/// <summary>
/// Solve A * x = b, where b is a column vector. This is more efficient
/// than computing the inverse in one-shot cases.
/// </summary>
/// <param name="b">The b.</param>
/// <returns></returns>
public FVector3 Solve33(FVector3 b)
{
float det = FVector3.Dot(ex, FVector3.Cross(ey, ez));
if (det != 0.0f)
{
det = 1.0f / det;
}
return(new FVector3(det * FVector3.Dot(b, FVector3.Cross(ey, ez)),
det * FVector3.Dot(ex, FVector3.Cross(b, ez)),
det * FVector3.Dot(ex, FVector3.Cross(ey, b))));
}
public static void CreateBillboard(ref FVector3 objectPosition, ref FVector3 cameraPosition,
ref FVector3 cameraUpVector, FVector3?cameraForwardVector, out FMatrix result)
{
FVector3 translation = objectPosition - cameraPosition;
FVector3 backwards, right, up;
FVector3.Normalize(ref translation, out backwards);
FVector3.Normalize(ref cameraUpVector, out up);
FVector3.Cross(ref backwards, ref up, out right);
FVector3.Cross(ref backwards, ref right, out up);
result = Identity;
result.Backward = backwards;
result.Right = right;
result.Up = up;
result.Translation = translation;
}
public static void CreateWorld(ref FVector3 position, ref FVector3 forward, ref FVector3 up, out FMatrix result)
{
FVector3 x, y, z;
FVector3.Normalize(ref forward, out z);
FVector3.Cross(ref forward, ref up, out x);
FVector3.Cross(ref x, ref forward, out y);
x.Normalize();
y.Normalize();
result = new FMatrix();
result.Right = x;
result.Up = y;
result.Forward = z;
result.Translation = position;
result.M44 = 1f;
}
public static void CreateLookAt(ref FVector3 cameraPosition, ref FVector3 cameraTarget, ref FVector3 cameraUpVector,
out FMatrix result)
{
// http://msdn.microsoft.com/en-us/library/bb205343(v=VS.85).aspx
FVector3 vz = FVector3.Normalize(cameraPosition - cameraTarget);
FVector3 vx = FVector3.Normalize(FVector3.Cross(cameraUpVector, vz));
FVector3 vy = FVector3.Cross(vz, vx);
result = Identity;
result.M11 = vx.X;
result.M12 = vy.X;
result.M13 = vz.X;
result.M21 = vx.Y;
result.M22 = vy.Y;
result.M23 = vz.Y;
result.M31 = vx.Z;
result.M32 = vy.Z;
result.M33 = vz.Z;
result.M41 = -FVector3.Dot(vx, cameraPosition);
result.M42 = -FVector3.Dot(vy, cameraPosition);
result.M43 = -FVector3.Dot(vz, cameraPosition);
}
public static FMatrix CreateLookAt(FVector3 cameraPosition, FVector3 cameraTarget, FVector3 cameraUpVector)
{
FMatrix ret;
CreateLookAt(ref cameraPosition, ref cameraTarget, ref cameraUpVector, out ret);
return(ret);
}
public static void CreateFromAxisAngle(ref FVector3 axis, float angle, out FMatrix result)
{
throw new NotImplementedException();
}
public static FMatrix CreateFromAxisAngle(FVector3 axis, float angle)
{
throw new NotImplementedException();
}
public static void CreateConstrainedBillboard(ref FVector3 objectPosition, ref FVector3 cameraPosition,
ref FVector3 rotateAxis, FVector3?cameraForwardVector,
FVector3?objectForwardVector, out FMatrix result)
{
throw new NotImplementedException();
}
public static FMatrix CreateConstrainedBillboard(FVector3 objectPosition, FVector3 cameraPosition,
FVector3 rotateAxis, Nullable <FVector3> cameraForwardVector,
Nullable <FVector3> objectForwardVector)
{
throw new NotImplementedException();
}
/// <summary>
/// Set this matrix to all zeros.
/// </summary>
public void SetZero()
{
ex = FVector3.Zero;
ey = FVector3.Zero;
ez = FVector3.Zero;
}
/// <summary>
/// Construct this matrix using columns.
/// </summary>
/// <param name="c1">The c1.</param>
/// <param name="c2">The c2.</param>
/// <param name="c3">The c3.</param>
public Mat33(FVector3 c1, FVector3 c2, FVector3 c3)
{
ex = c1;
ey = c2;
ez = c3;
}
/// Perform the cross product on two vectors.
public static FVector3 Cross(FVector3 a, FVector3 b)
{
return(new FVector3(a.Y * b.Z - a.Z * b.Y, a.Z * b.X - a.X * b.Z, a.X * b.Y - a.Y * b.X));
}
/// Perform the dot product on two vectors.
public static float Dot(FVector3 a, FVector3 b)
{
return(a.X * b.X + a.Y * b.Y + a.Z * b.Z);
}
/// Multiply a matrix times a vector.
public static FVector3 Mul(Mat33 A, FVector3 v)
{
return(v.X * A.ex + v.Y * A.ey + v.Z * A.ez);
}