A computer-implemented method for reconstructing a 3D modeled object that represents a real object, as part of a 3D design process, the real object being a manufacturing product or a part, from a 3D mesh and measured data representative of the real object, the method comprising: • obtaining the measured data via one or more physical signal sensors based on a physical instance of the real object; • selecting the 3D mesh from a template library as an initial template mesh (V,E) being geometrically similar to the represented real object, wherein the initial template satisfies a predetermined 3D distance with respect to the measured data; • providing a set of deformation modes, a deformation mode being a parameterized deformation function of the 3D mesh, a parameterized deformation function of the 3D mesh being a set of functions that take the 3D mesh as input and output a deformed version of the input depending on values of respective parameters, the values of the respective parameters each varying in a respective continuum, the set of deformation modes comprising a subset representative of geometrical modes that includes the rigid mode and the 3D scaling mode, the set of deformation modes further comprising a subset representative of at least one physics mode; • determining a composition (( f ( θ, V)) of the deformation modes, the composition being a deformed version of the input depending on the respective parameters ( θ) which optimizes a program that explores deformation modes and/or values of variable parameters of deformation modes, the program including an energy term, for instance e ( θ) = Σ x, y max [[ F ( x, y) - π ( f ( θ, V))( x, y)] 2, th], that rewards a geometrical fit between the 3D mesh (V,E) as deformed by the composition ( f ( θ, V)) and the measured data, the program further including a term μφ ( θ) with φ ( θ) = ∑ i = 1 p α i s A + ∑ i = 0 3 1 d + 1 ∑ j = 0 d ‖ δ i, j s D ‖ 2, where s = max(|inf J |, |sup J |) is a function re-scaling each parameter between [-1, 1] and coefficients α i are the coefficients of the at least one physics mode that further rewards sparsity of the deformation modes involved in the determined composition by minimizing the coefficients α i of the at least one physics mode, the term ∑ i = 0 3 1 d + 1 ∑ j = 0 d ‖ δ i, j s D ‖ 2 being a term intervening if geometrical modes different from the rigid mode and 3D scaling mode are present in the subset; and • applying the composition to the 3D mesh. • obtaining the measured data via one or more physical signal sensors based on a physical instance of the real object; • selecting the 3D mesh from a template library as an initial template mesh (V,E) being geometrically similar to the represented real object, wherein the initial template satisfies a predetermined 3D distance with respect to the measured data; • providing a set of deformation modes, a deformation mode being a parameterized deformation function of the 3D mesh, a parameterized deformation function of the 3D mesh being a set of functions that take the 3D mesh as input and output a deformed version of the input depending on values of respective parameters, the values of the respective parameters each varying in a respective continuum, the set of deformation modes comprising a subset representative of geometrical modes that includes the rigid mode and the 3D scaling mode, the set of deformation modes further comprising a subset representative of at least one physics mode; • determining a composition (( f ( θ, V)) of the deformation modes, the composition being a deformed version of the input depending on the respective parameters ( θ) which optimizes a program that explores deformation modes and/or values of variable parameters of deformation modes, the program including an energy term, for instance e ( θ) = Σ x, y max [[ F ( x, y) - π ( f ( θ, V))( x, y)] 2, th], that rewards a geometrical fit between the 3D mesh (V,E) as deformed by the composition ( f ( θ, V)) and the measured data, the program further including a term μφ ( θ) with φ ( θ) = ∑ i = 1 p α i s A + ∑ i = 0 3 1 d + 1 ∑ j = 0 d ‖ δ i, j s D ‖ 2, where s = max(|inf J |, |sup J |) is a function re-scaling each parameter between [-1, 1] and coefficients α i are the coefficients of the at least one physics mode that further rewards sparsity of the deformation modes involved in the determined composition by minimizing the coefficients α i of the at least one physics mode, the term ∑ i = 0 3 1 d + 1 ∑ j = 0 d ‖ δ i, j s D ‖ 2 being a term intervening if geometrical modes different from the rigid mode and 3D scaling mode are present in the subset; and • applying the composition to the 3D mesh.