Unsigned distance fields (UDFs) provide a versatile framework for representing a diverse array of 3D shapes, encompassing both watertight and non-watertight geometries. Traditional UDF learning methods typically require extensive training on large 3D shape datasets, which is costly and necessitates re-training for new datasets. This paper presents a novel neural framework, LoSF-UDF, for reconstructing surfaces from 3D point clouds by leveraging local shape functions to learn UDFs. We observe that 3D shapes manifest simple patterns in localized regions, prompting us to develop a training dataset of point cloud patches characterized by mathematical functions that represent a continuum from smooth surfaces to sharp edges and corners. Our approach learns features within a specific radius around each query point and utilizes an attention mechanism to focus on the crucial features for UDF estimation. Despite being highly lightweight, with only 653 KB of trainable parameters and a modest-sized training dataset with 0.5 GB storage, our method enables efficient and robust surface reconstruction from point clouds without requiring for shape-specific training. Furthermore, our method exhibits enhanced resilience to noise and outliers in point clouds compared to existing methods. We conduct comprehensive experiments and comparisons across various datasets, including synthetic and real-scanned point clouds, to validate our method’s efficacy. Notably, our lightweight framework offers rapid and reliable initialization for other unsupervised iterative approaches, improving both the efficiency and accuracy of their reconstructions. Our project and code are available at https://jbhu67.github.io/LoSF-UDF.github.io/.

Abstract Topological properties play a crucial role in the analysis, reconstruction, and generation of 3D shapes. Yet, most existing research focuses primarily on geometric features, due to the lack of effective representations for topology. In this paper, we introduce TopoGen , a method that extracts both discrete and continuous topological descriptors–Betti numbers and persistence points–using persistent homology. These features provide robust characterizations of 3D shapes in terms of their topology. We incorporate them as conditional guidance in generative models for 3D shape synthesis, enabling topology‐aware generation from diverse inputs such as sparse and partial point clouds, as well as sketches. Furthermore, by modifying persistence points, we can explicitly control and alter the topology of generated shapes. Experimental results demonstrate that TopoGen enhances both diversity and controllability in 3D generation by embedding global topological structure into the synthesis process.

Joint injuries, and their long-term consequences, present a substantial global health burden. Wearable prophylactic braces are an attractive potential solution to reduce the incidence of joint injuries by limiting joint movements that are related to injury risk. Given human motion and ground reaction forces, we present a computational framework that enables the design of personalized braces by optimizing the distribution of microstructures and elasticity. As varied brace designs yield different reaction forces that influence kinematics and kinetics analysis outcomes, the optimization process is formulated as a differentiable end-to-end pipeline in which the design domain of microstructure distribution is parameterized onto a neural network. The optimized distribution of microstructures is obtained via a self-learning process to determine the network coefficients according to a carefully designed set of losses and the integrated biomechanical and physical analyses. Since knees and ankles are the most commonly injured joints, we demonstrate the effectiveness of our pipeline by designing, fabricating, and testing prophylactic braces for the knee and ankle to prevent potentially harmful joint movements.

Designing thin-shell structures that are diverse, lightweight, and physically viable is a challenging task for traditional heuristic methods. To address this challenge, we present a novel parametric design framework for engraving regular, irregular, and customized patterns on thin-shell structures. Our method optimizes pattern parameters such as size and orientation, to ensure structural stiffness while minimizing material consumption. Our method is unique in that it works directly with shapes and patterns represented by functions, and can engrave patterns through simple function operations. By eliminating the need for remeshing in traditional FEM methods, our method is more computationally efficient in optimizing mechanical properties and can significantly increase the diversity of shell structure design. Quantitative evaluation confirms the convergence of the proposed method. We conduct experiments on regular, irregular, and customized patterns and present 3D printed results to demonstrate the effectiveness of our approach.

