Vanishing points in rubiks cube

Question

Hi I'm trying to do the Ex 6.5 from Szeliski's book ... But I'm stuck at points 3 and 4, I have the theory of what a vanishing point is, but what does it mean to find it for each face? and how about the focal lenght and rotation angle for those VP? If you can provide some resources easy to understand I will appreciate it. Thanks!

Answer 1

Vanishing points are points at which parallel lines in a plane approach the same point. So in order to find the vanishing points you would take lines from the plane that are parallel (there are 6 of these per face on a Rubik's cube, 3 in 2 different directions) then where those lines intersect in the image is where a vanishing point is for that plane. You should be able to find 2 vanishing points per face unless you're looking at the cube head on.

You are bit mistaken in saying " the focal length and rotation angle for those VP", the book wants you to find these FROM the vanishing points. After you've found these vanishing points using the other points from the face you can construct a plane (in the coordinate system it would be a single vector normal to the plane). The rotation angle for this would be the difference between the image plane and the plane of the face.

Unfortunately I'm not well versed in finding focal lengths. But there should be a way of determining focal length of the camera by knowing the actual distance between the cubes. You could try reading this: http://www.cs.umd.edu/class/spring2013/cmsc426/lectures/camera-calibration.pdf from an image processing class I took.