We introduce a generalization to the classic( bi-cubically blended) Coons Patch; one that extends the patch to any number of sides. The resulting N-sided patch continues to interpolate the underlying curves, but the curves may form any topological network -- as opposed to rectilinear networks for Coons. The consequent surfacing scheme maintains G1 continuity across the boundaries between patches.

Advantages of this technology are illustrated specifically for (1) freeform design and (2) scientific visualization. In (1) we create a curve-based design scheme, which frees the user from topological constraints. In (2), we create a marching-cubes like algorithm that uses the N-sided patches, instead of planar segments. The result is a smoother looking, more highly compressed visualization for iso-surface rendering as in the figure below, which shows a CO2 sequestration iso-surface in water.