Toward Error-free Manufacturing of Fractals

Ullah, Aman; Omori, Ryuta; Nagara, Yuji; Kubo, Akihiko; Tamaki, Jun’ichi

doi:10.1016/j.procir.2013.09.009

Cited by 9 publications

(11 citation statements)

References 15 publications

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“…Some authors have also worked in the other direction. For example, Ullah et al [56][57][58] and Ullah [59] have created some point-clouds the using the mathematical processes called iterative function systems and Monte Carlo simulation. They have used the point-clouds as the base models and manufactured the self-similar objects (e.g., fractals) and porous structures.…”

Section: Surface Model Creation Techniques For Pcammentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Surface Model Creation Techniques For Pcammentioning

confidence: 99%

“…In this case, a point-cloud can be created recursively using an algorithmic approach. Ullah et al [58] have shown an algorithmic approach where set points are created recursively by two user-defined parameters called distance and angle. We have modified their algorithm to the create point-cloud for geometric modeling.…”

Section: Algorithmic Approachmentioning

confidence: 99%

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

et al. 2018

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“…Li et al [15] have developed a voxel-based data structure to capture the geometric information of a fractal object in order to fabricate its physical model using layered manufacturing. Ullah et al [36] have reported the manufacturing defects of fractal objects while producing them with the aid of subtractive manufacturing (e.g., milling) and additive manufacturing (e.g., stereolithography). They have suggested the ways for creating defect-free physical models of fractals.…”

Section: Related Workmentioning

confidence: 99%

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Chang¹,

Shih²

2014

Computer-Aided Design and Applications

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This study deals with the design for manufacturing (DFM) of fractals created by a random walk called iterated function system (IFS). In particular, the DFM of an IFS-created fractal called Barnsley's fern-leaf is considered. The IFS dedicated for creating virtual models of a fern-leaf uses a set of four strictlycontracting affine mappings in the onto manner. The interactions among these mappings are studied in detail in order to identify some data structures. Based on the identified data structures, a DFM procedure is proposed. In the proposed DFM procedure, three out of the four mappings are employed in both the onto and one-to-one manner. The proposed DFM procedure is applied to the redesign of the shape (fern-leaf). Physical models of the redesigned fern-leaf are manufactured using both additive and subtractive manufacturing technologies (3-D printing and milling). The factors affecting accuracy of the physical models are also described. Although this study is limited to the shape of the fern-leaf, other IFS-created shapes can be redesigned using the proposed DFM procedure. Nevertheless, this study sheds some light on our understanding of how to develop more accurate physical models of IFS-created fractals.

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“…In this article, the focus is on the deterministic point cloud that is created by a recursive process as shown in [38,69,70]. This process uses two variables and three constants, which are user-defined.…”

Section: Introductionmentioning

confidence: 99%

“…In this regard, there are multiple approaches. An analytical point cloud can be created using a deterministic approach [38,70], a semi-random approach or affine mapping-based approach [34,71], and a fully random approach [72]. In each case, the 3D solid model construction process can be systematized using the information underlying the analytically created point cloud.…”

Section: Introductionmentioning

confidence: 99%

Geometric Modeling and 3D Printing Using Recursively Generated Point Cloud

Tashi

Ullah

Kubo

2019

MCA

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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.

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Toward Error-free Manufacturing of Fractals

Cited by 9 publications

References 15 publications

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

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

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Geometric Modeling and 3D Printing Using Recursively Generated Point Cloud

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