GeometryPrimitives

This package provides a set of geometric primitive types (balls, cuboids, cylinders, and so on) and operations on them designed to enable piecewise definition of functions, especially for finite-difference and finite-element 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) K-D 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 normal-vector computation.

This package was inspired by the geometry utilities in Steven G. Johnson's [Libctl] (http://ab-initio.mit.edu/wiki/index.php/Libctl) package.