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.
Highlights
In a design environment, there are situations in which the outlines of an object are missing or occluded
We introduce the implementation of G1 Log-Aestheic Curves (LAC) algorithm to fit the gap in between the outlines of missing/occlusion objects
We compare the performance of this algorithm with the results obtained by Kimia et al.’s [3] method on the same examples in order to show the effectiveness of LAC to solve shape completion problem
Summary
There are situations in which the outlines of an object are missing or occluded. A notable work which received much attention is by Kimia et al [3], where they proposed an algorithm which utilizes Euler spiral to solve shape completion problem. The algorithm proposed by Kimia et al [3] is the implementation of Euler spiral to solve the shape completion problem. It is a graph to measure the relationship between curvature radius (denoted by ρ) and arc length of the curve segment (denoted by s) They found that all the curves employed in automobile design depict linear gradient of LDDC. We compare the performance of this algorithm with the results obtained by Kimia et al.’s [3] method on the same examples in order to show the effectiveness of LAC to solve shape completion problem. Which the designer tweaks the segment in order to obtain the desired shape
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