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Alignment of two sets of points on the 2D plane
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| def pointAlignment(ref, move): | |
| """ | |
| Mahd Sadjadi (2017) | |
| This is a function which takes two sets of | |
| points each with N points (both inputs are assumd to be | |
| numpy arrays of N*2 shape). The first input is | |
| the reference grid and the second is the point set to | |
| be aligned with the reference. | |
| This function shifts and rotate points to | |
| make the two sets aligned and returns the | |
| result (with the shape N*2). | |
| """ | |
| N = ref.shape[0] # number of atoms | |
| IM = np.ones(N) #array of ones | |
| XG,YG,ZG = ref.T # ref coordinates | |
| XM,YM,ZM = move.T # move coordinates | |
| XGA,YGA,ZGA = np.mean(ref,axis=0) # center of mass | |
| XMA,YMA,ZMA = np.mean(move,axis=0) # center of mass | |
| XGS = XG - XGA * IM # std xg | |
| YGS = YG - YGA * IM # std yg | |
| XMS = XM - XMA * IM | |
| YMS = YM - YMA * IM | |
| A = np.sum(XGS * XMS + YGS * YMS)/N | |
| B = np.sum(XGS * YMS - YGS * XMS)/N | |
| R = np.sqrt(A**2 + B**2) | |
| sin = B/R | |
| cos = A/R | |
| a = XGA * cos - YGA * sin - XMA | |
| b = XGA * sin + YGA * cos - YMA | |
| theta = np.arctan(B/A) | |
| deltax = (a * cos + b * sin)*IM - (1-cos)*XM + sin*YM | |
| deltay = (-a * sin + b * cos)*IM - sin*XM -(1-cos)*YM | |
| results = np.column_stack((XM+deltax,YM+deltay,ZM)) | |
| return results |
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