lookAt that returns camera matrix instead of view matrix

Question

I can generate the camera matrix as follows:

void lookAt(vec3 center) {
    vec3 f = normalize(center - this->eye);
    vec3 u(0, 1, 0);
    vec3 r = normalize(cross(f, u));
    u = cross(r, f);
    this->cameraMatrix = inverse(mat4(
            r.x, u.x, -f.x, 0,
            r.y, u.y, -f.y, 0,
            r.z, u.z, -f.z, 0,
            -dot(r, this->eye), -dot(u, this->eye), dot(f, this->eye), 1
    ));
    // update MVP
}

I then update my MVP matrix, using V = inverse(this->cameraMatrix) . I want to store the camera matrix so I can do easy translations/rotations.

The above code works but isn't very efficient. I don't understand the maths enough, but I was hoping for a way to directly calculate the cameraMatrix , given f , u , r , this->eye .

Thanks

Answer 1

Given the camera position ( eye ), the camera target ( center ), and the up vector ( upVector ), the matrix that defines the position and orientation of the orientation can be calculated in a right-handed system where the x-axis is to the left, the y-axis is the up-vector, and the z-axis is points in the opposite direction of the line of sight, as follows:

glm::vec3 zAxis = glm::normalize(eye - center);
glm::vec3 xAxis = glm::normalize(glm::cross(upVector, zAxis));
glm::vec3 yAxis = glm::cross(zAxis, xAxis);
glm::mat4 cameraMatrix = glm::mat4(
    glm::vec4(xAxis, 0),
    glm::vec4(yAxis, 0),
    glm::vec4(zAxis, 0),
    glm::vec4(eye, 1.0f));

This is a matrix that transforms from view space to world space.