Controlled self-assembly of three-dimensional shapes holds great potential for fabrication
of functional materials. Their practical realization requires a theoretical framework to
quantify and guide the dynamic sculpting of the curved structures that often arise in
accretive mineralization. Motivated by a variety of bioinspired coprecipitation patterns of
carbonate and silica, we develop a geometrical theory for the kinetics of the growth front
that leaves behind thin-walled complex structures. Our theory explains the range of
previously observed experimental patterns and, in addition, predicts unexplored assembly
pathways. This allows us to design a number of functional base shapes of optical
microstructures, which we synthesize to demonstrate their light-guiding capabilities.
Overall, our framework provides a way to understand and control the growth and form of
functional precipitating microsculptures.