A C1 triangular interpolation patch for computer-aided geometric design

TL;DR: A geometric construction is described which ensures tangent plane (visualC1) continuity between adjacent polynomial surface patches that works for both three- and four-sided patches.

TL;DR: A vector valued interpolation scheme for a pentagon is described which is compatible with surface patches which have a rectangular domain of definition, which could be useful in computer-aided geometric design problems, where a pentagonal patch occurs within a rectangular patch framework.

TL;DR: A unifying survey of the published methods for solving variants of the problem of passing a surface through a set of data points to identify causes of shape defects, and suggestions for improving the aesthetic quality of the interpolants are presented.

TL;DR: This work presents a new technique for curve and surface design that combines a geometrically based specification with constrained optimization (minimization) of a fairness functional, and demonstrates the superiority of curvature variation as a fairness metric and efficacy of optimization as a tool in shape design, albeit at significant computational cost.

TL;DR: An up to date account of Coons methods and extensions thereof, drawing mainly on unpublished material is provided, from the stand point of the computer scientist or engineer who wishes to implement or use such methods.

TL;DR: Blending function methods permit the exact interpolation of data given along curves and/or surfaces to yield finite dimensional schemes.