Bézier Guarding for 2D Tensor Product Surfaces

This bachelor’s thesis investigates the generation of high order meshes from given quad layouts defined by Bézier curves. The resulting mesh comprises quadrilaterals represented by Bézier tensor product surfaces. The primary goal was to develop a novel algorithm to create quadrilateral Bézier tensor product surfaces that are both regular and injective. The algorithm was tested on various examples, ranging from simple, flat curves to complex, highly deformed, and intersecting curves. The results were evaluated based on quality metrics such as Scaled Jacobian and MIPS distortion. The generated surfaces generally exhibited better MIPS distortion values but tended to have lower Scaled Jacobian values. The study demonstrates the feasibility of creating injective high order meshes with Bézier tensor product surfaces, though there is room for improvement in surface quality.