scholarly journals Computation of Implicit Representation of Volumetric Shells with Predefined Thickness

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 125
Author(s):  
Martin Geier ◽  
Hussein Alihussein
Keyword(s):  
3D Printer ◽  
Implicit Surface ◽  
Implicit Representation ◽  
Varying Thickness ◽  
Original Surface ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
Solid Models ◽  
Triply Periodic Minimal Surface ◽  
Spatially Varying

We propose and validate a method to find an implicit representation of a surface placed at a distance h from another implicit surface. With two such surfaces on either side of the original surface, a volumetric shell of predefined thickness can be obtained. The usability of the proposed method is demonstrated through providing solid models of triply periodic minimal surface (TPMS) geometries with a predefined constant and variable thickness. The method has an adjustable order of convergence. If applied to surfaces with spatially varying thickness, the convergence order is limited to second order. This accuracy is still substantially higher than the accuracy of any contemporary 3D printer that could benefit from the function as an infill volume for shells with predefined thicknesses.

scholarly journals Tetrahedron-Based Porous Scaffold Design for 3D Printing

Designs ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 16 ◽  
Author(s):  
Ye Guo ◽  
Ke Liu ◽  
Zeyun Yu
Keyword(s):  
Minimal Surface ◽  
Porous Scaffold ◽  
3D Models ◽  
Structure Design ◽  
Implicit Surfaces ◽  
Implicit Surface ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
Hexahedral Meshes ◽  
Triply Periodic Minimal Surface

Tissue repairing has been the ultimate goal of surgery, especially with the emergence of reconstructive medicine. A large amount of research devoted to exploring innovative porous scaffold designs, including homogeneous and inhomogeneous ones, have been presented in the literature. The triply periodic minimal surface has been a versatile source of biomorphic structure design due to its smooth surface and high interconnectivity. Nonetheless, many 3D models are often rendered in the form of triangular meshes for its efficiency and convenience. The requirement of regular hexahedral meshes then becomes one of limitations of the triply periodic minimal surface method. In this paper, we make a successful attempt to generate microscopic pore structures using tetrahedral implicit surfaces. To replace the conventional Cartesian coordinates, a new coordinates system is built based on the perpendicular distances between a point and the tetrahedral faces to capture the periodicity of a tetrahedral implicit surface. Similarly to the triply periodic minimal surface, a variety of tetrahedral implicit surfaces, including P-, D-, and G-surfaces are defined by combinations of trigonometric functions. We further compare triply periodic minimal surfaces with tetrahedral implicit surfaces in terms of shape, porosity, and mean curvature to discuss the similarities and differences of the two surfaces. An example of femur scaffold construction is provided to demonstrate the detailed process of modeling porous architectures using the tetrahedral implicit surface.

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