Table 1 Mathematical expressions of different TPMS units
Unit | Mathematical expressions | Models | Refs. |
|---|---|---|---|
Gyroid | \(f(x,y,z)=\,\sin ({\omega }_{x}x)\,\cos ({\omega }_{y}y)+\,\sin ({\omega }_{z}z)\,\cos ({\omega }_{x}x)+\,\sin ({\omega }_{y}y)\,\cos ({\omega }_{z}z)=C\) |
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Schwarz Primitive | \(f(x,y,z)=\cos ({\omega }_{x}x)+\cos ({\omega }_{y}y)+\cos ({\omega }_{z}z)=C\) |
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Schwarz Diamond | \(\begin{array}{l}f(x,y,z)=\,\sin ({\omega }_{x}x)\sin ({\omega }_{y}y)\,\sin ({\omega }_{z}z)+\,\sin ({\omega }_{x}x)\,\cos ({\omega }_{y}y)\,\cos ({\omega }_{z}z)\\ +\,\cos ({\omega }_{x}x)\,sin({\omega }_{y}y)\,\cos ({\omega }_{z}z)+\,\cos ({\omega }_{x}x)\,\cos ({\omega }_{y}y)\sin ({\omega }_{z}z)=C\end{array}\) |
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Neovius | \(f(x,y,z)=3\left[\cos ({\omega }_{x}x)+\cos ({\omega }_{y}y)+\cos ({\omega }_{z}z)\right]+4\cos ({\omega }_{x}x)\,\cos ({\omega }_{y}y)\,\cos ({\omega }_{z}z)=C\) |
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