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


Using npm, type the following command into your shell:

npm install polytope-closest-point


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")(

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.


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

Other dimensions, (c) 2013 Mikola Lysenko

BOOST License.