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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
Two lines in are either skew or coplanar, and in the latter case they are either coincident or intersect in a unique point. If p ij and p′ ij are the Plücker coordinates of two lines, then they are coplanar precisely when
Line art drawing of parallel lines and curves. In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance. In three ...
Three distinct planes, no pair of which are parallel, can either meet in a common line, meet in a unique common point, or have no point in common. In the last case, the three lines of intersection of each pair of planes are mutually parallel. A line can lie in a given plane, intersect that plane in a unique point, or be parallel to the plane.
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the axis of the right conoid. Using a Cartesian coordinate system in three-dimensional space , if we take the z -axis to be the axis of a right conoid, then the right conoid can be ...
As outlined above, projective spaces were introduced for formalizing statements like "two coplanar lines intersect in exactly one point, and this point is at infinity if the lines are parallel". Such statements are suggested by the study of perspective , which may be considered as a central projection of the three dimensional space onto a plane ...
Z-fighting, also called stitching or planefighting, is a phenomenon in 3D rendering that occurs when two or more primitives have very similar distances to the camera. This would cause them to have near-similar or identical values in the z-buffer , which keeps track of depth.
The points of the design are the points of the plane, and the blocks of the design are the lines of the plane. [14] As such it is a valuable example in (block) design theory. With the points labelled 0, 1, 2, ..., 6 the lines (as point sets) are the translates of the (7, 3, 1) planar difference set given by {0, 1, 3} in the group Z / 7 Z . [ 14 ]