Julia package for calculating the fractions of a box's volume divided by a plane


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When a plane runs across a 3-dimensional box, it divides the box into two pieces. This Julia package calculates how large these pieces are in terms of volume fraction with respect to the original box volume.


The only function BoxChopper exports is volfrac():

rvol = volfrac(box, nout, r₀)

Here, box = ((xn, xp), (yn, yp), (zn, zp)) is a 3-by-2 matrix that indicates the locations of the x-, y-, z-boundaries of the box. The box needs to be aligned with the Cartesian axes.

nout = (nx, ny, nz) and r₀ = (rx, ry, rz) are the normal vector of the plane and a point on the plane, respectively. nout does not have to be normalized, but its sign has significance: among the two half-spaces divided by the plane, the one in the nout side of the plane is considered "outside", and the one in the -nout side of the plane is considered "inside".

Now, among the two subpieces of the box divided by the plane, take the one in the "inside" portion of the space. The return value rvol is the fraction of this "inside" piece's volume with respect to the original box's volume. The volume fraction of the other piece is 1 - rvol. Both rvol and 1 - rvol are between 0.0 and 1.0, inclusive.

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