Finding all midpoint values on numpy meshgrid [duplicate]

Question

I have a numpy meshgrid that outlines boxes on my image. I want to find the midpoint of each "box" and plot a point. I am doing that manually like this:

xg = np.linspace(0, (x1 - x0), inputx + 1)
yg = np.linspace(0, (y2 - y1), inputy + 1)
xgr, ygr = np.meshgrid(xg, yg)

xpnt, ypnt = ((xgr[1][1] - xgr[0][0]) // 2 + xgr[0][0], (ygr[1][1] - ygr[0][0]) // 2 + ygr[0][0])
circle = plt.Circle((xpnt, ypnt), 5, color='r')
a.add_patch(circle)

This would require me to go through each point and make x,y values for each midpoint. Is there a faster way to do this? I will show the image output of just the one midpoint circle.

You could make a new meshgrid with x that starts at xpt, and has input values, etc. Or ((xgr[1][,1] - xgr[0,0]) // 2 + xgr[0,0] can be generalized to xgr[1:,1:] - xgr[:-1,:-1]//2 + xgr[:-1,:-1] — hpaulj
– hpaulj, Commented Apr 21, 2023 at 1:43

hpaulj · Accepted Answer · 2023-04-21 02:31:59Z

Make a mesh same size as yours, but with simpler numbers:

In [1]: input = 5; 
In [2]: x1 = np.linspace(0,1,input+1)
In [3]: x1
Out[3]: array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
In [5]: I,J = np.meshgrid(x1,x1,indexing='ij')    
In [6]: I,J
Out[6]: 
(array([[0. , 0. , 0. , 0. , 0. , 0. ],
        [0.2, 0.2, 0.2, 0.2, 0.2, 0.2],
        [0.4, 0.4, 0.4, 0.4, 0.4, 0.4],
        [0.6, 0.6, 0.6, 0.6, 0.6, 0.6],
        [0.8, 0.8, 0.8, 0.8, 0.8, 0.8],
        [1. , 1. , 1. , 1. , 1. , 1. ]]),
 array([[0. , 0.2, 0.4, 0.6, 0.8, 1. ],
        [0. , 0.2, 0.4, 0.6, 0.8, 1. ],
        [0. , 0.2, 0.4, 0.6, 0.8, 1. ],
        [0. , 0.2, 0.4, 0.6, 0.8, 1. ],
        [0. , 0.2, 0.4, 0.6, 0.8, 1. ],
        [0. , 0.2, 0.4, 0.6, 0.8, 1. ]]))

We could make a new mesh with one less point in each direction:

In [7]: x2 = np.linspace(.1,.9,input)    
In [8]: x2
Out[8]: array([0.1, 0.3, 0.5, 0.7, 0.9])

In [10]: np.meshgrid(x2,x2,indexing='ij')
Out[10]: 
[array([[0.1, 0.1, 0.1, 0.1, 0.1],
        [0.3, 0.3, 0.3, 0.3, 0.3],
        [0.5, 0.5, 0.5, 0.5, 0.5],
        [0.7, 0.7, 0.7, 0.7, 0.7],
        [0.9, 0.9, 0.9, 0.9, 0.9]]),
 array([[0.1, 0.3, 0.5, 0.7, 0.9],
        [0.1, 0.3, 0.5, 0.7, 0.9],
        [0.1, 0.3, 0.5, 0.7, 0.9],
        [0.1, 0.3, 0.5, 0.7, 0.9],
        [0.1, 0.3, 0.5, 0.7, 0.9]])]

Alternatively we could average points in the original mesh:

In [11]: (I[1:,1:]+I[:-1,:-1])/2
Out[11]: 
array([[0.1, 0.1, 0.1, 0.1, 0.1],
       [0.3, 0.3, 0.3, 0.3, 0.3],
       [0.5, 0.5, 0.5, 0.5, 0.5],
       [0.7, 0.7, 0.7, 0.7, 0.7],
       [0.9, 0.9, 0.9, 0.9, 0.9]])

In [12]: (J[1:,1:]+J[:-1,:-1])/2
Out[12]: 
array([[0.1, 0.3, 0.5, 0.7, 0.9],
       [0.1, 0.3, 0.5, 0.7, 0.9],
       [0.1, 0.3, 0.5, 0.7, 0.9],
       [0.1, 0.3, 0.5, 0.7, 0.9],
       [0.1, 0.3, 0.5, 0.7, 0.9]])

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