/// <summary>
/// Builds a 3-D affine transformation matrix.
/// </summary>
/// <param name="scaling">The scaling vactor. Use zero to specify no scaling.</param>
/// <param name="rotationCenter">A <see cref="Vector3F"/> instance specifying the center of the rotation.</param>
/// <param name="rotation">A <see cref="QuaternionF"/> instance specifying the rotation. use <see cref="QuaternionF.Identity"/> to specify no rotation.</param>
/// <param name="translation">A <see cref="Vector3F"/> specifying the translation. Use <see cref="Vector3F.Zero"/> to specify no translation.</param>
/// <returns>A <see cref="Matrix4F"/> representing the affine transformation.</returns>
/// <remarks>
/// <p>
/// Calculates the transoformation matrix using the following formula:
/// Mout = Ms * (Mrc)^-1 * Mr * Mrc * Mt
/// </p>
/// <p>
/// where:
/// <list type="bullet">
/// <item>
/// <term>Ms</term>
/// <description>Scaling transformation.</description>
/// </item>
/// <item>
/// <term>Mrc</term>
/// <description>Rotation center transformation.</description>
/// </item>
/// <item>
/// <term>Mr</term>
/// <description>Rotation transformation.</description>
/// </item>
/// <item>
/// <term>Mt</term>
/// <description>Translation transformation.</description>
/// </item>
/// </list>
/// </p>
/// </remarks>
public static Matrix4F AffineTransformation(float scaling, Vector3F rotationCenter, QuaternionF rotation, Vector3F translation)
{
Matrix4F Ms = TransformationF.Scaling(scaling, scaling, scaling);
Matrix4F Mt = TransformationF.Translation(translation.X, translation.Y, translation.Z);
// TODO: Implement this.
throw new NotImplementedException();
}
/// <summary>
/// Calculates the exponent of a quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <returns>The quaternion's exponent.</returns>
public QuaternionF Exp(QuaternionF a)
{
QuaternionF result = new QuaternionF(0.0f,0.0f,0.0f,0.0f);
float angle = (float)System.Math.Sqrt(a.X*a.X + a.Y*a.Y + a.Z*a.Z);
float sin = (float)System.Math.Sin(angle);
if (MathFunctions.Abs(sin) > 0.0f)
{
float coeff = angle / sin;
result.X = coeff * a.X;
result.Y = coeff * a.Y;
result.Z = coeff * a.Z;
}
else
{
result.X = a.X;
result.Y = a.Y;
result.Z = a.Z;
}
return result;
}
/// <summary>
/// Subtracts a quaternion from a quaternion and puts the result into a third quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <param name="result">A <see cref="QuaternionF"/> instance to hold the result.</param>
public static void Subtract(QuaternionF a, QuaternionF b, ref QuaternionF result)
{
result.W = a.W - b.W;
result.X = a.X - b.X;
result.Y = a.Y - b.Y;
result.Z = a.Z - b.Z;
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <returns>A new <see cref="QuaternionF"/> instance containing the difference.</returns>
public static QuaternionF Subtract(QuaternionF a, QuaternionF b)
{
return new QuaternionF(a.W - b.W, a.X - b.X, a.Y - b.Y, a.Z - b.Z);
}
/// <summary>
/// Converts a given <see cref="QuaternionF"/> to a matrix.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <returns>A new <see cref="Matrix4F"/> instance.</returns>
public static Matrix4F QuaternionToMatrix(QuaternionF q)
{
float x = q.X;
float y = q.Y;
float z = q.Z;
float w = q.W;
float xx = x * x;
float yy = y * y;
float zz = z * z;
float xy = x * y;
float xz = x * z;
float yz = y * z;
float wx = w * x;
float wy = w * y;
float wz = w * z;
return new Matrix4F(
1.0f - 2.0f * yy - 2.0f * zz, 2.0f * xy - 2.0f * wz,
2.0f * xz + 2.0f * wy, 0.0f,
2.0f * xy + 2.0f * wz, 1.0f - 2.0f * xx - 2.0f * zz,
2.0f * yz - 2.0f * wx, 0.0f,
2.0f * xz - 2.0f * wy, 2.0f * yz + 2.0f * wx,
1.0f - 2.0f * xx - 2.0f * yy, 0.0f,
0.0f, 0.0f,
0.0f, 1.0f);
}
/// <summary>
/// Multiplies a quaternion by a scalar and put the result in a third quaternion.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="QuaternionF"/> instance to hold the result.</param>
public static void Multiply(QuaternionF q, float s, ref QuaternionF result)
{
result.W = q.W * s;
result.X = q.X * s;
result.Y = q.Y * s;
result.Z = q.Z * s;
}
/// <summary>
/// Multiplies a quaternion by a scalar.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A <see cref="QuaternionF"/> instance to hold the result.</returns>
public static QuaternionF Multiply(QuaternionF q, float s)
{
QuaternionF result = new QuaternionF(q);
