Layer Depth-normal Images for Complex Geometries - Part One: Accurate Modeling and Adpative Sampling

The layered depth-normal images (LDNIs) is an implicit representation of solid models that sparsely encodes the shape boundary in three orthogonal directions. We present a LDNIbased geometric modeling method for applications with high accuracy requirements. In our method, we first construct LDNIs models from input polygonal models. The accuracy of the generated LDNIs models can be controlled by setting pixel width during the construction process. Even for very complex geometries and high accuracy requirements, the construction process is fast with the aid of graphics hardware. Based on the LDNIs models, we then perform geometric modeling operations. Two types of operations are presented including regularizing and Boolean operations. The geometric modeling operations are straightforward and easy to be implemented robustly. From the processed LDNIs model, an adaptive sampling method is presented to construct a cell representation that includes both uniform and octree cells. Finally 2manifold polygonal mesh surfaces are constructed from the cell representation. For high accuracy requirements that are typical in CAD/CAM applications, we present a volume tiling technique and a parallel implementation to accelerate the computation. Our method achieves a good balance between the accuracy and computational resources. We report experimental results on a variety of CAD models. The results demonstrate the effectiveness and efficiency of our approach especially for modeling complex geometries.