public static Matrix3x3 getRotationMatrix(Vector3 from1, Vector3 to1)
{
Vector3 from = Vector3.Normalize(from1);
Vector3 to = Vector3.Normalize(to1);
Vector3 vs = Vector3.CrossProduct(from, to); // axis multiplied by sin
Vector3 v = Vector3.Normalize(vs); // axis of rotation
double c = Vector3.DotProduct(from, to); // cos angle
Vector3 vc = Vector3.Multiply(1.0 - c, v); //axis multiplied by (1-cos angle)
Vector3 vp = new Vector3(vc.X *= v.Y, vc.Z *= v.X, vc.Y *= v.Z); //some cross multiplies
Matrix3x3 rotM = new Matrix3x3();
//----------------------------------------------------------------------------------------------------------
rotM.matrix[0, 0] = vc.X * v.X + c; rotM.matrix[1, 0] = vp.X - vs.Z; rotM.matrix[2, 0] = vp.Y + vs.Y;
rotM.matrix[0, 1] = vp.X + vs.Z; rotM.matrix[1, 1] = vc.Y * v.Y + c; rotM.matrix[2, 1] = vp.Z - vs.X;
rotM.matrix[0, 2] = vp.Y - vs.Y; rotM.matrix[1, 2] = vp.Z + vs.X; rotM.matrix[2, 2] = vc.Z * v.Z + c;
//----------------------------------------------------------------------------------------------------------
//return rotM;
return(Matrix3x3.Normalize(rotM));
}
//computes a rotation matrix based on a previous rotation matrix and a series of angle rotations
//better algorithm then nextRotMatrix - still need to keep rotation < 180 degrees
//This uses the rectangular rule
public static Matrix3x3 nextRotMatrix2(Matrix3x3 rotMatrix, Vector3 rotations)
{
//This uses C2 = C1( I + (sin(w)/w)B + ((1 - cos(w))/w)B^2 )
//where w is the total rotation, I is the identity matrix and B is the scew symmetric form of the rotation vector
Matrix3x3 I = new Matrix3x3();
I.matrix[0, 0] = 1; I.matrix[1, 0] = 0; I.matrix[2, 0] = 0;
I.matrix[0, 1] = 0; I.matrix[1, 1] = 1; I.matrix[2, 1] = 0;
I.matrix[0, 2] = 0; I.matrix[1, 2] = 0; I.matrix[2, 2] = 1;
Matrix3x3 B = new Matrix3x3();
B.matrix[0, 0] = 0; B.matrix[1, 0] = -rotations.Z; B.matrix[2, 0] = rotations.Y;
B.matrix[0, 1] = rotations.Z; B.matrix[1, 1] = 0; B.matrix[2, 1] = -rotations.X;
B.matrix[0, 2] = -rotations.Y; B.matrix[1, 2] = rotations.X; B.matrix[2, 2] = 0;
double totalRotation = Vector3.Length(rotations);
Matrix3x3 smallRot;
//Don't divide by 0
if (totalRotation > 0)
{
smallRot = Matrix3x3.Add(Matrix3x3.Add(
I,
Matrix3x3.Multiply(Math.Sin(totalRotation) / totalRotation, B)),
Matrix3x3.Multiply((1 - Math.Cos(totalRotation)) / (totalRotation * totalRotation), Matrix3x3.Multiply(B, B))
);
}
else
{
smallRot = I;
}
Matrix3x3 newRotMatrix = Matrix3x3.Multiply(rotMatrix, smallRot);
//If these are off, it's because of slight errors - these are no longer Rotation matrices, strictly speaking
//The determinant should be 1
//double det = Matrix3x3.Determinant(newRotMatrix)
//This should give an Identity matrix
//Matrix3x3 I = Matrix3x3.Multiply(Matrix3x3.Transpose(newRotMatrix), newRotMatrix);
//Normalize to the the vectors Unit length
//return newRotMatrix;
return(Matrix3x3.Normalize(newRotMatrix));
//TODO: We should really be doing an orthonormalization
}
//computes a rotation matrix based on a previous rotation matrix and a series of angle rotations
public static Matrix3x3 nextRotMatrix(Matrix3x3 rotMatrix, Vector3 rotations)
{
//assuming C(t2) = C(t1)A(t1) where A(t1) is the rotation matrix relating the body frame between time t1 and t2 (I + B)
//A(t1) = [ 1 y z ] for small angles (<180 degrees). x, y and z are rotations about the axes
// [ -y 1 x ]
// [ -z -x 1 ]
Matrix3x3 A = new Matrix3x3();
A.matrix[0, 0] = 1; A.matrix[1, 0] = rotations.Y; A.matrix[2, 0] = rotations.Z;
A.matrix[0, 1] = -rotations.Y; A.matrix[1, 1] = 1; A.matrix[2, 1] = rotations.X;
A.matrix[0, 2] = -rotations.Z; A.matrix[1, 2] = -rotations.X; A.matrix[2, 2] = 1;
//Normalized to keep the vectors unit length
Matrix3x3 newRotMatrix = Matrix3x3.Normalize(Matrix3x3.Multiply(rotMatrix, A));
return(newRotMatrix);
}