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GltRandomSphere< R > Class Template Reference
[GLT Math]

Random points on the unit sphere. More...

#include <random.h>

List of all members.

Public Methods
	GltRandomSphere (R &random, const double radius=1.0)
	Constructor.
	GltRandomSphere (const double radius=1.0)
	Constructor using default RNG.
	GltRandomSphere (const GltRandomSphere< R > &gen)
	Copy constructor.
	~GltRandomSphere ()
	Destructor.
Vector	rand () const
	Random point on sphere surface.
R &	base ()
	Base random number generator.
const R &	base () const
	Base random number generator.

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Detailed Description

template<class R = GltRandomLFSRMix>
class GltRandomSphere< R >

Random points on the unit sphere.

Author:

Nigel Stewart, RMIT (nigels.com@gmail.com)

http://www.math.niu.edu/~rusin/known-math/96/sph.rand

The trig method. This method works only in 3-space, but it is very fast. It depends on the slightly counterintuitive fact that each of the three coordinates of a uniformly distributed point on S^2 is uniformly distributed on [-1,1] (but the three are not independent, obviously). Therefore, it suffices to choose one axis (Z, say) and generate a uniformly distributed value on that axis. This constrains the chosen point to lie on a circle parallel to the X-Y plane, and the obvious trig method may be used to obtain the remaining coordinates.

• Choose z uniformly distributed in [-1,1].
• Choose t uniformly distributed on [0, 2*pi).
• Let r = sqrt(1-z^2).
• Let x = r * cos(t).
• Let y = r * sin(t).

Definition at line 294 of file random.h.

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The documentation for this class was generated from the following file:

• math/random.h

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