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.