A High-quality And Adaptive Mesh Extraction Algorithm Based On GradNormal

Extracting a polygonal mesh from a discrete or continuous scalar field is an important step of approximation based surface reconstruction,receives increasingly attention.The marching cubes(MC)method,as one of the first iso-surface extraction algorithms,is able to generate a simple and efficient local triangulation using a lookup table.A variant implementation of MC is t.o divide each cube into six tetrahedra and use the tetrahedra to replace cube(MT).In spite of the high performance,MC has two main disadvantages.First,the resulting mesh by MC often contains many skinny triangles.Second,it suffers from ambiguities in approximating the underlying surface-feature lines,small topological holes,tube,thin plates or narrow gaps are hard to be accurately reconstructed by MC.The recently proposed GradNormal first tiles space with tetrahedra of a fixed shape.For smooth surfaces,GradNormal can guarantee that the angles of the extracted mesh are between 35.25° and 101.45°,significantly improving the quality of triangulation.However,it still has some drawbacks,such as being only used in implicit functions,requiring the use of tetrahedrons to tile the entire space(usually bounding boxes)and traverse it,and lacking research on geometric topology ambiguity.The idea of the GradNormal has some inspiration for the algorithm in this article.Firstly,due to its use of fixed shape tetrahedra for 3D space tiling,it has good scalability and is easy to detect and process areas with topological ambiguity,without considering the consistency issues brought by using different tetrahedra tiling.Secondly,the GradNormal achieves high-quality triangulation through midpoint projection,which can be easily inherited and implemented.Therefore,this thesis improve GradNormal from different aspects and proposes a high-quality and adaptive mesh extraction algorithm based on it.The contributions of this thesis mainly include the following three aspects:(1)Extending GradNormal to a general geometric domain equipped with a projection operation can be applied to all 3D models that can be represented by SDF,such as point clouds,SDF,implicit functions,polygon mesh,etc.,so that the geometry of 3D shapes can be encoded,regardless of the geometric domain of the model itself.(2)By using adaptive subdivision to replace fixed size tetrahedra in the GradNormal algorithm with layered tetrahedra and traversing using region growth,non-uniform triangulation can be generated to preserve the geometric features of the geometric surface while ensuring good temporal and spatial performance.(3)Compared with the existing technology,a fast and effective fuzzy detection strategy is proposed to eliminate geometric/topological ambiguity as much as possible.The experimental results show that compared to existing methods,the algorithm proposed in this paper can ensure the absence of geometric topology ambiguity while maintaining high triangulation quality,and has high application value.