在3D numpy网格中绘制/采样球体 [英] Drawing/sampling a sphere in a 3D numpy grid

问题描述

我想对基于体素的球体进行测量，用一个numpy数组表示。由于采样，这些球体被表示为一组立方体（因为它们在数组中被采样）。我想通过这个网格限制来模拟引入的错误。有没有什么办法在网格中绘制3D球体来运行我的模拟？ （所以基本上，一个单位长度为1的球体将会是数组中的一个点）。

或者还有另一种计算采样引入的误差的方法吗？

在2-D中看起来很简单...

解决方案

最直接的方法是创建一个边界框数组，在每个点处保持距离该球体：

 >>> radius = 3 
>>> r2 = np.arange（-radius，radius + 1）** 2 
>>> dist2 = r2 [:,无，无] + r2 [：，无] + r2 
>>> volume = np.sum（dist2 <=半径** 2）
>>>数量
 123 
  

二维情况更易于直观化：

 >>> dist2 = r2 [:,无] + r2 
>>> （dist2 <=半径** 2）.astype（np.int）
数组（[[0,0,0,1,0,0,0]，
 [0,1,1 ，1,1,1,0]，
 [0,1,1,1,1,1,0]，
 [1,1,1,1,1,1,1]， 
 [0,1,1,1,1,1,0]，
 [0,1,1,1,1,0,0]，
 [0,0,0 ，1,0,0,0]]）
>>> np.sum（dist2 <=半径** 2）
 29 
  

I want to do a voxel-based measurement of spherical objects, represented in a numpy array. Because of the sampling, these spheres are represented as a group of cubes (because they are sampled in the array). I want to do a simulation of the introduced error by this grid-restriction. Is there any way to paint a 3D sphere in a numpy grid to run my simulations on? (So basically, a sphere of unit length one, would be one point in the array)

Or is there another way of calculating the error introduced by sampling?

In 2-D that seems to be easy...

解决方案

The most direct approach is to create a bounding box array, holding at each point the distance to the center of the sphere:

>>> radius = 3
>>> r2 = np.arange(-radius, radius+1)**2
>>> dist2 = r2[:, None, None] + r2[:, None] + r2
>>> volume = np.sum(dist2 <= radius**2)
>>> volume
123

The 2D case is easier to visualize:

>>> dist2 = r2[:, None] + r2
>>> (dist2 <= radius**2).astype(np.int)
array([[0, 0, 0, 1, 0, 0, 0],
       [0, 1, 1, 1, 1, 1, 0],
       [0, 1, 1, 1, 1, 1, 0],
       [1, 1, 1, 1, 1, 1, 1],
       [0, 1, 1, 1, 1, 1, 0],
       [0, 1, 1, 1, 1, 1, 0],
       [0, 0, 0, 1, 0, 0, 0]])
>>> np.sum(dist2 <= radius**2)
29

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