygons , one can check the intersection of any pair of line segments of the polygons see above. For polygons with many segments this method is rather time-consuming.
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In practice one accelerates the intersection algorithm by using window tests. In this case one divides the polygons into small sub-polygons and determines the smallest window rectangle with sides parallel to the coordinate axes for any sub-polygon.
INTERSECT | meaning in the Cambridge English Dictionary
Before starting the time-consuming determination of the intersection point of two line segments any pair of windows is tested for common points. In 3-dimensional space there are intersection points common points between curves and surfaces. In the following sections we consider transversal intersection only. The intersection of a line and a plane in general position in three dimensions is a point. Inserting the parameter representation into the equation yields the linear equation.
If the scalar triple product equals to 0, then planes either do not have the triple intersection or it is a line or a plane, if all three planes are the same. Analogously to the plane case the following cases lead to non-linear systems, which can be solved using a 1- or 3-dimensional Newton iteration. A line—sphere intersection is a simple special case. Like the case of a line and a plane, the intersection of a curve and a surface in general position consists of discrete points, but a curve may be partly or totally contained in a surface.
Two transversally intersecting surfaces give an intersection curve. The most simple case the intersection line of two non-parallel planes. From Wikipedia, the free encyclopedia. For broader coverage of this topic, see Intersection mathematics. See guidance in Wikipedia:Summary style.
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Further information: Plane geometry and Two-dimensional space. Main article: Line—line intersection. Main article: Line segment intersection. Further information: three-dimensional space. Main article: Line—plane intersection. Partnership provides research organisations and large enterprises a proven path to accelerate cloud adoption and modernise IT infrastructure with the leading SaaS-managed hybrid Intersect submitted its Australian Research Council LIEF grant application for aggregated high performance computing access across member organisations.
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Intersection (set theory)
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