I am trying to find the point that is closest to a group of vectors. For context, the vectors are inverted rays emitted from center of aperture stop after exiting a lens, this convergence is meant to locate the entrance pupil. The backward projection of the exiting rays, while not converging at one single point due to spherical aberration, is quite close to converging toward a point, as illustrated in the figure below. (For easier simulation the positive z is pointing down) I believe that to find the closest point, I would be finding a point that has the shortest distance to all these lines. And wrote the method as follow: def FindConvergingPoint(position, direction): A = np.eye(3) * len(direction) - np.dot(direction.T, direction) b = np.sum(position - np.dot(direction, np.dot(direction.T, position)), axis=0) return np.linalg.pinv(A).dot(b) For the figure above and judging visually, I would have expected the point to be something around [0, 0, 20] However, this is not the case. The method yielded a result of [ 0., 188.60107764, 241.13690715], which is far from the converging point I was expecting. Is my algorithm faulty or have I missed something about python/numpy? Attached are the data for the vectors: position = np.array([ [0, 0, 0], [0, -1.62, 0.0314], [0, -3.24, 0.1262], [0, -4.88, 0.2859], [0, -6.53, 0.5136], [0, -8.21, 0.8135], [0, -9.91, 1.1913], [0, -11.64, 1.6551], [0, -13.43, 2.2166], [0, -15.28, 2.8944], [0, -17.26, 3.7289] ]) direction = np.array([ [0, 0, 1], [0, 0.0754, 0.9972], [0, 0.1507, 0.9886], [0, 0.2258, 0.9742], [0, 0.3006, 0.9537], [0, 0.3752, 0.9269], [0, 0.4494, 0.8933], [0, 0.5233, 0.8521], [0, 0.5969, 0.8023], [0, 0.6707, 0.7417], [0, 0.7459, 0.6661] ]) Continue reading...
