Computer Graphics Forum最新文献

Unoriented surface reconstruction is an important task in computer graphics. Recently, methods based on the Gauss formula or winding number have achieved state-of-the-art performance in both orientation and surface reconstruction. The Gauss formula or winding number, derived from the fundamental solution of the Laplace equation, initially found applications in calculating potentials in electromagnetism. Inspired by the practical necessity of calculating potentials in diverse electromagnetic media, we consider the anisotropic Laplace equation to derive the anisotropic Gauss formula and apply it to surface reconstruction, called “anisotropic Gauss reconstruction”. By leveraging the flexibility of anisotropic coefficients, additional constraints can be introduced to the indicator function. This results in a stable linear system, eliminating the need for any artificial regularization. In addition, the oriented normals can be refined by computing the gradient of the indicator function, ultimately producing high-quality normals and surfaces. Regarding the space/time complexity, we propose an octree-based acceleration algorithm to achieve a space complexity of O(N) and a time complexity of O(NlogN). Our method can reconstruct ultra-large-scale models (exceeding 5 million points) within 4 minutes on an NVIDIA RTX 4090 GPU. Extensive experiments demonstrate that our method achieves state-of-the-art performance in both orientation and reconstruction, particularly for models with thin structures, small holes, or high genus. Both CuPy-based and CUDA-accelerated implementations are made publicly available at https://github.com/mayueji/AGR.

This paper studies the problem of unconstrained (e.g. not orthogonal or unit) symmetric frame field design in volumes. Our principal contribution is a novel (and theoretically well-founded) local integrability condition for frame fields represented as a triplet of symmetric tensors of second, fourth, and sixth order. We also formulate a novel smoothness energy for this representation. To validate our discritization, we study the problem of seamless parameterization of volumetric objects. We compare against baseline approaches by formulating a smooth, integrable, and approximately octahedral frame objective in our discritization. Our method is the first to solve these problems with automatic placement of singularities while also enforcing a symmetric proxy for local integrability as a hard constraint, achieving significantly higher quality parameterizations, in expectation, relative to other frame field design based approaches.

Finding correspondences between 3D deformable shapes is an important and long-standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in size, restricting their adaptation to different problem settings, including both full and partial shape matching. In particular the existing partial shape matching datasets are small (fewer than 100 shapes) and thus unsuitable for data-hungry machine learning approaches. Moreover, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations, we introduce a generic and flexible framework for the procedural generation of challenging full and partial shape matching datasets. Our framework allows the propagation of custom annotations across shapes, making it useful for various applications. By utilising our framework and manually creating cross-dataset correspondences between seven existing (complete geometry) shape matching datasets, we propose a new large benchmark BeCoS with a total of 2543 shapes. Based on this, we offer several challenging benchmark settings, covering both full and partial matching, for which we evaluate respective state-of-the-art methods as baselines. Visualisations and code of our benchmark can be found at: https://nafieamrani.github.io/BeCoS/.

This work presents the Affine Heat Method for computing logarithmic maps. These maps are local surface parameterizations defined by the direction and distance along shortest geodesic paths from a given source point, and arise in many geometric tasks from local texture mapping to geodesic distance-based optimization. Our main insight is to define a connection Laplacian with a homogeneous coordinate accounting for the translation between tangent coordinate frames; the action of short-time heat flow under this Laplacian gives both the direction and distance from the source, along shortest geodesics. The resulting numerical method is straightforward to implement, fast, and improves accuracy compared to past approaches. We present two variants of the method, one of which enables pre-computation for fast repeated solves, while the other resolves the map even near the cut locus in high detail. As with prior heat methods, our approach can be applied in any dimension and to any spatial discretization, including polygonal meshes and point clouds, which we demonstrate along with applications of the method.

We present a framework to integrate secondary motion into the existing animation pipelines. Skinning provides fast computation for real-time animation and intuitive control over the deformation. Despite the benefits, traditional skinning methods lack secondary dynamics such as the jiggling of fat tissues. We address the rigidity of skinning methods by physically simulating the deformation handles with spring forces. Most studies introduce secondary motion into skinning by employing FEM simulation on volumetric mesh vertices, coupling their computational complexity with mesh resolution. Unlike these approaches, we do not require any volumetric mesh input. Our method scales to higher mesh resolutions by directly simulating deformation handles. The simulated handles, namely the spring bones, enrich rigid skinning deformation with a diverse range of secondary animation for subjects including rigid bodies, elastic bodies, soft tissues, and cloth simulation. In essence, we leverage the benefits of physical simulations in the scope of deformation handles to achieve controllable real-time dynamics on a wide range of subjects while remaining compatible with existing skinning pipelines. Our method avoids tetrahedral remeshing and it is significantly faster compared to FEM-based volumetric mesh simulations.

The mesh kernel for a star-shaped mesh is a convex polyhedron given by the intersection of all half-spaces defined by the faces of the input mesh. For all non-star-shaped meshes, the kernel is empty. We present a method to robustly and efficiently compute the kernel of an input triangle mesh by using exact plane-based integer arithmetic to compute the mesh kernel. We make use of several ways to accelerate the computation time. Since many applications just require information if a non-empty mesh kernel exists, we also propose a method to efficiently determine whether a kernel exists by developing an exact plane-based linear program solver. We evaluate our method on a large dataset of triangle meshes and show that in contrast to previous methods, our approach is exact and robust while maintaining a high performance. It is on average two orders of magnitude faster than other exact state-of-the-art methods and often about one order of magnitude faster than non-exact methods.

Shape interpolation is a long standing challenge of geometry processing. As it is ill-posed, shape interpolation methods always work under some hypothesis such as semantic part matching or least displacement. Among such constraints, volume preservation is one of the traditional animation principles. In this paper we propose a method to interpolate between shapes in arbitrary poses favoring volume and topology preservation. To do so, we rely on a level set representation of the shape and its advection by a velocity field through the level set equation, both shape representation and velocity fields being parameterized as neural networks. While divergence free velocity fields ensure volume and topology preservation, they are incompatible with the Eikonal constraint of signed distance functions. This leads us to introduce the notion of adaptive divergence velocity field, a construction compatible with the Eikonal equation with theoretical guarantee on the shape volume preservation. In the non constant volume setting, our method is still helpful to provide a natural morphing, by combining it with a parameterization of the volume change over time. We show experimentally that our method exhibits better volume preservation than other recent approaches, limits topological changes and preserves the structures of shapes better without landmark correspondences.

We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.

Many common approaches for reconstructing surfaces from point clouds leverage normal information to fit an implicit function to the points. Normals typically play two roles: the direction provides a planar approximation to the surface and the sign distinguishes inside from outside. When the sign is missing, reconstructing a surface with globally consistent sidedness is challenging.

In this work, we investigate the idea of squaring the Poisson Surface Reconstruction, replacing the normals with their outer products, making the approach agnostic to the signs of the input/estimated normals. Squaring results in a quartic optimization problem, for which we develop an iterative and hierarchical solver, based on setting the cubic partial derivatives to zero. We show that this technique significantly outperforms standard L-BFGS solver and demonstrate reconstruction of surfaces from unoriented noisy input in linear time.

Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present DualCube: an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a dual representation of polycubes. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. DualCube is robust by construction: at any point during the iterative process the current segmentation is valid. Its iterative nature furthermore facilitates a seamless trade-off between quality and complexity of the solution. DualCube can be implemented using comparatively simple algorithmic building blocks; our experimental evaluation establishes that the quality of our polycube segmentations is on par with, or exceeding, the state-of-the-art.