Modelling and Simulation of Lily flowers using PDE Surfaces This paper presents a partial differential equation (PDE)based surface modelling and simulation framework for lily flowers. We use a PDEbased surface modelling technique to represent shape of a lily flower and PDEbased dynamic simulation to animate blossom and decay processes of lily flowers. To this aim, we first automatically construct the geometry of lily flowers from photos to obtain feature curves. Second, we apply a PDEbased surface modelling technique to generate sweeping surfaces to obtain geometric models of the flowers. Then, we use a physicsdriven and databased method and introduce the flower shapes at the initial and final positions into our proposed dynamic deformation model to generate a realistic deformation of flower blossom and decay. The results demonstrate that our proposed technique can create realistic flower models and their movements and shape changes against time efficiently with a small data size.

Parametrization quantization with free boundaries for trimmed quad meshing The generation of quad meshes based on surface parametrization techniques has proven to be a versatile approach. These techniques quantize an initial seamless parametrization so as to obtain an integer grid map implying a pure quad mesh. Stateoftheart methods following this approach have to assume that the surface to be meshed either has no boundary, or has a boundary which the resulting mesh is supposed to be aligned to. In a variety of applications this is not desirable and nonboundaryaligned meshes or gridparametrizations are preferred. We thus present a technique to robustly generate integer grid maps which are either boundaryaligned, nonboundaryaligned, or partially boundaryaligned, just as required by different applications. We thereby generalize previous work to this broader setting. This enables the reliable generation of trimmed quad meshes with partial elements along the boundary, preferable in various scenarios, from tiled texturing over design and modeling to fabrication and architecture, due to fewer constraints and hence higher overall mesh quality and other benefits in terms of aesthetics and flexibility.