Construction of 3D models for additive manufacturing based on three-periodic surfaces of the Fourier polynomia
DOI:
https://doi.org/10.32347/2410-2547.2026.116.120-132Keywords:
modeling, 3D model, Fourier polynomial, tri-periodic surfaces, computer-aided design, additive manufacturing, heat exchangerAbstract
With advances in 3D printing, the construction of increasingly intricate designs has become possible. Metamaterials and devices based on tri-periodic minimal surfaces (TPMS) have proven useful in various applications, including tissue engineering, acoustics, and heat exchange. These surfaces have minimal average curvature at every point, although certain studies show that minimality in a strictly geometric sense is not necessary or even desirable for some applications.
This paper proposes an algorithm for Fourier polynomial approximation combined with interpolation that enables the construction of generic tri-periodic surfaces (TPS), which are not minimal but appear more governable. In the context of tri-periodic implicit surfaces construction, the interpolating property of the polynomial allows setting the expected function values in points directly, while the approximating property allows for an unlimited number of non-strict guiding points. Such points can be obtained by discretizing curves and surfaces. This enables both explicit and implicit control over the shape of a TPS within the same algorithm.
The implicit level of control enables the creation of 3D-models applicable in all fields where TPMS are already in use. The explicit level of control ensures that such models can be produced using additive manufacturing technologies. Not to become too broad, this particular paper only discusses the applicability of Fourier-based 3-periodic surfaces in heat exchangers design, and printability of the models based on these surfaces in laser powder bed fusion (LPBF) and electron beam melting (EBM) additive manufacturing processes.
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