Abstract Efficiently optimizing the internal structure of 3D printing models is a critical focus in the field of industrial manufacturing, particularly when designing self‐supporting structures that offer high stiffness and lightweight characteristics. To tackle this challenge, this research introduces a novel approach featuring a self‐supporting polyhedral structure and an efficient optimization algorithm. Specifically, the internal space of the model is filled with a combination of self‐supporting octahedrons and tetrahedrons, strategically arranged to maximize structural integrity. Our algorithm optimizes the wall thickness of the polyhedron elements to satisfy specific stiffness requirements, while ensuring efficient alignment of the filled structures in finite element calculations. Our approach results in a considerable decrease in optimization time. The optimization process is stable, converges rapidly, and consistently delivers effective results. Through a series of experiments, we have demonstrated the effectiveness and efficiency of our method in achieving the desired design objectives.

In this approach, we present an efficient topology and geometry optimization of triply periodic minimal surfaces (TPMS) based porous shell structures, which can be represented, analyzed, optimized and stored directly using functions. The proposed framework is directly executed on functions instead of remeshing (tetrahedral/hexahedral), and this framework substantially improves the controllability and efficiency. Specifically, a valid TPMS-based porous shell structure is first constructed by function expressions. The porous shell permits continuous and smooth changes of geometry (shell thickness) and topology (porous period). The porous structures also inherit several of the advantageous properties of TPMS, such as smoothness, full connectivity (no closed hollows), and high controllability. Then, the problem of filling an object's interior region with porous shell can be formulated into a constraint optimization problem with two control parameter functions. Finally, an efficient topology and geometry optimization scheme is presented to obtain optimized scale-varying porous shell structures. In contrast to traditional heuristic methods for TPMS, our work directly optimize both the topology and geometry of TPMS-based structures. Various experiments have shown that our proposed porous structures have obvious advantages in terms of efficiency and effectiveness.

Informative and discriminative feature descriptors are vital in qualitative and quantitative shape analysis for a large variety of graphics applications. Conventional feature descriptors primarily concentrate on discontinuity of certain differential attributes at different orders that naturally give rise to their discriminative power in depicting point, line, small patch features, etc. This paper seeks novel strategies to define generalized, user-specified features anywhere on shapes. Our new region-based feature descriptors are constructed primarily with the powerful spectral graph wavelets (SGWs) that are both multi-scale and multi-level in nature, incorporating both local (differential) and global (integral) information. To our best knowledge, this is the first attempt to organize SGWs in a hierarchical way and unite them with the bi-harmonic diffusion field towards quantitative region-based shape analysis. Furthermore, we develop a local-to-global shape feature detection framework to facilitate a host of graphics applications, including partial matching without point-wise correspondence, coarse-to-fine recognition, model recognition, etc. Through the extensive experiments and comprehensive comparisons with the state-of-the-art, our framework has exhibited many attractive advantages such as being geometry-aware, robust, discriminative, isometry-invariant, etc.

ABSTRACT This paper systematically advocates an interactive volumetric image manipulation framework, which can enable the rapid deployment and instant utility of patient‐specific medical images in virtual surgery simulation while requiring little user involvement. We seamlessly integrate multiple technical elements to synchronously accommodate physics‐plausible simulation and high‐fidelity anatomical structures visualization. Given a volumetric image, in a user‐transparent way, we build a proxy to represent the geometrical structure and encode its physical state without the need of explicit 3‐D reconstruction. On the basis of the dynamic update of the proxy, we simulate large‐scale deformation, arbitrary cutting, and accompanying collision response driven by a non‐linear finite element method. By resorting to the upsampling of the sparse displacement field resulted from non‐linear finite element simulation, the cut/deformed volumetric image can evolve naturally and serves as a time‐varying 3‐D texture to expedite direct volume rendering. Moreover, our entire framework is built upon CUDA (Beihang University, Beijing, China) and thus can achieve interactive performance even on a commodity laptop. The implementation details, timing statistics, and physical behavior measurements have shown its practicality, efficiency, and robustness. Copyright © 2013 John Wiley & Sons, Ltd.

