I was delighted to contribute to this paper:
Abstract:
Many problems in science and engineering require the ability to grow
tubular or polymeric structures up to large volume fractions within a
bounded region of three-dimensional space. Examples range from the
construction of fibrous materials and biological cells such as neurons,
to the creation of initial configurations for molecular simulations. A
common feature of these problems is the need for the growing structures
to wind throughout space without intersecting. At any time, the growth
of a morphology depends on the current state of all the others, as well
as the environment it is growing in, which makes the problem
computationally intensive. Neuron synthesis has the additional
constraint that the morphologies should reliably resemble biological
cells, which possess nonlocal structural correlations, exhibit high
packing fractions, and whose growth responds to anatomical boundaries in
the synthesis volume. We present a spatial framework for simultaneous
growth of an arbitrary number of nonintersecting morphologies that
presents the growing structures with information on anisotropic and
inhomogeneous properties of the space. The framework is computationally
efficient because intersection detection is linear in the mass of
growing elements up to high volume fractions and versatile because it
provides functionality for environmental growth cues to be accessed by
the growing morphologies. We demonstrate the framework by growing
morphologies of various complexity.
