Adaptive Remeshing With Bounded Error

With the development of computer graphics,3D mesh models have become an important component of many geometric applications,especially those require high-quality mesh such as numerical simulation,3D printing and so on.However,due to the inherent limitation of the acquisition methods,existing 3D meshes often have poor quality and cannot be directly used for real-world applications.To tackle this problem,various remeshing methods are continuously emerging.The remeshed effect may vary due to the changing application needs.One of the goals is that the approximate error between the generated mesh and the initial mesh should be guaranteed to be bounded in order to represent the initial shape well,which accordingly leads to the emergence of error-bounded remeshing methods.However,previous methods always let remeshed mesh stay in the error-bounded space to ensure the bounded error.The local operators that violate the error-bounded constraint are pro-hibited,thereby limiting the ability of the algorithm.What's worse,they may trapped in infinite loops.To this end,finding a more robust and efficient error-bounded remeshing algorithm is of great significance.In this paper,we propose an error-bounded remeshing algorithm by adaptive re-finement.Different from previous methods,our approach allows the intermediate meshes to violate the error-bounded principle during the remeshing process.And specif-ically,we have developed a technique that may violate the error-bounded constraint during the remeshing process,but eventually generates results that satisfy the error-bounded constraint.Our approach is based on a key observation,that is,when more uniformly distributed vertices are added into the remeshed mesh,the error-bounded constraint is usually satisfied.For the input mesh,we first compute a geometrically sigificant target edge length field that measures the desired edge length value,then do an edge-based remehing,next we adaptively adjust the target edge length field and it-eratively perform the above steps until the error between the generated mesh and initial mesh is bounded.Further,in order to reduce the computational cost,we employ an approximate-to-accurate strategy,and the error could be firstly approximated and then accurate.Specifically,for the iterative steps described above,we first make the approx-imate error bounded and then ensure the exact error bounded.Experiments show that our method is robust,efficient and more practical for complex models.