Bugs in Lesson 6 code, function lookat

[sihan-chen-yes]

https://github.com/ssloy/tinyrenderer/blob/f037c7a0517a632c7391b35131f9746a8f8bb235/our_gl.cpp

void lookat(Vec3f eye, Vec3f center, Vec3f up) {
    Vec3f z = (eye-center).normalize();
    Vec3f x = cross(up,z).normalize();
    Vec3f y = cross(z,x).normalize();
    ModelView = Matrix::identity();
    for (int i=0; i<3; i++) {
        ModelView[0][i] = x[i];
        ModelView[1][i] = y[i];
        ModelView[2][i] = z[i];
        ModelView[i][3] = -center[i];
    }
}

From the formula we derived, ModelView transformation matrix should be (R.T|-R.T x T) = (M_inv|0) x (Identity|-Tr).
But here the translation is not combined with rotation part.

Should be like this:

void lookat(Vec3f eye, Vec3f center, Vec3f up) {
    // find camera local basis to build rotation matrix
    Vec3f z = (eye - center).normalize();
    // up and z share the same plane
    Vec3f x = (up ^ z).normalize();
    // up and y not necessarily aligned
    Vec3f y = (z ^ x).normalize();
    // build transformation matrix
    // M_inv = M.T
    // R|T inv ==> R.T|-R.T T
    Matrix M_inv = Matrix::identity(4);
    Matrix Tr = Matrix::identity(4);
    for (int i = 0; i < 3; ++i) {
        M_inv[0][i] = x[i];
        M_inv[1][i] = y[i];
        M_inv[2][i] = z[i];
        Tr[i][3] = -center[i];
    }
    ModelView = M_inv * Tr;
}