

In [1]:

    
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

Analyse the impact of the ball radius on the gauge angle

The tangential surface of a discrete sphere can be considered to be flat if the span between chord and surface is less than 0.5 pixels. Using this constraint it is possible to calculate the cone angle of the gauge area.



In [8]:

    
def ballarc(h, R) :
    q=np.zeros(len(R))
    L=np.zeros(len(R))
    
    for i in np.arange(0,len(R)):
        r=R[i];
        q[i]=0.5*np.arcsin(np.sqrt(2*h*r-h**2)/r)
        L[i]=2*np.sqrt(2*r*h-h**2)
        
    return (q,L)



In [13]:

    
R=np.arange(1,200)
(q,L)=ballarc(0.5,R)
plt.subplot(1,2,1)
plt.plot(R,q*180/np.pi)
plt.title('Gauge cone angle')
plt.subplot(1,2,2)
plt.plot(R,L)
plt.title('Width of the chord')









    Out[13]:





<matplotlib.text.Text at 0x10ebc0668>



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