Question

I have a parallelepiped volume data defined by three vector:

a 2.468000 0.000000 0.000000

b -1.234000 2.137351 0.000000

c 0.000000 0.000000 32.000000

my grid is described by 40 40 500 points, respectively for the axes a,b,c. As you can see the three vectors are not mutually orthogonal and this causes a lot of problems for the reading of the grid.

My original plan was to read my raw data and then to extract several volumetric slices to be processed with sagemath to produce super nice pictures. Regrettably I looked in the python documentation for something like that and I found several command that can be used for an orthogonal volume (ndgrid, easyviz.slice_) but none for not-mutually orthogonal volume data.

In the Scitools package and numpy I found the following command

Numpy provides:

• mgrid
• ogrid
• meshgrid

Scitools provides:

• ndgrid
• boxgrid

then I was looking also among the matplotlib functions but they are so many that I simply gave up.

Is there some friendly programmer that can put me in the right way?

Answer 1

What exactly are you after?

You can easily create an array of shape (40, 40, 500, 3) where the item at position [a, b, c] is a 3 element array holding the x, y, z coordinates of the corresponding parallelepiped grid point as follows:

a = np.array([2.468000, 0.000000, 0.000000]).reshape(1, 1, 1, 3)
b = np.array([-1.234000, 2.137351, 0.000000]).reshape(1, 1, 1, 3)
c = np.array([0.000000, 0.000000, 32.000000]).reshape(1, 1, 1, 3)
A = np.linspace(0, 1, num=40).reshape(40, 1, 1, 1)
B = np.linspace(0, 1, num=40).reshape(1, 40, 1, 1)
C = np.linspace(0, 1, num=500).reshape(1, 1, 500, 1)
grid = a * A + b * B + c * C