Techniques for controlling nucleic acid structures include determining, for each junction type, values for parameters indicating ground-state geometry and both translational and rotational stiffness coefficients. Topological design data indicates a number of bases in each helix connected to corresponding junctions. Initial positions of each base are determined by connecting helices to junctions using the ground-state geometry and arbitrary coordinates not confined to lattice coordinates. Misalignment vectors each indicate a difference in coordinates and orientations between initial positions of a pair of bases that are not adjacent in the initial positions but are adjacent or coincident in the design data. Forces and moments at the junctions to reduce misalignment magnitudes are determined based on the translational and rotational stiffness coefficients at each junction. Position and orientation in 3D coordinates of each base are determined by reducing or eliminating the misalignment magnitudes and balancing forces and moments across the nanostructure.