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Interest continues to grow for lattice structures produced by additive manufacturing methods that are described by triply periodic minimal surface (TPMS). Tunable parameters that define the TPMS provide unique design flexibility where prior research has focused on designing hybrid or functionally graded TPMS structures. In this paper, a new strategy is proposed to include an orientation angle and volume fraction of each lattice cell simultaneously when defining structures derived from TPMS. The algorithm iteratively solves an underlying partial differential equation with the finite difference method to obtain a smooth, continuous lattice structure with a spatially varying orientation angle. The resulting lattice structure can be combined with other types of TPMS models using Gaussian radial basis and distance functions to achieve multi-TPMS lattice designs. The spatially varying lattice structures can also take the advantage of the directional effective modulus of TPMS to improve the strength the performance of lattice design.