Computational geometry degeneracy

How do you know if a polygon is degenerate?
A convex polygon is degenerate if at least two consecutive sides coincide at least partially, or at least one side has zero length, or at least one angle is 180\xb0.
Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides..

A degeneracy occurs if the half-line contains one or both endpoints of the line segment. A set of objects is now called simple, or nondegenerate, or in general position, if it does not contain any degeneracy. We thus de ne \simplicity" relative to the primitives used to solve a problem.

Many descriptions of algorithms in computational geometry exclude degeneracies by fiat. Practitioners are left to their own devices for.

We believe that this technique will become a standard tool in writing geometric software. Keywords: Computational geometry, degenerate data, implementation,

Unique existence of the Levi-Civita connection

In the mathematical field of Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita connection or nowrap>(pseudo-)Riemannian connection of the given metric.
Because it is canonically defined by such properties, often this connection is automatically used when given a metric.

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Computational geometry degeneracy

How do you know if a polygon is degenerate?