GeometryPrimitives
This package provides a set of geometric primitive types (spheres, boxes, cylinders, and so on) and operations on them designed to enable piecewise definition of functions, especially for finitedifference and finiteelement simulations, in the Julia language.
For example, suppose that you are discretizing a PDE like the Poisson
equation ∇⋅c∇u = f, and you want to provide a simple user interface
for the user to specify the function c(x)
. In many applications,
c
will be piecewise constant, and you want to be able to specify
c = 1
in one box, c = 2
in some cylinders, etcetera. The
GeometryPrimitives package allows the user to provide a list of
shapes with associated data (in this case, the value of c
) to
define such a c(x)
.
Furthermore, the application to discretized simulations imposes a couple of additional requirements:

One needs to be able to evaluate
c(x)
a huge number of times (once for every point on a grid). So, we provide a fast O(log n) KD tree data structure for rapid searching of shapes. 
Often, one wants to compute the average of
c(x)
over a voxel, so we provide routines for rapid approximate voxel averages. 
Often, one needs not only the value
c(x)
but the normal vector to the nearest shape, so we provide normalvector computation.
This package was inspired by the geometry utilities in my Libctl package.