https://github.com/stevengj/geometryprimitives.jl

geometric primitives for piecewise functions on grids
https://github.com/stevengj/geometryprimitives.jl

geometry julia math

Last synced: over 1 year ago
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geometric primitives for piecewise functions on grids

• Host: GitHub
• URL: https://github.com/stevengj/geometryprimitives.jl
• Owner: stevengj
• License: other
• Created: 2016-11-02T02:40:57.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2024-06-28T22:47:32.000Z (almost 2 years ago)
• Last Synced: 2025-02-24T09:48:32.990Z (over 1 year ago)
• Topics: geometry, julia, math
• Language: Julia
• Size: 186 KB
• Stars: 18
• Watchers: 6
• Forks: 8
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

          
# GeometryPrimitives

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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.