/// <summary>
/// Returns a random number in range [0,1] from an exponential distribution.
/// </summary>
/// <returns>Random number in range [0,1] from given exponential distribution.</returns>
/// <param name="exponent">
/// Exponent for distribution. Must be >= 0.
/// 0 will be uniform distribution; 1 will be linear distribution w/ slope 1.
/// </param>
/// <param name="direction">The direction for the curve (right/left).</param>
public static float RandomFromExponentialDistribution(float exponent, Direction_e direction)
{
// our curve will go from 0 to 1.
var max_cdf = ExponentialRightCDF(1.0f, exponent);
var u = Random.Range(0.0f, max_cdf);
var x_val = EponentialRightInverseCDF(u, exponent);
if (direction == Direction_e.Left)
{
x_val = 1.0f - x_val;
}
return(x_val);
}
/// <summary>
/// Returns random in range [0,1] from a curved right slope.
/// </summary>
/// <returns>Random in range [0,1] from a curved right slope.</returns>
/// <param name="skew">The difference in height between max and min of curve.</param>
public static float RandomFromSlopedDistribution(float skew, Direction_e direction)
{
// the difference in scale is just the same as the max y-value..
var max_y = skew;
// our curve will go from 0 to max_x.
var max_x = Inverse_Sec_Sqrd(max_y);
var max_cdf = Sec_Sqrd_CumulativeDistributionFunction(max_x);
var u = Random.Range(0.0f, max_cdf);
var x_val = Sec_Sqrd_InverseCumulativeDistributionFunction(u);
// scale to [0,1]
var value = x_val / max_x;
if (direction == Direction_e.Left)
{
value = 1.0f - value;
}
return(value);
}
/// <summary>
/// Returns a random number in range [0,1] from an exponential distribution.
/// </summary>
/// <returns>Random number in range [0,1] from given exponential distribution.</returns>
/// <param name="exponent">
/// Exponent for distribution. Must be >= 0.
/// 0 will be uniform distribution; 1 will be linear distribution w/ slope 1.
/// </param>
/// <param name="direction">The direction for the curve (right/left).</param>
public static float RandomFromExponentialDistribution(float exponent, Direction_e direction) {
// our curve will go from 0 to 1.
float max_cdf = ExponentialRightCDF(1.0f, exponent);
float u = Random.Range(0.0f, max_cdf);
float x_val = EponentialRightInverseCDF(u, exponent);
if (direction == Direction_e.Left) {
x_val = 1.0f - x_val;
}
return x_val;
}
//--------------------------------------------------------------------------------------------
// Exponential Distribution
//--------------------------------------------------------------------------------------------
/// <summary>
/// Returns a random number in range [min,max] from an exponential distribution.
/// </summary>
/// <returns>Random number in range [min,max] from given exponential distribution.</returns>
/// <param name="min">Minimum random number (inclusive).</param>
/// <param name="max">Maximum random number (inclusive).</param>
/// <param name="exponent">
/// Exponent for distribution. Must be >= 0.
/// 0 will be uniform distribution; 1 will be linear distribution w/ slope 1.
/// </param>
/// <param name="direction">The direction for the curve (right/left).</param>
public static float RandomRangeExponential(float min, float max, float exponent, Direction_e direction) {
return min + RandomFromExponentialDistribution(exponent, direction) * (max-min);
}
/// <summary>
/// Returns random in range [0,1] from a curved right slope.
/// </summary>
/// <returns>Random in range [0,1] from a curved right slope.</returns>
/// <param name="skew">The difference in height between max and min of curve.</param>
public static float RandomFromSlopedDistribution(float skew, Direction_e direction) {
// the difference in scale is just the same as the max y-value..
float max_y = skew;
// our curve will go from 0 to max_x.
float max_x = Inverse_Sec_Sqrd(max_y);
float max_cdf = Sec_Sqrd_CumulativeDistributionFunction(max_x);
float u = Random.Range(0.0f, max_cdf);
float x_val = Sec_Sqrd_InverseCumulativeDistributionFunction(u);
// scale to [0,1]
float value = x_val / max_x;
if (direction == Direction_e.Left) {
value = 1.0f - value;
}
return value;
}
/// <summary>
/// Returns a random number in range [min,max] from a curved slope following sec^2(x).
/// </summary>
/// <returns>Random in range [min,max] from a curved left slope.</returns>
/// <param name="skew">The difference in height between max and min of curve.</param>
public static float RandomRangeSlope(float min, float max, float skew, Direction_e direction) {
return min + RandomFromSlopedDistribution(skew, direction) * (max-min);
}
//--------------------------------------------------------------------------------------------
// Exponential Distribution
//--------------------------------------------------------------------------------------------
/// <summary>
/// Returns a random number in range [min,max] from an exponential distribution.
/// </summary>
/// <returns>Random number in range [min,max] from given exponential distribution.</returns>
/// <param name="min">Minimum random number (inclusive).</param>
/// <param name="max">Maximum random number (inclusive).</param>
/// <param name="exponent">
/// Exponent for distribution. Must be >= 0.
/// 0 will be uniform distribution; 1 will be linear distribution w/ slope 1.
/// </param>
/// <param name="direction">The direction for the curve (right/left).</param>
public static float RandomRangeExponential(float min, float max, float exponent, Direction_e direction)
{
return(min + RandomFromExponentialDistribution(exponent, direction) * (max - min));
}
/// <summary>
/// Returns a random number in range [min,max] from a curved slope following sec^2(x).
/// </summary>
/// <returns>Random in range [min,max] from a curved left slope.</returns>
/// <param name="skew">The difference in height between max and min of curve.</param>
public static float RandomRangeSlope(float min, float max, float skew, Direction_e direction)
{
return(min + RandomFromSlopedDistribution(skew, direction) * (max - min));
}
