Study On Spline Modeling And Discretization In Architectural Geometry

As the rapid development of society and economy, the free-form models are widely employed in architecture. In order to save cost, and make the design and construction easier, geometric design methods are used to design, analyze and construct the architectural model in recent years. In this paper, we do some research on quad-remeshing, optimization and designing of model. We develop and improve some algorithms in the fields such as quad-remeshing, optimization and model design. In quad-remeshing, we use curvature-lines, features and boundary curves of model to constrain the directions of edges on the mesh, where points on the curvature-lines and exact geodesic curves are inserted into the mesh to make the segmentation accurate. Then, the quad-mesh is generated by template-based parameterization. In mesh optimization, we improve the algorithms originally proposed by Pottmann et al. Our algorithms are more efficient, flexible and universal. Moreover, we construct the models by combining subdivision and optimization alternately, and generate the strip-surfaces around singular vertices. In surface modeling, we develop the extended T-mesh, which can be represented in an obj-like format file. With such data structure, the computation of T-spline will be much easier. Furthermore, we develop a new local refinement algorithm by virtue of the extended T-mesh.