Volume 13, Issue 4
Uniformly Distributed Circular Porous Pattern Generation on Surface for 3D Printing

Sungha Yoon, Chaeyoung Lee, Jintae Park, Darae Jeong & Junseok Kim

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 845-862.

Published online: 2020-06

Preview Purchase PDF 372 1646
Export citation
  • Abstract

We present an algorithm for uniformly distributed circular porous pattern generation on surface for three-dimensional (3D) printing using a phase-field model. The algorithm is based on the narrow band domain method for the nonlocal Cahn–Hilliard (CH) equation on surfaces. Surfaces are embedded in 3D grid and the narrow band domain is defined as the neighborhood of surface. It allows one can perform numerical computation using the standard discrete Laplacian in 3D instead of the discrete surface Laplacian. For complex surfaces, we reconstruct them from point cloud data and represent them as the zero-level set of their discrete signed distance functions. Using the proposed algorithm, we can generate uniformly distributed circular porous patterns on surfaces in 3D and print the resulting 3D models. Furthermore, we provide the test of accuracy and energy stability of the proposed method.

  • Keywords

Diblock copolymer, porous surface, 3D printing, nonlocal Cahn–Hilliard equation.

  • AMS Subject Headings

65D18, 68U05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-845, author = {Sungha Yoon , and Chaeyoung Lee , and Jintae Park , and Darae Jeong , and Junseok Kim , }, title = {Uniformly Distributed Circular Porous Pattern Generation on Surface for 3D Printing}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {845--862}, abstract = {

We present an algorithm for uniformly distributed circular porous pattern generation on surface for three-dimensional (3D) printing using a phase-field model. The algorithm is based on the narrow band domain method for the nonlocal Cahn–Hilliard (CH) equation on surfaces. Surfaces are embedded in 3D grid and the narrow band domain is defined as the neighborhood of surface. It allows one can perform numerical computation using the standard discrete Laplacian in 3D instead of the discrete surface Laplacian. For complex surfaces, we reconstruct them from point cloud data and represent them as the zero-level set of their discrete signed distance functions. Using the proposed algorithm, we can generate uniformly distributed circular porous patterns on surfaces in 3D and print the resulting 3D models. Furthermore, we provide the test of accuracy and energy stability of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0199}, url = {http://global-sci.org/intro/article_detail/nmtma/16956.html} }
TY - JOUR T1 - Uniformly Distributed Circular Porous Pattern Generation on Surface for 3D Printing AU - Sungha Yoon , AU - Chaeyoung Lee , AU - Jintae Park , AU - Darae Jeong , AU - Junseok Kim , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 845 EP - 862 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0199 UR - https://global-sci.org/intro/article_detail/nmtma/16956.html KW - Diblock copolymer, porous surface, 3D printing, nonlocal Cahn–Hilliard equation. AB -

We present an algorithm for uniformly distributed circular porous pattern generation on surface for three-dimensional (3D) printing using a phase-field model. The algorithm is based on the narrow band domain method for the nonlocal Cahn–Hilliard (CH) equation on surfaces. Surfaces are embedded in 3D grid and the narrow band domain is defined as the neighborhood of surface. It allows one can perform numerical computation using the standard discrete Laplacian in 3D instead of the discrete surface Laplacian. For complex surfaces, we reconstruct them from point cloud data and represent them as the zero-level set of their discrete signed distance functions. Using the proposed algorithm, we can generate uniformly distributed circular porous patterns on surfaces in 3D and print the resulting 3D models. Furthermore, we provide the test of accuracy and energy stability of the proposed method.

Sungha Yoon, Chaeyoung Lee, Jintae Park, Darae Jeong & Junseok Kim. (2020). Uniformly Distributed Circular Porous Pattern Generation on Surface for 3D Printing. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 845-862. doi:10.4208/nmtma.OA-2019-0199
Copy to clipboard
The citation has been copied to your clipboard