def _get_change_basis_xform(center, up, normal):
"""Return a matrix that changes from the given basis to the x-y-z
basis. Basically, this 'straightens' out the plane described by
the basis. The 'right' axis is calculated from the up and normal."""
normal = normal.normalized()
right = up.cross(normal).normalize()
up = normal.cross(right).normalize()
xform = Mat4.new_translate(*center)
xform *= Mat4.new_change_basis(right, up, normal, center).inverse()
return xform
def _get_camera_xform(image):
"""Return the xform that maps world coordinates to image
coordinates. Uses the Iphone's lens characteristics."""
film_size = 6.35 # Iphone sensor size, in mm
focal_length = 3.85 # Iphone focal length, in mm
width, height = image.size
aspect = float(width) / height
fov_y = 2 * math.atan2(film_size/aspect, 2 * focal_length)
xform = Mat4.new_translate(width/2.0, height/2.0, 0)
xform.scale(-width/2.0, -height/2.0, 1)
xform *= Mat4.new_perspective(fov_y, aspect, 1, 10)
return xform
