  Porous structures are widely used in various industries because of their
excellent properties. Porous surfaces have no thickness and should be thickened
to sheet structures for further fabrication. However, conventional methods for
generating sheet structures are inefficient for porous surfaces because of the
complexity of the internal structures. In this study, we propose a novel method
for generating porous sheet structures directly from point clouds sampled on a
porous surface. The generated sheet structure is represented by an implicit
B-spline function, which ensures smoothness and closure. Moreover, based on the
persistent homology theory, the topology structure of the generated porous
sheet structure can be controlled, and a reasonable range of the uniform
thickness of the sheet structure can be calculated to ensure manufacturability
and pore existence. Finally, the implicitly B-spline represented sheet
structures are sliced directly with the marching squares algorithm, and the
contours can be used for 3D printing. Experimental results show the superiority
of the developed method in efficiency over the traditional methods.
