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In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is the empty set if the line is parallel to the plane but outside it. Otherwise, the line cuts through the plane at a single point.
The intersection points are: (−0.8587, 0.7374, −0.6332), (0.8587, 0.7374, 0.6332). 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.
We wish to find a point which is on both planes (i.e. on their intersection), so insert this equation into each of the equations of the planes to get two simultaneous equations which can be solved for and .
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, in order to calculate points of ...
The power diagram of a set of circles divides the plane into regions within which the circle minimizing the power is constant. More generally, French mathematician Edmond Laguerre defined the power of a point with respect to any algebraic curve in a similar way.
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.
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.
An oriented plane segment or bivector generalizes the directed line segment. Beyond Euclidean geometry, geodesic segments play the role of line segments. A line segment is a one-dimensional simplex ; a two-dimensional simplex is a triangle.
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