Contents of the Geometric Bounding Toolbox Verson 7.0

Routines for polytope creation

convh computes convex hull of points

fconvh computes the intersection of a set of half-spaces

defbox generates an axis aligned box

defpipe defines parallelepiped

defsimp defines a regular centred simplex with edge size 1

ellapprx computes a polytope approximation to given ellipsoid

Characteristics of polytopes

dim computes dimension of polytope

ranges computes lower and upper corners of tight axis aligned box to polytope

diameter computes diameter

dirext computes extremal points in given direction

maxface computes vector of maximum no. faces

maxvert computes vector of maximum no. vertices

polcent computes centre of polytope

polvol computes the volume of polytope

surfarea computes the surface area of polytope

Polytope operations

intersct computes the intersection of two polytopes

ltran performs affin transformation on polytope

poladd computes the sum of two polytopes

poldual computes the dual of polytope

mindim minimises dimension of representation

subtract computes Minkowski difference of two polytopes

Extracting features from polytopes

faces extracts half-space inequalities of polytope

facet computes polytope of facet in lower dimension

fv produces facet-vertex Boolean table of adjacency

vvf produces a vertex-vertex and vertex-facet adjacency tables

fvfitacc extracts maximum fitting error of vertices and facets

planeigh lists neighbouring facet planes

Interaction of polytopes with points and half-spaces

p\underline{ conv computes point inclusion into convex hull

intest tests whether set of points is in polytope

intpoints finds an internal point within polytope

projpont projects point onto polytope

update computes the intersection of half-space and polytope

Polytope graphics

view2d displays 2D wire-frame projections of polytope on pairs of axes

view3d displays 3D view of 3D polytope \pagebreak

Ellipsoid creation

defell defines an ellipsoid

sel finds minimal volume ellipsoid around set of points

Ellipsoid operations

elladd computes an outer bounding ellipsoid to the sum of two ellipsoids

elladde computes outer bounding ellipsoid-variant to the sum of two ellipsoids

elladdi computes inner bounding ellipsoid to the sum of two ellipsoids

elldife computes an outer bounding ellipsoid to the difference of two ellipsoids

elldifi computes an inner bounding ellipsoid to the difference of two ellipsoids

ellint computes an ellipsoid around the intersection of two ellipoids

ellproj computes the projection of an ellipsoid onto a linear subspace

sphsep computes the joining surface area of spheres

Ellipsoid graphics

view3del displays 3D view of a 3D ellipsoid

view2del displays 2D views of ellipsoids of any dimensions greater than 2

Characteristics of ellipsoids

ellrange computes the width (range) of ellipsoid in each dimension

ellvolum calculates the volume of ellipsoid

ellcent extracts the centre of ellipsoid

ellicov extracts the matrix of an ellipsoid

inell tests whether given point is in ellipsoid

mcvol estimates the volume of the intersection of ellipsoids

Point and vector set operations

dif computes set difference of vector sets

dirgen generates approximately uniform set of direction vectors

dualpon computes set of half-spaces "normal" to set of vectors

uni computes the union of two point sets

vreduce eliminates multiple points from array of points

Routines for compatibility with GBT 6.1

bounded tests whether a polyhedron is bounded

gbt627 converts from GBT 6.1 formats to GBT 7.0 format

gbt726 converts GBT 7 format to type 4 GBT 6 format