 The Holmes–Thompson area of the filling can be computed by the formula

where for each point formula_19, the set formula_20 is the dual unit ball of the norm formula_21 (the unit ball of the dual norm formula_22), and formula_23 is its usual area as a subset of formula_24.Choose a collection formula_25 of boundary points, listed in counterclockwise order.For each point formula_26, we define on "M" the scalar function formula_27.