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Definition of curvature 1 : the act of curving : the state of being curved. 2 : a measure or amount of curving specifically : the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius.
How Do You Measure Curvature of a path? The curvature(K) of a path is measured using the radius of the curvature of the path at the given point. If y = f(x) is a curve at a particular point, then the formula for curvature is given as K = 1/R.
I am measuring x,y coordinates (in cm) of an object with a special camera in fixed time intervals of 1s. I have the data in a numpy array:
a = np.array([ [ 0. , 0. ],[ 0.3 , 0. ],[ 1.25, -0.1 ],[ 2.1 , -0.9 ],[ 2.85, -2.3 ],[ 3.8 , -3.95],[ 5. , -5.75],[ 6.4 , -7.8 ],[ 8.05, -9.9 ],[ 9.9 , -11.6 ],[ 12.05, -12.85],[ 14.25, -13.7 ],[ 16.5 , -13.8 ],[ 19.25, -13.35],[ 21.3 , -12.2 ],[ 22.8 , -10.5 ],[ 23.55, -8.15],[ 22.95, -6.1 ],[ 21.35, -3.95],[ 19.1 , -1.9 ]]) And the curve looks like this:
plt.scatter(a[:,0], a[:,1]) 
Question:
How can I calculate the tangential and the radial aceleration vectors at each point? I found some formulas that might be relevant:
I am able to easily calculate the vx and the vy projections with np.diff(a, axis=0) but I am a numpy/python noob and it is way over my head to continue. If I could calculate the curvature at each point, also my problem would be solved. Can somebody help?
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