BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}

Composing quadrilateral meshes for animation

The modeling-by-composition paradigm can be a powerful tool in modern animation pipelines. We propose two novel interactive techniques to compose 3D assets that enable the artists to freely remove, detach and combine components of organic models. The idea behind our methods is to preserve most of the original information in the input characters and blend accordingly where necessary. The first method, QuadMixer, provides a robust tool to compose the quad layouts of watertight pure quadrilateral meshes, exploiting the boolean operations defined on triangles. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving the shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. The resulting meshes preserve the originally designed edge flows that, by construction, are captured and incorporated into the new quads. SkinMixer extends this approach to compose skinned models, taking into account not only the surface but also the data structures for animating the character. We propose a new operation-based technique that preserves and smoothly merges meshes, skeletons, and skinning weights. The retopology approach of QuadMixer is extended to work on quad-dominant and arbitrary complex surfaces. Instead of relying on boolean operations on triangle meshes, we manipulate signed distance fields to generate an implicit surface. The results preserve most of the information in the input assets, blending accordingly in the intersection regions. The resulting characters are ready to be used in animation pipelines. Given the high quality of the results generated, we believe that our methods could have a huge impact on the entertainment industry. Integrated into current software for 3D modeling, they would certainly provide a powerful tool for the artists. Allowing them to automatically reuse parts of their well-designed characters could lead to a new approach for creating models, which would significantly reduce the cost of the process

Biharmonic fields and mesh completion

We discuss bi-harmonic fields which approximate signed distance fields. We conclude that the bi-harmonic field approximation can be a powerful tool for mesh completion in general and complex cases. We present an adaptive, multigrid algorithm to extrapolate signed distance fields. By defining a volume mask in a closed region bounding the area that must be repaired, the algorithm computes a signed distance field in well-defined regions and uses it as an over-determined boundary condition constraint for the biharmonic field computation in the remaining regions. The algorithm operates locally, within an expanded bounding box of each hole, and therefore scales well with the number of holes in a single, complex model. We discuss this approximation in practical examples in the case of triangular meshes resulting from laser scan acquisitions which require massive hole repair. We conclude that the proposed algorithm is robust and general, and is able to deal with complex topological casesPeer ReviewedPostprint (author's final draft

Neural Volumetric Mesh Generator

Deep generative models have shown success in generating 3D shapes with different representations. In this work, we propose Neural Volumetric Mesh Generator(NVMG) which can generate novel and high-quality volumetric meshes. Unlike the previous 3D generative model for point cloud, voxel, and implicit surface, the volumetric mesh representation is a ready-to-use representation in industry with details on both the surface and interior. Generating this such highly-structured data thus brings a significant challenge. We first propose a diffusion-based generative model to tackle this problem by generating voxelized shapes with close-to-reality outlines and structures. We can simply obtain a tetrahedral mesh as a template with the voxelized shape. Further, we use a voxel-conditional neural network to predict the smooth implicit surface conditioned on the voxels, and progressively project the tetrahedral mesh to the predicted surface under regularizations. The regularization terms are carefully designed so that they can (1) get rid of the defects like flipping and high distortion; (2) force the regularity of the interior and surface structure during the deformation procedure for a high-quality final mesh. As shown in the experiments, our pipeline can generate high-quality artifact-free volumetric and surface meshes from random noise or a reference image without any post-processing. Compared with the state-of-the-art voxel-to-mesh deformation method, we show more robustness and better performance when taking generated voxels as input

Measuring the Discrepancy between 3D Geometric Models using Directional Distance Fields

Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the correspondence between two models and then aggregating point-wise distance between corresponding points, resulting in them being either inefficient or ineffective. In this paper, we propose DirDist, an efficient, effective, robust, and differentiable distance metric for 3D geometry data. Specifically, we construct DirDist based on the proposed implicit representation of 3D models, namely directional distance field (DDF), which defines the directional distances of 3D points to a model to capture its local surface geometry. We then transfer the discrepancy between two 3D geometric models as the discrepancy between their DDFs defined on an identical domain, naturally establishing model correspondence. To demonstrate the advantage of our DirDist, we explore various distance metric-driven 3D geometric modeling tasks, including template surface fitting, rigid registration, non-rigid registration, scene flow estimation and human pose optimization. Extensive experiments show that our DirDist achieves significantly higher accuracy under all tasks. As a generic distance metric, DirDist has the potential to advance the field of 3D geometric modeling. The source code is available at \url{https://github.com/rsy6318/DirDist}