SHIP LINES USING CONVEXITY-PRESERVING RATIONAL CUBIC INTERPOLATION

A convexity-preserving, twice continuously differentiable, piecewise rational cubic interpolant f to offset data S = {(X(j),Y(j))\j = 1, ..., n; DELTA-j2 not-equal 0; X(j+1) > X(j)} is defined in terms of "tension" parameters tau-j, j = 1, ..., n - 1 and the end conditions f"(X1) = f"(X(n)) = 0. The condition f"(X(j))DELTA-j-2 greater-than-or-equal-to 0, j = 2, ..., n - 1 imposed on f is both necessary and sufficient to ensure that the interpolant preserves the local convexity/concavity properties of the set S. An algorithm for generating f is given and applied to the generation of ship lines from design station offset data. The specific advantages of this interpolant are its smoothness, simplicity, speed of computation and convexity-preserving properties.