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Point-cloud is a valuable piece of information for geometric modeling and additive manufacturing of different types of objects. In most cases, a point-cloud is obtained by using the 3D scanners or by using image processing. Alternatively, one can rely on an analytical approach for creating the required point-cloud. In this study, we develop an analytical method that uses both equation and algorithm-based approaches for creating a point-cloud for modeling a given object (or shape). The analytically created point-cloud can then be processed by using a commercially available CAD package to create a virtual model (or solid CAD model) of the object. Finally, the virtual model can be used to create a physical model (or replica) of the underlying object using a commercially available additive manufacturing device (e.g., a 3D printer). The abovementioned procedure of analytical point-cloud based geometric modeling for additive manufacturing can be applied to preserve artifacts having cultural significance. In particular, we consider the Ainu motifs that represent the cultural heritage of Ainus living in the northern part of Japan (Hokkaido). We first classify the motifs and then model them in the form of a point-clouds using both equations and a recursive process (algorithm) proposed in this study. Finally, we create the CAD model and physical models of the artifacts having Ainu motifs on them. This way, we show the effectiveness of the analytical point-cloud based geometric modeling for additive manufacturing.

Analytical Point-Cloud Based Geometric Modeling for Additive Manufacturing and Its Application to Cultural Heritage Preservation