Geometric Modeling using Stochastically Manipulated Triangular Tessellation

抄録

This paper addresses geometric modeling using stochastically manipulated triangular tessellation or meshing. We employ two different methods. The first method randomly selects triangles on a rectangular or circular plane. The use can adjust the overall porosity and fineness of the triangular mesh. This method can create complex structures that have pores scattered randomly. However, the pores themselves are not necessarily irregular. The other method first creates a point cloud around a given closed boundary. Triangles are formed among some randomly selected points inside the boundary. Finally, the triangles are merged to form tunnel-like openings. This way, the method produces a complex structure exhibiting highly irregular and randomized pores. Unlike the first method, this method does not help adjust the porosity that much, but the sizes of the pores can be adjusted by changing the density of the points in the point cloud. Thus, a hybrid method can be used to create porous structures exhibiting highly randomized pores with predefined porosity. Consequently, the hybrid approach method can be used to develop products for biomedical engineering (e.g., implants) and engineering devices (heat and mass transfer equipment where percolation is necessary). In the next phase of the study, we plan to study the manufacturability of the stochastic shapes we designed in this study.