Gets the approximate circumference of the ellipse.

Namespace:  ceometric.VectorGeometry
Assembly:  ceometric.VectorGeometry (in ceometric.VectorGeometry.dll) Version: 1.8.0.0 (1.8.0.0)

Syntax

C#
public double Circumference { get; }
Visual Basic (Declaration)
Public ReadOnly Property Circumference As Double
Visual C++
public:
property double Circumference {
	double get ();
}

Field Value

The approximate circumference of the ellipse.

Remarks

Uses an approximation. The precision of the approximation is relative to the numerical eccentricity of the ellipse. It is:
  • always better than 4.03e-4
  • 1e-4 for e less than 0.9995
  • 1e-6 for e less than 0.9812
  • 1e-8 for e less than 0.9242
  • 1e-9 for e less than 0.8820
wherein e denotes the numerical eccentricity of the ellipse.

The exact circumference of an ellipse can only be computed numerically. This computation converges very slow with increasing numerical eccentricity. Due to this reason, an approximate formula is used here. This formula is very fast and likely to be the most accurate known for a general ellipse.

See Also