/// <summary>
/// Returns a random unit vector, uniformly distributed, within the specified cone.
/// </summary>
/// <param name="dir">The center direction of the cone</param>
/// <param name="horizontalConeHalfAngleRad">Horizontal half-angle of cone, in radians.</param>
/// <param name="verticalConeHalfAngleRad">Vertical half-angle of cone, in radians.</param>
/// <returns>Normalized vector within the specified cone.</returns>
public FVector VRandCone(FVector dir, float horizontalConeHalfAngleRad, float verticalConeHalfAngleRad)
{
if ((verticalConeHalfAngleRad > 0.0f) && (horizontalConeHalfAngleRad > 0.0f))
{
float randU = FRand();
float randV = FRand();
// Get spherical coords that have an even distribution over the unit sphere
// Method described at http://mathworld.wolfram.com/SpherePointPicking.html
float theta = 2.0f * FMath.PI * randU;
float phi = FMath.Acos((2.0f * randV) - 1.0f);
// restrict phi to [0, ConeHalfAngleRad]
// where ConeHalfAngleRad is now a function of Theta
// (specifically, radius of an ellipse as a function of angle)
// function is ellipse function (x/a)^2 + (y/b)^2 = 1, converted to polar coords
float coneHalfAngleRad = FMath.Square(FMath.Cos(theta) / verticalConeHalfAngleRad) + FMath.Square(FMath.Sin(theta) / horizontalConeHalfAngleRad);
coneHalfAngleRad = FMath.Sqrt(1.0f / coneHalfAngleRad);
// clamp to make a cone instead of a sphere
phi = FMath.Fmod(phi, coneHalfAngleRad);
// get axes we need to rotate around
FMatrix dirMat = FMatrix.CreateRotation(dir.Rotation());
// note the axis translation, since we want the variation to be around X
FVector dirZ = dirMat.GetUnitAxis(EAxis.X);
FVector dirY = dirMat.GetUnitAxis(EAxis.Y);
FVector result = dir.RotateAngleAxis(phi * 180.0f / FMath.PI, dirY);
result = result.RotateAngleAxis(theta * 180.0f / FMath.PI, dirZ);
// ensure it's a unit vector (might not have been passed in that way)
result = result.GetSafeNormal();
return(result);
}
else
{
return(dir.GetSafeNormal());
}
}
/// <summary>
/// Returns a random unit vector, uniformly distributed, within the specified cone.
/// </summary>
/// <param name="dir">The center direction of the cone</param>
/// <param name="coneHalfAngleRad">Half-angle of cone, in radians.</param>
/// <returns>Normalized vector within the specified cone.</returns>
public FVector VRandCone(FVector dir, float coneHalfAngleRad)
{
if (coneHalfAngleRad > 0.0f)
{
float randU = FRand();
float randV = FRand();
// Get spherical coords that have an even distribution over the unit sphere
// Method described at http://mathworld.wolfram.com/SpherePointPicking.html
float theta = 2.0f * FMath.PI * randU;
float phi = FMath.Acos((2.0f * randV) - 1.0f);
// restrict phi to [0, ConeHalfAngleRad]
// this gives an even distribution of points on the surface of the cone
// centered at the origin, pointing upward (z), with the desired angle
phi = FMath.Fmod(phi, coneHalfAngleRad);
// get axes we need to rotate around
FMatrix dirMat = FMatrix.CreateRotation(dir.Rotation());
// note the axis translation, since we want the variation to be around X
FVector dirZ = dirMat.GetUnitAxis(EAxis.X);
FVector dirY = dirMat.GetUnitAxis(EAxis.Y);
FVector result = dir.RotateAngleAxis(phi * 180.0f / FMath.PI, dirY);
result = result.RotateAngleAxis(theta * 180.0f / FMath.PI, dirZ);
// ensure it's a unit vector (might not have been passed in that way)
result = result.GetSafeNormal();
return(result);
}
else
{
return(dir.GetSafeNormal());
}
}
