Selected applications of subdivision surfaces and numerical quadratures for Gregory patches

Advancements in geometric modelling and processing have played a key role in various applications, including computer games, computer-aided design, and vector graphics. Surfaces of arbitrary complexity are indispensable in these areas, as they provide a flexible representation of various shapes.

Leveraging the concept of feature-adaptive refinement, we design a new and flexible vector graphics representation. The designs can be refined locally where needed so that the resulting representation is less dense and more efficient to render to screen. Our second application enhances the visual appearance of shapes by using a special construction near creases of the modelled objects.

Our final contribution focuses on a certain type of surfaces that have been used in the modelling context, but their use in numerical simulations has been limited so far, largely owing to the lack of efficient and accurate integral evaluation rules. We fill this gap by producing such rules for these surfaces.