Geometric Modeling and 3D Printing Using Recursively Generated Point Cloud

Previous studies have reported that a recursive process called the point cloud creation algorithm (PCA) that generates a point cloud is useful for reverse engineering a planner shape. This study elucidates the characteristics of the parameters used in the recursive process as well as its ability in geometric modeling and 3D printing of 3D shapes. In the recursive process, three constants (center point, initial distance, and initial angle) and two variables (instantaneous distance and instantaneous rotational angle) are employed. The shape-modeling characteristics of the constants and variables are elucidated using some commonly used shapes (straight-line, circle, ellipses, spiral, astroid, S-shape, and leaf-shape). In addition, the shape-modeling capability of the recursive process as a whole is quantified using two parameters called the radius of curvature and aesthetic value. Moreover, an illustrative example that shows the efficacy of the recursive process in virtual and physical prototyping of a relatively complex 3D object is presented. The results show that reverse engineering performed by the recursive-process-created point cloud is free from computational complexity compared to reverse engineering performed by the 3D-scanner-created point cloud. As such, the outcomes of this study enrich the field of reverse engineering.