result.W *= s;
result.X *= s;
result.Y *= s;
result.Z *= s;
return result;
}
/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <returns>A new <see cref="QuaternionF"/> instance containing the sum.</returns>
public static QuaternionF Add(QuaternionF a, QuaternionF b)
{
return new QuaternionF(a.W + b.W, a.X + b.X, a.Y + b.Y, a.Z + b.Z);
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/>.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <returns>A new <see cref="QuaternionF"/> containing the result.</returns>
public static QuaternionF Multiply(QuaternionF a, QuaternionF b)
{
QuaternionF result = new QuaternionF();
result.W = a.W * b.W - a.X * b.X - a.Y * b.Y - a.Z * b.Z;
result.X = a.W * b.X + a.X * b.W + a.Y * b.Z - a.Z * b.Y;
result.Y = a.W * b.Y + a.Y * b.W + a.Z * b.X - a.X * b.Z;
result.Z = a.W * b.Z + a.Z * b.W + a.X * b.Y - a.Y * b.X;
return result;
}
/// <summary>
/// Calculates the logarithm of a given quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <returns>The quaternion's logarithm.</returns>
public static QuaternionF Log(QuaternionF a)
{
QuaternionF result = new QuaternionF(0.0f,0.0f,0.0f,0.0f);
if (MathFunctions.Abs(a.W) < 1.0f)
{
float angle = (float)System.Math.Acos(a.W);
float sin = (float)System.Math.Sin(angle);
if (MathFunctions.Abs(sin) >= 0.0f)
{
float coeff = angle / sin;
result.X = coeff * a.X;
result.Y = coeff * a.Y;
result.Z = coeff * a.Z;
}
else
{
result.X = a.X;
result.Y = a.Y;
result.Z = a.Z;
}
}
return result;
}
/// <summary>
/// Calculates the dot product of two quaternions.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <returns>The dot product value.</returns>
public static float Dot(QuaternionF a, QuaternionF b)
{
return a.W * b.W + a.X * b.X + a.Y * b.Y + a.Z * b.Z;
}
/// <summary>
/// Divides a quaternion by a scalar and put the result in a third quaternion.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="QuaternionF"/> instance to hold the result.</param>
public static void Divide(QuaternionF q, float s, ref QuaternionF result)
{
if(s == 0)
{
throw new DivideByZeroException( "Dividing quaternion by zero" );
}
result.W = q.W / s;
result.X = q.X / s;
result.Y = q.Y / s;
result.Z = q.Z / s;
}
/// <summary>
/// Divides a quaternion by a scalar.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A <see cref="QuaternionF"/> instance to hold the result.</returns>
public static QuaternionF Divide(QuaternionF q, float s)
{
if(s == 0)
{
throw new DivideByZeroException( "Dividing quaternion by zero" );
}
QuaternionF result = new QuaternionF(q);
result.W /= s;
result.X /= s;
result.Y /= s;
result.Z /= s;
return result;
}
/// <summary>
/// Adds two quaternions and put the result in the third quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <param name="result">A <see cref="QuaternionF"/> instance to hold the result.</param>
public static void Add(QuaternionF a, QuaternionF b, ref QuaternionF result)
{
result.W = a.W + b.W;
result.X = a.X + b.X;
result.Y = a.Y + b.Y;
result.Z = a.Z + b.Z;
}
/// <summary>
/// Builds a rotation matrix from a quaternion.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> instance.</param>
/// <returns>A <see cref="Matrix4F"/> representing the rotation.</returns>
public static Matrix4F RotationQuaternion(QuaternionF q)
{
// TODO: Implement this.
throw new NotImplementedException();
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/> and put the result in a third quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionF"/> instance.</param>
/// <param name="b">A <see cref="QuaternionF"/> instance.</param>
/// <param name="result">A <see cref="QuaternionF"/> instance to hold the result.</param>
public static void Multiply(QuaternionF a, QuaternionF b, ref QuaternionF result)
{
result.W = a.W * b.W - a.X * b.X - a.Y * b.Y - a.Z * b.Z;
result.X = a.W * b.X + a.X * b.W + a.Y * b.Z - a.Z * b.Y;
result.Y = a.W * b.Y + a.Y * b.W + a.Z * b.X - a.X * b.Z;
result.Z = a.W * b.Z + a.Z * b.W + a.X * b.Y - a.Y * b.X;
}
/// <summary>
/// Initializes a new instance of the <see cref="QuaternionF"/> class using coordinates from a given <see cref="QuaternionF"/> instance.
/// </summary>
/// <param name="q">A <see cref="QuaternionF"/> to get the coordinates from.</param>
public QuaternionF(QuaternionF q)
{
_w = q.W;
_x = q.X;
_y = q.Y;
_z = q.Z;
}