General position

In geometry, general position forsetpoints, or other configuration, meansgeneral case situation, as opposedsome more special or coincidental cases thatpossible. Its precide meaning differsdifferent settings.

This notionimportantmathematicsits applications, because degenerate cases may require an exceptional treatment;example, when stating exactly certain theoremswhen writing computer programs.

The most frequent use isfollowing.

A setpoints ind-dimensional Euclidean spacesaidbegeneral position, if no d + 1them lie in(d − 1)-dimensional plane. Such setpointsalso saidbe affinely independent. See affine transformationmore.

If d + 1 pointsin(d − 1)-dimensional plane, itcalled degenerate case or degenerate configuration.

In particular,setpoints inplanesaidbegeneral position, if no threethemonsame straight line. (Three points online isdegenerate case here).

In some contexts, e.g., when discussing Voronoi tesselationsDelaunay triangulations inplane,following definitionused.

A setpoints inplanesaidbegeneral position, if no threethemneither onsame straight line nor onsame circle.

This definition can be generalized further: one may speakpointsgeneral positionrespect tofixed classalgebraic relations (e.g. conic sections). In algebraic geometry this kindconditionfrequently met,that points should impose independent conditions on curves passing through them.