  In the field of topology optimization, the homogenization approach has been
revived as an important alternative to the established, density-based methods
because it can represent the microstructural design at a much finer
length-scale than the computational grid. The optimal microstructure for a
single load case is an orthogonal rank-3 laminate. A rank-3 laminate can be
described in terms of frame fields, which are also an important tool for mesh
generation in both 2D and 3D.
  We propose a method for generating multi-laminar structures from frame
fields. Rather than relying on integrative approaches that find a
parametrization based on the frame field, we find stream surfaces, represented
as point clouds aligned with frame vectors, and we solve an optimization
problem to find well-spaced collections of such stream surfaces. The stream
surface tracing is unaffected by the presence of singularities outside the
region of interest. Neither stream surface tracing nor selecting well-spaced
surface rely on combed frame fields.
  In addition to stream surface tracing and selection, we provide two methods
for generating structures from stream surface collections. One of these methods
produces volumetric solids by summing basis functions associated with each
point of the stream surface collection. The other method reinterprets point
sampled stream surfaces as a spatial twist continuum and produces a
hexahedralization by dualizing a graph representing the structure.
  We demonstrate our methods on several frame fields produced using the
homogenization approach for topology optimization, boundary-aligned, algebraic
frame fields, and frame fields computed from closed-form expressions.
