Question: Problem 3 (30 pts) Consider the case in an image that you have extracted the homogenous coordinates of a pair of points p1 , p2

Problem 3 (30 pts) Consider the case in an image that you have extracted the homogenous coordinates of a pair of points p1 , p2 as well as a second pair of points q1, q2; these four points are in the image plane. Their counterparts in the world, P1, P2, Q1, Q2 are coplanar. Furthermore, the line formed by P1 and P2 is parallel to the line formed by Q1 and Q2. The line formed by p1 and p2 may or may not be parallel to the line formed ql and (12 (this does not change the question at all). Also note that you do not have the coordinates of the world points P1, P2, Q1 , Q2. 3a. (15 pts) Derive a closed form equation for the vanishing point induced by these two parallel lines. 3b. (15 pts) Suppose you have also extracted the homogenous coordinates of another point 113, whose counterpart in the world is P3. You also know that P1, P2, P3 are colinear and that the 3D distance between P1 and P2 is D. Derive a closed form equation for the 3D distance between P1 and P3

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