gistfile1.c

void generate_view_matrix(GLfloat *matrix, point *cam_pos, point *cam_dir)
{
    // http://www.opengl.org/sdk/docs/man2/xhtml/gluLookAt.xml
    // f = cam_dir, up = (0|1|0)
    // s = normalize(f X up)
    // u = s X f
    double x = cam_dir->x, y = cam_dir->y, z = cam_dir->z;
    double l = sqrt(z*z + x*x);
    double s_x = -z/l, s_z = x/l;
    double u_x = -s_z*y, u_y = s_z*x - s_x*z, u_z = s_x*y;
    // 4x4 matrix
    // 4th element is the translation
    // s[0]  s[1]  s[2]  x
    // u[0]  u[1]  u[2]  y
    // -f[0] -f[1] -f[2] z
    // 0     0     0     1

    matrix[0]  = s_x;
    matrix[1]  = u_x;
    matrix[2]  = -x;
    matrix[3]  = 0;

    matrix[4]  = 0;
    matrix[5]  = u_y;
    matrix[6]  = -y;
    matrix[7]  = 0;

    matrix[8]  = s_z;
    matrix[9]  = u_z;
    matrix[10] = -z;
    matrix[11] = 0;

    matrix[12] = cam_pos->x;
    matrix[13] = cam_pos->y;
    matrix[14] = cam_pos->z;
    matrix[15] = 1;
}

...

void turn_view(GLFWwindow* window, point *cam_dir)
{
    double mouse_x, mouse_y;
    glfwGetCursorPos(window, &mouse_x, &mouse_y);

    // Get the vector from the center of the screen to current mouse position and normalize it relative to screen size
    mouse_x = (mouse_x - WINDOW_WIDTH/2.0) * HORIZONTAL_TURNSPEED / WINDOW_WIDTH;
    mouse_y = (mouse_y - WINDOW_HEIGHT/2.0) * VERTICAL_TURNSPEED / WINDOW_HEIGHT;

    // Rotate the view vector in accordance
    double tmp;
    tmp = cam_dir->x;
    cam_dir->x += mouse_x * -cam_dir->z;
    cam_dir->y = sin(mouse_y + asin(cam_dir->y));
    cam_dir->z += mouse_x * tmp;

    normalize(cam_dir);
}

...

layout(location = 0) in vec4 vertex_position;
uniform mat4 projection_matrix;
uniform mat4 view_matrix;

void main()
{
    gl_Position = view_matrix * projection_matrix * vertex_position;
}