We propose a novel method to generate high-quality triangular meshes with specified anisotropy. Central to our algorithm is to present metric-adapted embeddings for converting the anisotropic meshing problem to an isotropic meshing problem with constant density. Moreover, the orientation of the input Riemannian metric forms a field, enabling us to use field-based meshing techniques to improve regularity and penalize obtuse angles. To achieve such metric-adapted embeddings, we use the cone singularities , which are generated to adapt to the input Riemannian metric. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves higher quality on all metrics in most models.

Many geometric optimization problems contain manifold constraints that restrict the optimized vertices on some specified manifold surface. The constraints are highly nonlinear and non-convex, therefore existing methods usually suffer from a breach of condition or low optimization quality. In this article, we present a novel divide-and-conquer methodology for manifold-constrained geometric optimization problems. Central to our methodology is to use local parameterizations to decouple the optimization with hard constraints, which transforms nonlinear constraints into linear constraints. We decompose the input mesh into a set of developable or nearly-developable overlapping patches with disc topology, then flatten each patch into the planar domain with very low isometric distortion, optimize vertices with linear constraints and recover the patch. Finally, we project it onto the constrained manifold surface. We demonstrate the applicability and robustness of our methodology through a variety of geometric optimization tasks. Experimental results show that our method performs much better than existing methods.

A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

A deep learning-based intelligent scalp diagnosis system will be demonstrated. This live demonstration system is composed of a scalp detector, a mobile device app, an AI computing server, and a cloud-based service platform. During the live demonstration, this system can inference five scalp symptoms based on deep-learning technology for helping the treatment of hair salon or therapy services to achieve the purpose of scalp healthcare.

Abstract As high‐precision 3D scanners become more and more widespread, it is easy to obtain very‐large‐scale meshes containing at least millions of vertices. However, processing these very‐large‐scale meshes is still a very challenging task due to memory limitations. This paper focuses on a fundamental geometric processing task, i.e., bijective parameterization construction. To this end, we present a spline‐enhanced method to compute bijective and low distortion parameterizations for very‐large‐scale disk topology meshes. Instead of computing descent directions using the mesh vertices as variables, we estimate descent directions for each vertex by optimizing a proxy energy defined in spline spaces. Since the spline functions contain a small set of control points, it significantly decreases memory requirement. Besides, a divide‐and‐conquer method is proposed to obtain bijective initializations, and a submesh‐based optimization strategy is developed to reduce distortion further. The capability and feasibility of our method are demonstrated over various complex models. Compared to the existing methods for bijective parameterizations of very‐large‐scale meshes, our method exhibits better scalability and requires much less memory.

We propose a novel method to efficiently compute bijective parameterizations with low distortion on disk topology meshes. Our method relies on a second-order solver. To design an efficient solver, we develop two key techniques. First, we propose a coarse shell to substantially reduce the number of collision constraints that are used to guarantee overlap-free boundaries. During the optimization process, the shell ensures the Hessian matrix with a fixed nonzero structure and a low density, thereby significantly accelerating the optimization. The second is a triangle inequality-based barrier function that effectively ensures non-intersecting boundaries. Our barrier function is C ∞ inside the locally supported region and its convex second-order approximation is able to be analytically obtained. Compared to state-of-the-art methods for optimizing bijective parameterizations, our method exhibits better scalability and is about six times faster. The performance of our bijective parameterization algorithm is comparable to state-of-the-art methods of locally flip-free parameterizations. A large number of experimental results have shown the capability and feasibility of our method.

Abstract In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.