Continuity-Forcing for Derivatives in Data Reconstruction

TL;DR

This paper emphasizes the importance of enforcing derivative continuity in data reconstruction to improve smooth surface modeling, extending the concept of gradually varied derivatives for practical applications.

Contribution

It introduces the necessity of continuity-forcing derivatives in data reconstruction, expanding the methodology of gradually varied derivatives for broader use.

Findings

Continuity-forcing derivatives enhance smoothness in data reconstruction.

Gradually varied derivatives are crucial for real-world surface modeling.

The methodology extends to general purposes beyond initial applications.

Abstract

The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are needed. In the this paper, we present more reasons to enlighten of forcing derivatives to be continuous is necessary. This requirement seems not a must in theory for functions in continuous space, but it is truly important in function reconstruction for real problems. This paper is also to extend the meaning of the methodology for gradually varied derivatives to general purposes by considering forcing calculated derivatives to be "continuous" or gradually varied.