Convex preserving scattered data interpolation using bivariate \(C^1\) cubic splines
The author uses a bivariate \(C^1\) cubic spline space over a triangulated quadrangulation to the convexity preserving surface design problem. This interpolation problem expressed in terms of Bernstein-Bézier polynomials is presented as a quadratically constraint quadratic programming problem. Then the author derives three linearly constraint quadratic programming problems to solve the interpolatory convexity preserving problem. He shows the existence of convexity preserving interpolatory surface under certain conditions on the data.
scientific article; zbMATH DE number 1491260