## 1 Introduction  
In contrary to the conventional manufacturing processes (e.g., subtractive manufacturing processes, such as, milling, drilling, turning, and alike), Additive Manufacturing (AM) processes have been introduced to manufacture physical objects by adding materials layer by layer [1]. AM (also known as 3D printing (3 DP), rapid prototyping, or freeform fabrication) can now be used to manufacture objects having complex shapes and multi-scale structures. AM can also manufacture objects by adding different types of materials at different layers. As a result, AM has transformed the way that the objects are being designed and manufactured [2; 3; 4]. AM is now applied to manufacture automotive parts [5], aerospace parts [2], biomedical products (e.g., dental braces, artificial tissues,hearing aids, dummy cadaver, and prosthetic) [6; 7; 8; 9; 10; 11; 12], educational objects [13; 14; 15], fashion items (e.g., cloth, shoes, and jewelry) [16; 17; 18; 19; 20], foodstuffs (e.g., pizza, chocolate, crackers, and pasta) [21; 22; 23], construction objects (e.g., 3D printed house) [24; 25; 26], and items for preserving and restoring cultural heritage [27]. Small, affordable, and user-friendly AM machines (e.g., 3D printers) are now available for running small businesses, too [28; 29; 30]. As schematically illustrated in Figure 1, a typical AM operation consists of the following five steps: (1) creation of a 3D computer-aided design (CAD) model of the desired object (virtual model); (2) triangulation of the CAD model (known as STL data); (3) slicing of triangulated CAD model; (4) execution of AM process; and (5) surface finishing of the physical model [1; 2]. However, the advent of AM has introduced a technology called Reverse Engineering (RE), as schematically illustrated in Figure 2. In RE based AM, a 3D scanner first scans an object and represents it by a relatively large number of points called point-cloud. Using a CAD package, the point-cloud is transformed into a solid CAD model. The CAD model can be modified as preferred by the user before manufacturing it by AM. Thus, RE is mainly used for preserving artistic and culturally significant objects by creating the replicas or manufacturing another object based on the physic of the existing object for which the solid CAD model is not available. See [10; 11; 31; 32; 33; 34; 35] for more details regarding RE. Figure 1: The working principle of Additive Manufacturing (AM). Figure 2: A workflow for Reverse Engineering (RE) based AM. Nevertheless, as described in Figure 2, when a solid CAD model is not available in the first place, one can rely on the most primitive representation of an object, i.e., a point-cloud, and execute the steps shown in Figure 1. Therefore, point-cloud based geometric modeling has earned a great deal of attention from the AM community. However, it has been emphasized that the conventional CAD systems need additional functionalities to generate solid models of complex shapes (e.g., multi-scale cellular and lattice structures) from point-clouds [2]. In addition, creating a complex shape from a point-cloud using conventional CAD systems requires a great deal of skill, making it a heavily user-skill-dependent activity. This means that the typical steps of AM as shown in Figures 1 and 2 can be modified to accommodate the point-cloud in a befitting manner. This creates a notion called Point-Cloud based AM (PCAM). In most cases, a point-cloud is obtained by using the 3D scanners and processed before creating a CAD modeling. This issue is described elaborately in the literature review section. However, one can rely on some analytical approaches for creating the required point-cloud for PCAM. This direction of PCAM has not yet been explored compared to other direction, i.e., 3D-scanner based point-cloud creation for PCAM. Thus, the objective of this article is to shed some lights on an analytical point-cloud based AM. As an application, the cultural heritage preservation is considered. Based on the abovementioned contemplation, this article is written.