Crystal-Like geometric modeling

Crystals are natural phenomena that exhibit high degrees of order, symmetry, and recursion. They naturally form interesting and inspiring geometric shapes. This thesis provides geometric modeling techniques for creating shapes with crystallike geometry. The tiered extrusion method, along with a face grouping technique, simplifies the creation of complex, intricate faceted shapes. In combination with remeshing, these methods provide the capability to generate geometric shapes exhibiting planar faces, symmetry, and fractal geometry. The techniques have also been implemented in software, as a proof of concept. They are used in an interactive geometric modeling system, in which users can use these techniques to create crystal-like shapes. The crystal-like modeling operations are shown to successfully create beautiful geometric shapes. The methods improve upon traditional modeling capabilities, providing an easier way to create crystal-like geometric shapes.