Search results
Results From The WOW.Com Content Network
Line–line intersection. 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. In three-dimensional Euclidean geometry, if two lines are not in ...
For broader coverage of this topic, see Intersection (mathematics). The red dot represents the point at which the two lines intersect. 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 line–line intersection ...
Creating the one point or two points in the intersection of two circles (if they intersect). For example, starting with just two distinct points, we can create a line or either of two circles (in turn, using each point as centre and passing through the other point). If we draw both circles, two new points are created at their intersections.
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is ...
For every two distinct points, there is exactly one line that contains both points. The intersection of any two distinct lines contains exactly one point. There exists a set of four points, no three of which belong to the same line. Duality in the Fano plane: Each point corresponds to a line and vice versa.
The intersection point of the associated lines k and l describes the circle. A locus can also be defined by two associated curves depending on one common parameter. If the parameter varies, the intersection points of the associated curves describe the locus. In the figure, the points K and L are fixed points on a given line m.
Intersection theory. Not to be confused with Intersection (set theory) or Intersectionality. In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. [ 1 ] The theory for varieties is older, with roots in Bézout's theorem on ...
Line–plane intersection. The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) 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 ...