function CON = transform(CON,T,v)% Apply affine transformation Tx + v to a linear constraint object, where% T is an n by n matrix and v is a constant vector%% Syntax:%   "C = transform(con,T,v)"%% Description:%   "transform(con,T,v)" returns a linear constraint object representing%   the constraint set "con" with respect to the transformed variable%   "y = Tx + v". %% Examples:%   Given the linear constraint object "con" representing a cube with%   corners at (x1,x2,x3) triples (2,1,0), (2,1,2), (2,3,0), (2,3,2),%   (4,3,0), (4,3,2), (4,1,0), and (4,1,2),%%%%     "T = [0.5 0 0;0 0.25 0;0 0 1]; v = [0 0 2]';"%%     "C = transform(con,T,v)"%%%%   returns "C", a linear constraint object representing the cube with%   corners at (x1,x2,x3) triples (1,0.25,2), (1,0.25,4), (1,0.75,2),%   (1,0.75,4), (2,0.75,2), (2,0.75,4), (2,0.25,2), and (2,0.25,4).%% See Also:%   linearcon,vertices,transform% Test whether T has full rang. In this case we transform the % hyperplanes, otherwise the vertices.if rank(T)==size(T,2)    CE = CON.CE; dE = CON.dE;    CI = CON.CI; dI = CON.dI;    [CE,dE] = transform_hyperplanes(CE,dE,T,v);    [CI,dI] = transform_hyperplanes(CI,dI,T,v);    CON = linearcon(CE,dE,CI,dI);else    vert=vertices(CON);    for i=1:length(vert)        Tvert(:,i)=T*vert(i)+v;    end;    CON =linearcon(polyhedron(Tvert));end;returnfunction [C,d] = transform_hyperplanes(C,d,T,v)Ti = inv(T);for k = 1:size(C,1)  % update the normal vector and the constant for the  % hyperplane representing each face  ck = C(k,:)*Ti;  dk = d(k) + ck*v;  norm_ck = sqrt(ck*ck');  C(k,:) = ck/norm_ck;  d(k) = dk/norm_ck;end % for kreturn