tasapinnal

Tasapinnal is a term in geometry describing objects that lie in the same plane. In Estonian usage, tasapinnaline or tasapinnal refers to coplanar elements: points, lines, or polygons that share a common plane.

In Euclidean space, three non-collinear points determine a plane. A point is coplanar with a line if it lies on the plane that contains the line and a given point not on that line; more generally, four points are coplanar if the vectors from one chosen point to the others are linearly dependent, which can be tested by a zero scalar triple product. The equation of a plane can be written as ax + by + cz + d = 0, where (a, b, c) is a normal vector to the plane. A point (x, y, z) satisfies the plane equation precisely when it is coplanar with that plane.

Two lines are coplanar if they lie in the same plane; such lines are either parallel or intersecting. If two lines are not in a common plane, they are skew and not coplanar.

Applications of the concept include geometry problem solving, computer graphics and computer-aided design, where identifying coplanar vertices, edges or faces helps in mesh construction, shading calculations, and simplification tasks. Understanding coplanarity also aids in projecting three-dimensional configurations onto planes for analysis.