Eine auf Randpunkten basierte hierarchische Spline Parametrisierung für zwei- und dreidimensionale Strukturen

A method for discretizing solid 2D and 3D models obtained from surface representation is developed. The method uses a hierarchical quad-tree (2D) or octree (3D) structure to efficiently represent the surface details without a significant increase in the number of interior elements. Moreover, the geometry of the surface including normal information can be accurately incorporated in the model by using cubic (or higher-order) splines. The resulting model uses the same basis functions (Bezier-Bernstein polynomials) that are used in standard Computer Aided Design (CAD) software. The method has the potential to reduce the difficulties and human intervention required for meshing and creating volumetric models, as it allows the use of general surface representations including those obtained from image data, 3D scanners or B-Rep (boundary representation) models. Potential applications in the field of civil engineering, including rapid modeling of complex 3D structures are being discussed.