// YOUR CODE HERE
// Given a vector n, form an orthogonal matrix with n as the last column, i.e.,
// a coordinate system aligned such that n is its local z axis.
static __forceinline Mat3f formBasis( const Vec3f& n )
{
Mat3f r;
Vec3f q, b, t;
// Get the minimum component of n
int minIdx = 0;
for (int i = 0; i < 3; ++i) {
if ( abs(n[i]) < abs(n[minIdx]) ) minIdx = i;
}
// Replace the minimum component by 1.0f and take a cross-product to get a vector perpendicular to n
q = n;
q[minIdx] = 1.0f;
t = (cross(q, n)).normalized();
// Get the last perpendicular vector by taking n x t
b = (cross(n, t)).normalized();
// Construct the rotation matrix
r.setCol(0, t);
r.setCol(1, b);
r.setCol(2, n);
return r;
}
Mat3f formBasis(const Vec3f& n) {
// YOUR CODE HERE (R3)
Mat3f R;
Vec3f Q = n;
float min = 99;
int ind = -1;
for(int i = 0; i<3; ++i)
if(abs(n[i]) < min)
{
min = abs(n[i]);
ind = i;
}
Q[ind] = 1;
Q.normalize();
Vec3f T = cross(Q, n).normalized();
Vec3f B = cross(n, T).normalized();
R.setCol(0, T);
R.setCol(1, B);
R.setCol(2, n);
float f = det(R);
return R;
}