Log-Aesthetic Curves for Shape Completion Problem

Abstract

An object with complete boundary or silhouette is essential in various design and computer graphics feats. Due to various reasons, some parts of the object can be missing hence increasing the complexity in designing process. It is therefore important to reconstruct the missing parts of an object while retaining its aesthetic appearance. In this paper, we propose Log-Aestheic Curves (LAC) for shape completion problem. We propose an algorithm to construct LAC segment and subsequently fit into the gap of the missing parts with C-shape or S-shape. For C-shape completion, we define LAC segment by specifying two endpoints and their respective tangent directions between the gaps while, for S-shape, the user defines an inflection point in between the endpoints. The final section illustrates three examples to showcase the efficiency of the proposed algorithm. The results are further compared with Kimia’s method to prove that the algorithm produces equally good result. Additionally, the proposed algorithm provides an extra degree of freedom in which the user would be able to choose the type of spiral that they desire to solve the shape completion problem.