/// <summary>
/// Performs the dot product of two vectors.
/// </summary>
/// <param name="vec">The first vector.</param>
/// <param name="vec2">The second vector.</param>
/// <returns>The dot product.</returns>
public static double Dot(Vec3D vec, Vec3D vec2)
{
return vec.X * vec2.X + vec.Y * vec2.Y + vec.Z * vec2.Z;
}
/// <summary>
/// Performs the cross product of two vectors.
/// </summary>
/// <param name="vec">The first vector.</param>
/// <param name="vec2">The second vector.</param>
/// <returns>The cross product.</returns>
public static Vec3D Cross(Vec3D vec, Vec3D vec2)
{
return new Vec3D((vec.Y * vec2.Z) - (vec.Z * vec2.Y), (vec.Z * vec2.X) - (vec.X * vec2.Z), (vec.X * vec2.Y) - (vec.Y * vec2.X));
}
/// <summary>
/// Returns a translation matrix with the given offset.
/// </summary>
/// <param name="offset">The offset.</param>
/// <returns>The translation matrix.</returns>
public static Matrix4 Translation(Vec3D offset)
{
return new Matrix4(1, 0, 0, offset.X,
0, 1, 0, offset.Y,
0, 0, 1, offset.Z,
0, 0, 0, 1);
}
/// <summary>
/// Returns a scale matrix with the given scale.
/// </summary>
/// <param name="scale">The scale vector.</param>
/// <returns>The scale matrix.</returns>
public static Matrix4 Scale(Vec3D scale)
{
return new Matrix4(scale.X, 0, 0, 0,
0, scale.Y, 0, 0,
0, 0, scale.Z, 0,
0, 0, 0, 1);
}
/// <summary>
/// Returns a quaternion that rotates the given angle around the given axis.
/// </summary>
/// <param name="axis">The axis to rotate about.</param>
/// <param name="angle">The amount to rotate.</param>
/// <returns>The quaternion.</returns>
public static Quaternion AxisAngle(Vec3D axis, double angle)
{
double sin = Math.Sin(angle / 2);
return new Quaternion(axis.X * sin, axis.Y * sin, axis.Z * sin, Math.Cos(angle / 2));
}
/// <summary>
/// Scales the quaternion by the given scalar.
/// </summary>
/// <param name="quat">The quat.</param>
/// <param name="val">The value.</param>
/// <returns>The product quat.</returns>
public static Quaternion operator *(Quaternion quat, double val)
{
double angle = 2 * Math.Acos(quat.W);
Vec3D axis = new Vec3D(quat.X, quat.Y, quat.Z) / Math.Sqrt(1 - quat.W * quat.W);
angle *= val;
return AxisAngle(axis, angle);
}