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The Convex Geometry toolbox
The Convex Geometry toolbox is a Matlab toolbox designed to provide useful tools in Convex Geometry optimization. This toolbox is based on the very efficient "qhull" library developped by the The Geometry Center of Minneapolis.
1) Installation
You first have to install and compile the sources of the C "qhull" library which can be freely downloaded at the following adress :The toolbox can be downloaded here.
2) Compilation
You just have to check the adress of the library in the >compil_mexfile.m and run the mex instructions.3) Two examples
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Example of bigest balls inscribed in a given polytop
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Example
of steiner
symetrization
4) Details of the functions of the Convex Geometry toolbox
- compil_mexfile.m :
Compile the mex files of the toolbox.
- compute_normals.m : Computes the normal vectors of the convex polytop defined as the hull of the input points.
- dodec.m : Computes the normal vectors of a dodecahedron.
- edges_matlab.m : Computes the edges of the convex polytop defined as the hull of the input points.
- inscribe_ball.m : Computes the center and the radius of the largest ball inscribed in a convex polytop defined by its vertices (one of linear solvers linprog.m or cddmex.m is needed).
- minkowski_sum.m : Computes the Minkowski's sum of two convex bodies (in dimension 2 or 3) described as the convex hull of points.
- minkow_thickness.m : Computes the thickness of a convex polytop in prescribed directions.
- polytope_H2V.m : This function computes the V-representation of a polytop (i.e. its extrem points) given by P = {x, Hx<=K} (i.e. its H-representation).
- polytope_V2H.m : This function computes the H-representation of a polytop given by its extrem points.
- projection_hyperplan.m : This function project a set of points on an hyperplan discribed by one point and one normal direction.
- steiner_symetrization.m : This function compute the Steiner symetrization of a convex polytop defined by its extremal points (in dimension 2 or 3) whith respect to the plan or the line discribed by a point and a normal direction.
- tetra.m : Computes the normal vectors of a regular tetrahedron.
- test_inscribe.m : An example function of the use of the inscribe_ball.m function.
- test_steiner.m : An example function of the use of the steiner_symetrization.m function.
- test_minkowsum.m : An example function of the use of the minkowski_sum.m function.