Design and Applications of Triply Periodic Minimal Surfaces: A Survey

Triply Periodic Minimal Surface is a kind of algebraic surface expressed by implicit function. The rapid development of additive manufacturing technology has greatly enhanced the manufacturing capabilities of complex geometries and topological structures, Triply Periodic Minimal Surface, as a powerful geometric modeling tool, has received more and more attention. Firstly, this paper introduces the current research status of Triply Periodic Minimal Surface in terms of mathematical expression, properties, applications, and geometric design methods. Secondly, the mechanical property, heat and mass transfer, tissue engineering and acoustics performance are summarized. The existing works related to Triply Periodic Minimal Surface are classified and combed from the perspective of geometric modeling methods. They are grouped into four categories: regular unit method, parametric unit method, region splicing method and overall optimization method. The characteristics of each method are analyzed. Finally, in accordance with practical applications, we summarized challenges and prospected future works in this field.