Sun model matrix

Question

I'm playing with sun implementation in my engine and I correctly built model matrix using below order of matrix operations:

1. Translate to camera position.
2. Calculate x and y axis of rotation matrix using cross product. Z axis is equal to sun direction.

However I'd like to use function which takes into account two unit vectors and based on them build rotation matrix (explanation here). When I replace 2nd step with function call the sun is in completely different position on the sky (but correctly oriented). As a input vectors I set direction vector and [0, 1, 0] vector.

Could someone provide a solution/hint/explanation of that topic?

Code

Working solution:

Matrix matrix; matrix.setPosition(ActiveCamera.getInversedMatrix().pos);

Vector xaxis = Cross(Vector(0,1,0), direction);
xaxis.normalize();

Vector yaxis = Cross(direction, xaxis);
yaxis.normalize();

matrix.x.x = xaxis.x;
matrix.y.x = yaxis.x;
matrix.z.x = direction.x;

matrix.x.y = xaxis.y;
matrix.y.y = yaxis.y;
matrix.z.y = direction.y;

matrix.x.z = xaxis.z;
matrix.y.z = yaxis.z;
matrix.z.z = direction.z;

Not working solution:

Matrix matrix; matrix.setPosition(ActiveCamera.getInversedMatrix().pos);
matrix.setRotation(Vector(0, 1, 0), direction);

Matrix3& Matrix3::setRotation(const Vector &u, const Vector &v) {
    Vector cross = Cross(u, v);
    float sin = cross.magnitude(); // sine of angle
    cross.normalize();
    float cos = Dot(u, v); // cosine of angle

    this->x.x = cross.x * cross.x * (1 - cos) + cos;
    this->x.y = cross.x * cross.y * (1 - cos) + sin * cross.z;
    this->x.z = cross.x * cross.z * (1 - cos) - sin * cross.y;

    this->y.x = cross.x * cross.y * (1 - cos) - sin * cross.z;
    this->y.y = cross.y * cross.y * (1 - cos) + cos;
    this->y.z = cross.y * cross.z * (1 - cos) + sin * cross.x;

    this->z.x = cross.x * cross.z * (1 - cos) + sin * cross.y;
    this->z.y = cross.y * cross.z * (1 - cos) - sin * cross.x;
    this->z.z = cross.z * cross.z * (1 - cos) + cos;

    return (*this);
}

Answer 1

The code was ok. Start direction depends on the sun quad coordinates. I changed it to [0, 0, 1] and I got expected result. I also moved the sun quad by its direction. Otherwise I was unable to scale it.