Sphere sampling method

Within the context of the First and Second Order of the Reliability Method, the Strong Maximum Test helps to check whether the design point computed is:

  • the true design point, which means a global maximum point,

  • a strong design point, which means that there is no other local maximum verifying the event and associated to a value near the global maximum.

The Strong Maximum Test samples a sphere in the standard space. the gaussian random sampling technique used is described hereafter.

  1. sampling of points in \Rset^N according to a radial distribution: we generate N independent standard normal samples,

  2. projection of the points onto \cS^{*} : we map the points different from the origin using the transformation M\longmapsto m such as \displaystyle\mathbf{Om}=R\frac{\mathbf{OM}}{\|\mathbf{OM}\|} where R is the radius of the sphere of interest. This transformation does not depend on the angular coordinates. Thus, the generated points follow a uniform distribution on \cS^{*}.

(Source code, png, hires.png, pdf)




  • Luban, Marshall, Staunton, 1988, “An efficient method for generating a uniform distribution of points within a hypersphere,” Computer in Physics, 2(6), 55.