Shape reconstruction from a normal map in terms of uniform bi-quadratic B-spline surfaces

This paper studies the recovery of the height field function of an object from its surface normal vectors in terms of uniform bi-quadratic B-spline surfaces. The study is motivated by two modern technological needs namely, the recovery of the height field function of an object from its surface normal vectors obtained by photometric stereo techniques, and the introduction of new design methodology of streamlined aesthetic surfaces through the direct editing of normal vectors. Our mathematical formulation for explicit surface reconstruction is based on differential geometry and geometric modeling techniques. Complex examples are provided to demonstrate the effectiveness of the proposed method.