Smoothly Blending Successive Circular Interpolants in Two and Three Dimensions

Curvilinear edges and surfaces are developed to span a given logically-cuboid distribution of nodes. The underlying construction uses four successive nodes to de ne a curve spanning the middle pair as follows: One interpolates each of the two successive triples of nodes with the segment of a circle or straight line. Then one blends the two segments continuously between the middle pair of nodes. The blend is relatively linear in terms of arc-length along each segment. The union of such successive curvesections forms a G1 curve. Wire-frames of such curves de ne cell edges. Similar intermediate curvilinear interpolation of the wires de nes cell faces, and their union de nes G1 coordinate-like surfaces. The Euclidean image of coordinate lines and surfaces of rectangular, cylindrical, and spherical coordinate systems are reconstructed exactly, given the nodes associated with tensor product data from the coordinate lines of each system. Otherwise|if the nodes are a tensor product grid associated with a su ciently smooth reference coordinate system|the cell edges are third-order accurate. We append a natural two-dimensional blending of overlapping surface interpolants.