Univalency conditions for the control point form method (Q1272807)

The control point form is an algebraic method to generate computational grids on domains with complex geometry. Using certain \(C^0\) and \(C^1\) interpolation functions a transformation from the computational domain into the physical domain can be defined to construct conforming boundary grids and being able to manipulate the grid through a sparse net of control points. In the paper necessary and sufficient conditions for the invertibility of these transformations are studied.