# compare new SimpleHull with legacy hull methods

symbolic m,n;

r1 := {[i,j]: i>=0 && j>=0 && i+j<=1};
r2 := {[i,j]: j>=0 && i<=1 && j<=i};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1 := {[i]:i<=n && n>=7};
r2 := {[i]:i<=n-2 && n>=6};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1 := {[i,j]:0<=i,j<=2};
r2 := {[i,j]:0<=i && 1<=j && i+j<=4};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1 := {[i,j]: 1<=i<=n && j=0};
r2 := {[i,j]: 2<=i<=n+1 && j=1};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1 := {[i,j,k]: 1<=i<=n && j=0 && k=17i};
r2 := {[i,j,k]: 2<=i<=n+5 && j=1 && k=17i+10};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1:={[x,y]:y<=x && y>=0 && y<=2-x};
r2:={[x,y]:y>=0 && x<=2 && 2y<=x};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1 := {[i,j]: 0<=i<=1000 && 500<=j<=600};
r2 := {[i,j]: 500<=i<=600 && 0<=j<=1000};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1:= {[t1,t2,t3,t4,t5] : 1+t4 = t3 && 32t1+1 <= t3 <= 499, 32t1+32 && 16t2+1 <= t5 <= 499, 16t2+16 && 0 <= t1 && 0 <= t2};
r2:= {[t1,t2,t3,t4,t5] : t4 = t3 && 16t2 <= t5 <= 498, 16t2+15 && 32t1+1 <= t3 <= 499, 32t1+32 && 0 <= t1 && 0 <= t2 };

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r1:={[i]:i<=n && n<=100 && i>=m-10};
r2:={[i]:i<=2n && n<=200 && i>=m};

ConvexHull (r1 union r2);
DecoupledConvexHull (r1 union r2);
RectHull (r1 union r2);
SimpleHull (r1 union r2);
QuickHull (r1 union r2);
Hull (r1 union r2);

r:= {[1,1]} union {[2,2]} union {[3,3]} union {[4,4]};

ConvexHull r;
DecoupledConvexHull r;
RectHull r;
SimpleHull r;
QuickHull r;
Hull r;