Free Form Deformation

• Given
• - \(g_{ijk}\): position of the grid coordinates
• - \(p_m=(x_m,y_m,z_m)\in[0,1]^3\): Initial vertex coordinates (expressed with respect to the grid)

• \(\Rightarrow \displaystyle q_m = \sum_i \sum_j \sum_k b_i(x_m)\, b_j(y_m)\, b_k(z_m)\; g_{ijk}\)

• Note:
• • \(w_{m\,ijk} = b_i(x_m) b_j(y_m) b_k(z_m)\)
  • is a scalar weights independant of the deformation
  • \(\rightarrow\) can be precomputed

• • \(\Rightarrow \displaystyle q_m = \sum_{ijk} w_{m\,ijk}\; g_{ijk}\)