Curve and surface reconstruction based on a set of improved interpolatory basis functions

To avoid the potential distortion problem in curve and surface design, a set of improved basis functions is introduced to construct interpolatory curves and surfaces passing through given data points. Compared with the basis functions used in Zhang and Ma (2011) [33], the accuracy of the partition of unity of the improved basis functions exceeds the computation limit of the floating-point in common computers. Various properties, such as interpolatory property and infinite continuity, are still valid for the improved basis functions, and local support and linear precision are valid under a small tolerance. The method can not only prevent the Runge phenomenon, but also retains various desired operation properties, such as connecting different smooth curves or surfaces easily, constructing closed curves and surfaces conveniently, adjusting the shape of the curves or surfaces locally, etc. An interpolatory curve or surface constructed can be expressed by one equation, and is C∞C∞ continuous. The method may be applied to the graphics community and other related fields.