/// <summary>
/// @note Exp should really only be used after Log.
/// Assumes a quaternion with W=0 and V=theta*v (where |v| = 1).
/// Exp(q) = (sin(theta)*v, cos(theta))
/// </summary>
public FQuat Exp()
{
float angle = FMath.Sqrt(X * X + Y * Y + Z * Z);
float sinAngle = FMath.Sin(angle);
FQuat result;
result.W = FMath.Cos(angle);
if (FMath.Abs(sinAngle) >= FMath.SmallNumber)
{
float scale = sinAngle / angle;
result.X = scale * X;
result.Y = scale * Y;
result.Z = scale * Z;
}
else
{
result.X = X;
result.Y = Y;
result.Z = Z;
}
return(result);
}
/// <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>
/// Converts spherical coordinates on the unit sphere into a Cartesian unit length vector.
/// </summary>
public FVector SphericalToUnitCartesian()
{
float SinTheta = FMath.Sin(X);
return(new FVector(FMath.Cos(Y) * SinTheta, FMath.Sin(Y) * SinTheta, FMath.Cos(X)));
}