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<h3><a name="s03_07_11">3.7.11 </a>rand.inc</h3>
<p>
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.
</p>
<h4><a name="s03_07_11_01">3.7.11.1 </a>Flat Distributions</h4>
<a name="s03_07_11_01_i1"><a name="SRand"></a>
<p>
<code>SRand(Stream)</code>. "Signed rand()", returns random numbers in the range [-1, 1]. <br>Parameters:
</p>
<ul>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_01_i2"><a name="RRand"></a>
<p>
<code>RRand(Min, Max, Stream)</code>. Returns random numbers in the range [Min, Max].<br> Parameters:
</p>
<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>
<a name="s03_07_11_01_i3"><a name="VRand"></a>
<p>
<code>VRand(Stream)</code>. Returns random vectors in a box from < 0, 0, 0> to < 1, 1, 1><br>
Parameters:
</p>
<ul>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_01_i4"><a name="VRand_In_Box"></a>
<p>
<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.<br> Parameters:
</p>
<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>
<a name="s03_07_11_01_i5"><a name="VRand_In_Sphere"></a>
<p>
<code>VRand_In_Sphere(Stream)</code>. Returns a random vector in a unit-radius sphere located at the origin.<br>
Parameters:
</p>
<ul>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_01_i6"><a name="VRand_On_Sphere"></a>
<p>
<code>VRand_On_Sphere(Stream)</code>. Returns a random vector on the surface of a unit-radius sphere located at the
origin.<br> Parameters:
</p>
<ul>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_01_i7"><a name="VRand_In_Obj"></a>
<p>
<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).<br> Parameters:
</p>
<ul>
<li>
<code>Object</code> = The object the macro chooses the points from.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<h4><a name="s03_07_11_02">3.7.11.2 </a>Other Distributions</h4>
<h5><a name="s03_07_11_02_01">3.7.11.2.1 </a>Continuous Symmetric Distributions</h5>
<a name="s03_07_11_02_01_i1"><a name="Rand_Cauchy"></a>
<p>
<code>Rand_Cauchy(Mu, Sigma, Stream)</code>. Cauchy distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Mu</code> = Mean.
</li>
<li>
<code>Sigma</code> = Standard deviation.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_01_i2"><a name="Rand_Student"></a>
<p>
<code>Rand_Student(N, Stream)</code>. Student's-t distribution.<br> Parameters:
</p>
<ul>
<li>
<code>N</code> = degrees of freedom.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_01_i3"><a name="Rand_Normal"></a>
<p>
<code>Rand_Normal(Mu, Sigma, Stream)</code>. Normal distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Mu</code> = Mean.
</li>
<li>
<code>Sigma</code> = Standard deviation.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_01_i4"><a name="Rand_Gauss"></a>
<p>
<code>Rand_Gauss(Mu, Sigma, Stream)</code>. Gaussian distribution. Like Rand_Normal(), but a bit faster.<br>
Parameters:
</p>
<ul>
<li>
<code>Mu</code> = Mean.
</li>
<li>
<code>Sigma</code> = Standard deviation.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<h5><a name="s03_07_11_02_02">3.7.11.2.2 </a>Continuous Skewed Distributions</h5>
<a name="s03_07_11_02_02_i1"><a name="Rand_Spline"></a>
<p>
<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.<br> Parameters:
</p>
<ul>
<li>
<code>Spline</code> = A spline determining the distribution.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i2"><a name="Rand_Gamma"></a>
<p>
<code>Rand_Gamma(Alpha, Beta, Stream)</code>. Gamma distribution.<br> Parameters:
</p>
<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>
<a name="s03_07_11_02_02_i3"><a name="Rand_Beta"></a>
<p>
<code>Rand_Beta(Alpha, Beta, Stream)</code>. Beta variate.<br> Parameters:
</p>
<ul>
<li>
<code>Alpha</code> = Shape Gamma1.
</li>
<li>
<code>Beta</code> = Scale Gamma2.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i4"><a name="Rand_Chi_Square"></a>
<p>
<code>Rand_Chi_Square(N, Stream)</code>. Chi Square random variate.<br> Parameters:
</p>
<ul>
<li>
<code>N</code> = Degrees of freedom (integer).
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i5"><a name="Rand_F_Dist"></a>
<p>
<code>Rand_F_Dist(N, M, Stream)</code>. F-distribution.<br> Parameters:
</p>
<ul>
<li>
<code>N, M</code> = Degrees of freedom.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i6"><a name="Rand_Tri"></a>
<p>
<code>Rand_Tri(Min, Max, Mode, Stream)</code>. Triangular distribution <br> Parameters:
</p>
<ul>
<li>
<code>Min, Max, Mode</code>: Min < Mode < Max.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i7"><a name="Rand_Erlang"></a>
<p>
<code>Rand_Erlang(Mu, K, Stream)</code>. Erlang variate.<br> Parameters:
</p>
<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>
<a name="s03_07_11_02_02_i8"><a name="Rand_Exp"></a>
<p>
<code>Rand_Exp(Lambda, Stream)</code>. Exponential distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Lambda</code> = rate = 1/mean.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i9"><a name="Rand_Lognormal"></a>
<p>
<code>Rand_Lognormal(Mu, Sigma, Stream)</code>. Lognormal distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Mu</code> = Mean.
</li>
<li>
<code>Sigma</code> = Standard deviation.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i10"><a name="Rand_Pareto"></a>
<p>
<code>Rand_Pareto(Alpha, Stream)</code>. Pareto distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Alpha</code> = ?
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_02_i11"><a name="Rand_Weibull"></a>
<p>
<code>Rand_Weibull(Alpha, Beta, Stream)</code>. Weibull distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Alpha</code> = ?
</li>
<li>
<code>Beta</code> = ?
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<h5><a name="s03_07_11_02_03">3.7.11.2.3 </a>Discrete Distributions </h5>
<a name="s03_07_11_02_03_i1"><a name="Rand_Bernoulli"></a>
<p>
<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.<br> Parameters:
</p>
<ul>
<li>
<code>P</code> = probability range (0-1).
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_03_i2"><a name="Rand_Binomial"></a>
<p>
<code>Rand_Binomial(N, P, Stream)</code>. Binomial distribution.<br> Parameters:
</p>
<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>
<a name="s03_07_11_02_03_i3"><a name="Rand_Geo"></a>
<p>
<code>Rand_Geo(P, Stream)</code>. Geometric distribution.<br> Parameters:
</p>
<ul>
<li>
<code>P</code> = Probability (0-1).
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
<a name="s03_07_11_02_03_i4"><a name="Rand_Poisson"></a>
<p>
<code>Rand_Poisson(Mu, Stream)</code>. Poisson distribution.<br> Parameters:
</p>
<ul>
<li>
<code>Mu</code> = Mean.
</li>
<li>
<code>Stream</code> = Random number stream.
</li>
</ul>
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