Computing Tangent in Ogre is very good!

Code

Vector3 Math: calculateTangentSpaceVector (
Const Vector3 & position1, const Vector3 & position2, const Vector3 & position3,
Real u1, Real v1, Real u2, Real v2, Real u3, Real v3)
{
// Side0 is the vector along one side of the triangle of vertices passed in,
// And side1 is the vector along another side. Taking the cross product of these returns the normal.
Vector3 side0 = position1-position2;
Vector3 side1 = position3-position1;
// Calculate face normal
Vector3 normal = side1.crossProduct (side0 );
Normal. normalise ();
// Now we use a formula to calculate the tangent.
Real deltaV0 = v1-v2;
Real deltaV1 = v3-v1;
Vector3 tangent = deltaV1 * side0-deltaV0 * side1;
Tangent. normalise ();
// Calculate binormal
Real deltaU0 = u1-u2;
Real deltaU1 = u3-u1;
Vector3 binormal = deltaU1 * side0-deltaU0 * side1;
Binormal. normalise ();
// Now, we take the cross product of the tangents to get a vector which
// Shocould point in the same direction as our normal calculated above.
// If it points in the opposite direction (the dot product between the normals is less than zero ),
// Then we need to reverse the s and t tangents.
// This is because the triangle has been mirrored when going from tangent space to object space.
// Reverse tangents if necessary
Vector3 tangentCross = tangent. crossProduct (binormal );
If (tangentCross. dotProduct (normal) <0.0f)
{
Tangent =-tangent;
Binormal =-binormal;
}

Return tangent;

}