Minimizing the Gaussian curvature of meshes can play a fundamental role in 3D mesh processing. However, there is a lack of computationally efficient and robust Gaussian curvature optimization method. In this paper, we present a simple yet effective method that can efficiently reduce Gaussian curvature for 3D meshes. We first present the mathematical foundation of our method. Then, we introduce a simple and robust implicit Gaussian curvature optimization method named Gaussian Curvature Filter (GCF). GCF implicitly minimizes Gaussian curvature without the need to explicitly calculate the Gaussian curvature itself. GCF is highly efficient and this method can be used in a large range of applications that involve Gaussian curvature. We conduct extensive experiments to demonstrate that GCF significantly outperforms state-of-the-art methods in minimizing Gaussian curvature, and geometric feature preserving soothing on 3D meshes. GCF program is available at https://github.com/tangwenming/GCF-filter.
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