Surface Reconstruction via Interpolating Boundary Curves and Cross-Boundary Derivatives Simultaneously Approximating Inner Points

Abstract

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given boundary curves and the cross-boundary derivatives meanwhile approximates some given inner points. The main idea of our method is: first, we construct an initial surface which interpolates the four given boundary curves and the cross-boundary derivatives on them with minimizing the energy; then, while keeping the boundary control points of the initial surface unchanged, we reposition the inner control points of the surface such that it approximates the inner points with optimization. Examples show that our algorithm is practicable and effective.