nietcollineaire

Nietcollineaire is a term used in geometry to describe a configuration in which a set of points does not all lie on a single straight line. In Dutch-language mathematical texts it corresponds to the English term non-collinear. A fundamental case is three points: they are nietcollineaire if they determine a triangle with nonzero area; for larger sets, they are nietcollineaire if not all points are contained in one line.

In two-dimensional space, three points A, B, and C are nietcollineaire when the area of triangle ABC is nonzero. This is equivalent to the determinant det(B−A, C−A) being nonzero, or to the vectors B−A and C−A being linearly independent. In higher dimensions, a set of points is nietcollineaire if the affine hull of the points has dimension at least 2, meaning they cannot all be placed on a single line.

Nietcollineaire configurations are important in practical computation and design because collinear (degenerate) cases can lead to undefined or unstable results. They are a common degeneracy check in mesh generation, polygon triangulation, computer-aided design, and various geometric algorithms, where a proper triangle or polygon requires non-collinearity among the defining points.

See also: collinear, non-collinear, nondegenerate, affine geometry. The concept is related to broader ideas of dimensionality and degeneracy in geometry and is used across computational geometry, graphics, and design disciplines.