About: Line–plane intersection

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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. Distinguishing these cases, and determining equations for the point and line in the latter cases, have use in computer graphics, motion planning, and collision detection.

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rdfs:label	Line–plane intersection (en) Перетин прямої і площини (uk) 线面交点 (zh)
rdfs:comment	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. Distinguishing these cases, and determining equations for the point and line in the latter cases, have use in computer graphics, motion planning, and collision detection. (en) В аналітичній геометрії, перетин прямої і площини може бути порожньою множиною, точкою, або прямою. Розрізнення цих випадків, і визначення рівнянь для точки і прямої має своє застосування комп'ютерній графіці, плануванні руху, івиявленні зіткнень. (uk) 在解析几何中, 一条直线与一个平面的交点可能是空集、一个点或一条直线。在计算机图形学、运动规划和碰撞检测中，经常需要分析相交类型，以及计算出点坐标或线的方程。 (zh)
foaf:depiction
dcterms:subject	Euclidean geometry Geometric intersection Geometric algorithms Computational physics
Wikipage page ID	3279949 (xsd:integer)
Wikipage revision ID	1030561834 (xsd:integer)
Link from a Wikipage to another Wikipage	Normal vector Euclidean geometry Intersection of a polyhedron with a line Matrix inversion Geometry Geometric intersection Geometric algorithms Line (mathematics) Collision detection Computer graphics Empty set Point (geometry) Three-dimensional space Stereoscopy Computational physics Ray tracing (graphics) Dot product Plane (mathematics) Plane–plane intersection Real number Parallelogram Plücker coordinates Motion planning Vector notation System of linear equations
Link from a Wikipage to an external page	http://geomalgorithms.com/a05-_intersect-1.html
sameAs	Line–plane intersection Line–plane intersection Line–plane intersection Line–plane intersection Line–plane intersection
dbp:wikiPageUsesTemplate	dbt:Unreferenced
thumbnail	wiki-commons:Special:FilePath/Plane-line_intersection.svg?width=300
Link from a Wikipa... related subject.	Analytic geometry
has abstract	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. Distinguishing these cases, and determining equations for the point and line in the latter cases, have use in computer graphics, motion planning, and collision detection. (en) В аналітичній геометрії, перетин прямої і площини може бути порожньою множиною, точкою, або прямою. Розрізнення цих випадків, і визначення рівнянь для точки і прямої має своє застосування комп'ютерній графіці, плануванні руху, івиявленні зіткнень. (uk) 在解析几何中, 一条直线与一个平面的交点可能是空集、一个点或一条直线。在计算机图形学、运动规划和碰撞检测中，经常需要分析相交类型，以及计算出点坐标或线的方程。 (zh)
prov:wasDerivedFrom	wikipedia-en:Line–plane_intersection?oldid=1030561834&ns=0
page length (characters) of wiki page	8675 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Line–plane_intersection
is Link from a Wikipage to another Wikipage of	Intersection (geometry) Plane–line intersection Line–line intersection Plane (geometry) Line–sphere intersection Intersection between a line and a plane Intersection of a line and a plane Intersection of a plane and a line Line-plane intersection Plane-line intersection
is Wikipage redirect of	Plane–line intersection Intersection between a line and a plane Intersection of a line and a plane Intersection of a plane and a line Line-plane intersection Plane-line intersection
is foaf:primaryTopic of	wikipedia-en:Line–plane_intersection

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