Local tension methods for bivariate scattered data interpolation
Mathematical Methods for Curves and Surfaces
Algorithm 833: CSRFPACK---interpolation of scattered data with a C1 convexity-preserving surface
ACM Transactions on Mathematical Software (TOMS)
Technical section: Convexity control of a bivariate rational interpolating spline surfaces
Computers and Graphics
Convexity preserving scattered data interpolation using Powell--Sabin elements
Computer Aided Geometric Design
Convexity preserving splines over triangulations
Computer Aided Geometric Design
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We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set of nodal gradients for which there exists a convex Hermite interpolant, and constructing a smooth convex surface that interpolates the nodal values and gradients. The method involves two data-dependent triangulations along with a straight-line dual of each, and we describe some interesting relationships among them.