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2012-03-11T22:31:21Z

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A collection of macros for generating random numbers, as well as 4 predefined random number streams: <code>RdmA, RdmB, RdmC,</code> and <code>RdmD</code>. There are macros for creating random numbers in a flat distribution (all numbers equally likely) in various ranges, and a variety of other distributions.

==Flat Distributions==
{{#indexentry:SRand}}
<code>SRand(Stream)</code>: Signed rand(), returns random numbers in the range [-1, 1].
Parameters:
<ul>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:RRand}}
<code>RRand(Min, Max, Stream)</code>: Returns random numbers in the range [Min, Max].
Parameters:
<ul>
<li><code>Min</code> = The lower end of the output range.</li>
<li><code>Max</code> = The upper end of the output range.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:VRand}}
<code>VRand(Stream)</code>: Returns random vectors in a box from < 0, 0, 0> to < 1, 1, 1>
Parameters:
<ul>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:VRand_In_Box}}
<code>VRand_In_Box(PtA, PtB, Stream)</code>: Like VRand(), this macro returns a random vector in a box, but this version lets you specify the two corners of the box.
Parameters:
<ul>
<li><code>PtA</code> = Lower-left-bottom corner of box.</li>
<li><code>PtB</code> = Upper-right-top corner of box.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:VRand_In_Sphere}}
<code>VRand_In_Sphere(Stream)</code>: Returns a random vector in a unit-radius sphere located at the origin.
Parameters:
<ul>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:VRand_On_Sphere}}
<code>VRand_On_Sphere(Stream)</code>: Returns a random vector on the surface of a unit-radius sphere located at the origin.
Parameters:
<ul>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:VRand_In_Obj}}
<code>VRand_In_Obj(Object, Stream)</code>: This macro takes a solid object and returns a random point that is inside it. It does this by randomly sampling the bounding box of the object, and can be quite slow if the object occupies a small percentage of the volume of its bounding box (because it will take more attempts to find a point inside the object). This macro is best used on finite, solid objects (non-solid objects, such as meshes and bezier patches, do not have a defined inside, and will not work).
Parameters:
<ul>
<li><code>Object</code> = The object the macro chooses the points from.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

==Other Distributions==

===Continuous Symmetric Distributions===
{{#indexentry:Rand_Cauchy}}
<code>Rand_Cauchy(Mu, Sigma, Stream)</code>: Cauchy distribution.
Parameters:
<ul>
<li><code>Mu</code> = Mean.</li>
<li><code>Sigma</code> = Standard deviation.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Student}}
<code>Rand_Student(N, Stream)</code>: Student's distribution.
Parameters:
<ul>
<li><code>N</code> = degrees of freedom.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Normal}}
<code>Rand_Normal(Mu, Sigma, Stream)</code>: Normal distribution.
Parameters:
<ul>
<li><code>Mu</code> = Mean.</li>
<li><code>Sigma</code> = Standard deviation.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Gauss}}
<code>Rand_Gauss(Mu, Sigma, Stream)</code>: Gaussian distribution. Like Rand_Normal(), but a bit faster.
Parameters:
<ul>
<li><code>Mu</code> = Mean.</li>
<li><code>Sigma</code> = Standard deviation.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

===Continuous Skewed Distributions===
{{#indexentry:Rand_Spline}}
<code>Rand_Spline(Spline, Stream)</code>: This macro takes a spline describing the desired distribution. The T value of the spline is the output value, and the .y value its chance of occuring.
Parameters:
<ul>
<li><code>Spline</code> = A spline determining the distribution.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Gamma}}
<code>Rand_Gamma(Alpha, Beta, Stream)</code>: Gamma distribution.
Parameters:
<ul>
<li><code>Alpha</code> = Shape parameter > 0.</li>
<li><code>Beta</code> = Scale parameter > 0.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Beta}}
<code>Rand_Beta(Alpha, Beta, Stream)</code>: Beta variate.
Parameters:
<ul>
<li><code>Alpha</code> = Shape Gamma1.</li>
<li><code>Beta</code> = Scale Gamma2.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Chi_Square}}
<code>Rand_Chi_Square(N, Stream)</code>: Chi Square random variate.
Parameters:
<ul>
<li><code>N</code> = Degrees of freedom (integer).</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_F_Dist}}
<code>Rand_F_Dist(N, M, Stream)</code>: F-distribution.
Parameters:
<ul>
<li><code>N, M</code> = Degrees of freedom.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Tri}}
<code>Rand_Tri(Min, Max, Mode, Stream)</code>: Triangular distribution 
Parameters:
<ul>
<li><code>Min, Max, Mode</code>: Min < Mode < Max.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Erlang}}
<code>Rand_Erlang(Mu, K, Stream)</code>: Erlang variate.
Parameters:
<ul>
<li><code>Mu</code> = Mean >= 0.</li>
<li><code>K</code> = Number of exponential samples.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Exp}}
<code>Rand_Exp(Lambda, Stream)</code>: Exponential distribution.
Parameters:
<ul>
<li><code>Lambda</code> = rate = 1/mean.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Lognormal}}
<code>Rand_Lognormal(Mu, Sigma, Stream)</code>: Lognormal distribution.
Parameters:
<ul>
<li><code>Mu</code> = Mean.</li>
<li><code>Sigma</code> = Standard deviation.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Pareto}}
<code>Rand_Pareto(Alpha, Stream)</code>: Pareto distribution.
Parameters:
<ul>
<li><code>Alpha</code> = ?</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Weibull}}
<code>Rand_Weibull(Alpha, Beta, Stream)</code>: Weibull distribution.
Parameters:
<ul>
<li><code>Alpha</code> = ?</li>
<li><code>Beta</code> = ?</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

===Discrete Distributions ===
{{#indexentry:Rand_Bernoulli}}
{{#indexentry:Prob}}
<code>Rand_Bernoulli(P, Stream)</code> and <code>Prob(P, Stream)</code>: Bernoulli distribution. Output is true with probability equal to the value of P and false with a probability of 1 - P.
Parameters:
<ul>
<li><code>P</code> = probability range (0-1).</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Binomial}}
<code>Rand_Binomial(N, P, Stream)</code>: Binomial distribution.
Parameters:
<ul>
<li><code>N</code> = Number of trials.</li>
<li><code>P</code> = Probability (0-1)</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Geo}}
<code>Rand_Geo(P, Stream)</code>: Geometric distribution.
Parameters:
<ul>
<li><code>P</code> = Probability (0-1).</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

{{#indexentry:Rand_Poisson}}
<code>Rand_Poisson(Mu, Stream)</code>: Poisson distribution.
Parameters:
<ul>
<li><code>Mu</code> = Mean.</li>
<li><code>Stream</code> = Random number stream.</li>
</ul>

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