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March 14, 2018 11:12
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Convert between different ways of describing a camera
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| import numpy as np | |
| from scipy.linalg import rq | |
| def getKRC(P): | |
| # https://ksimek.github.io/2012/08/14/decompose/ | |
| # P = [M|-MC] | |
| M = P[:,:3] | |
| # camera position | |
| C = -np.linalg.inv(M).dot(P[:,3]) | |
| # intrinsic matix and extrinsic (rotaition) matrix | |
| K, R = rq(M) # this decomposition is not unique so we make diagonal elements (focal lengths) positive | |
| sign = np.diag(np.sign(np.diag(K))) | |
| K = K.dot(sign) | |
| R = sign.dot(R) | |
| return K, R, C | |
| # todo | |
| #def changeCooordinateSystem(A, transition=T): | |
| def projectionToLookAt(P): | |
| # conversion to a different coordinate system | |
| # todo: extract it from here | |
| t = np.array([[1.0, 0, 0, 0], [0, -1.0, 0, 0], [0, 0, -1.0, 0], [0, 0, 0, 1]]) | |
| P = P.dot(t) | |
| K, R, C = getKRC(P) | |
| # position is the camera position in world coordinates | |
| position = C.T | |
| # look_at is the object camera looks at | |
| direction = np.array([0, 0, -1.0]).T | |
| direction = R.dot(direction) | |
| look_at = position + direction | |
| # up is just up | |
| up = np.array([0.0, 1.0, 0.0]) | |
| # fov = 2 arctan (x / (2 f)) | |
| # note here K[0,2] is already x/2 | |
| fov = np.rad2deg(2 * np.arctan2(K[0,2], K[0,0])) | |
| return position, look_at, up, fov |
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