codac2_Slice_polygon.h

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namespace codac2
{
  template<typename T>
  ConvexPolygon Slice<T>::polygon_slice(const Slice<T>& v) const
    requires std::is_same_v<T,Interval>
  {
    const Interval& t = t0_tf();
 
    ConvexPolygon p(IntervalVector({t,codomain()
       & Interval(next_float(-oo),prev_float(oo)) // todo: remove this
     }));
 
    if(v.codomain().is_unbounded())
      return p;
 
    ConvexPolygon p_fwd(std::vector<Vector>({
      {t.ub(), (input_gate().ub()+Interval(t.diam())*v.codomain().ub()).ub()},
      {t.ub(), (input_gate().lb()+Interval(t.diam())*v.codomain().lb()).lb()},
      {t.lb(), input_gate().lb()},
      {t.lb(), input_gate().ub()}
    }), false); // false: avoid costly computation of convex hull (vertices are already ordered)
 
    ConvexPolygon p_bwd(std::vector<Vector>({
      {t.lb(), (output_gate().ub()-Interval(t.diam())*v.codomain().lb()).ub()},
      {t.lb(), (output_gate().lb()-Interval(t.diam())*v.codomain().ub()).lb()},
      {t.ub(), output_gate().lb()},
      {t.ub(), output_gate().ub()}
    }), false); // false: avoid costly computation of convex hull (vertices are already ordered)
 
    return p & p_fwd & p_bwd;
  }
}