# polytope-closest-point

Computes the closest point in a convex polytope to a given point.

# Install

Using npm, type the following command into your shell:

```
npm install polytope-closest-point
```

# Usage

Here is an example of how to find the closest point to a triangle in a mesh:

```
var mesh = require("bunny");
var result = new Array(3);
var sqr_distance = require("polytope-closest-point")(
mesh.cells[0],
mesh.positions,
[0,0,0],
result);
```

Which computes the closest point in the first facet of the mesh to the point `[0,0,0]`

, storing the resulting point in `result`

and the squared distance in `sqr_distance`

.

For more examples, see test/simple.js.

`require("polytope-closest-point")(cell, positions, x[, result])`

Computes the closest point in a polytope to `x`

, storing the result in `result`

.

`cell`

is a list of indices into a positions representing the vertices of the polytope.`positions`

is an array of tuples representing the vertices of the polytope`x`

is the point we are querying against`result`

(optional) is the array to store the closest point in.

Returns a float representing the squared Euclidean distance from x to the polytope. If no such point can be found, it returns Number.NaN

Notes: For polytopes with fewer than 4 vertices, the code uses hand optimized routines derived from WildMagick. For higher dimensions, it falls back to a general purpose quadratic programming solver that is ported from somewhat slower R/FORTRAN codes. If you are planning on using this code to do distance queries on meshed surfaces, it is recommend you triangulate all your polygons first.

# Credits

Triangle/tetrahedra closest point code derived from WildMagick (c) David Eberly 1998-2012.

Other dimensions, (c) 2013 Mikola Lysenko

BOOST License.