Geometry images are important representations of 3D geometry models. Smooth geometry images contributes to low approximation error and high image compressibility. We present an adapted parameterization method to generate a smooth geometry image. It is quite challenging to directly modify the parameter domain to smooth geometry images. Our novel idea is that we use an indirect way to construct a resulting parameter domain according to the desired geometry image. We first move image pixels according to the current parameter domain to decrease the local linear error. Then we formulate a relationship between the moved image pixels and the current parameter domain. Finally, we use the relationship to update the parameter domain by restituting the image pixels to their original positions. The process will continue until the local linear error is less than a given threshold or the number of iterations is larger than a given threshold. Experimental results illustrate that geometry images generated by our method have low linear errors and low approximation errors under different sampling resolutions.

This paper articulates a novel method for the heterogeneous feature extraction and classification directly on volumetric images, which covers multi-scale point feature, multi-scale surface feature, multi-level curve feature, and blob feature. To tackle the challenge of complex volumetric inner structure and diverse feature forms, our technical solution hinges upon the integrated approach of locally-defined diffusion tensor (DT), DT-based anisotropic convolution kernel (DACK), DACK-based multi-scale analysis, and DT-governed curve feature growing. The extracted structural features can be further semantically classified. At the computational fronts, we design CUDA-based algorithm to conduct parallel computation for time consuming tasks. Various experiments and timing tests demonstrate the effectiveness, robustness, and high performance of our method.

The extraction and classification of multitype (point, curve, patch) features on manifolds are extremely challenging, due to the lack of rigorous definition for diverse feature forms. This paper seeks a novel solution of multitype features in a mathematically rigorous way and proposes an efficient method for feature classification on manifolds. We tackle this challenge by exploring a quasi-harmonic field (QHF) generated by elliptic PDEs, which is the stable state of heat diffusion governed by anisotropic diffusion tensor. Diffusion tensor locally encodes shape geometry and controls velocity and direction of the diffusion process. The global QHF weaves points into smooth regions separated by ridges and has superior performance in combating noise/holes. Our method's originality is highlighted by the integration of locally defined diffusion tensor and globally defined elliptic PDEs in an anisotropic manner. At the computational front, the heat diffusion PDE becomes a linear system with Dirichlet condition at heat sources (called seeds). Our new algorithms afford automatic seed selection, enhanced by a fast update procedure in a high-dimensional space. By employing diffusion probability, our method can handle both manufactured parts and organic objects. Various experiments demonstrate the flexibility and high performance of our method.

E-collaboration and collaborative systems bring geographically dispersed teams together, and support communication, coordination and cooperation among the enterprises. Based on the collaborative design system developed by the author's lab for some automotive parts company in China, several key technologies for developing enterprise collaborative manufacturing platform (ECMP) are presented. A multi-layer architecture of ECMP is established, and the workflow of ECMP is designed. The application integration with Web services technology is explained. A four-layered ontology model for information description in ECMP is proposed. The method of constructing dynamic alliance based on multi-agent theory, and the strategies of task scheduling optimization are discussed. Finally, an application case of ECMP prototypical system is introduced

In order to implement the share and reuse of parts resource in networked collaborative design, method combining standard technology with XML to build parts library was put forward. At first, based on PLIB the conceptual model and hierarchical organization of parts resource were built. Then, the formalized-expression and storage for parts resource adopting tabular layouts of article characteristics were implemented. Thirdly, each rule of mapping the two kinds of data mode, EXPRESS and tabular layouts of article characteristics, to XML schema was presented to realize the parts library data conversion and transmission in network environment. At last, Web-based parts library sharing platform for networked collaborative design was built

The existing knowledge management system for CSCWD is analyzed. We aim at the shortages that the design knowledge can't be transmitted actively to the proper designer at the proper time in the present system, a framework based on knowledge management and driven by workflow is proposed and its main levels are analyzed. A novel active pushing method driven by workflow is proposed. The design task, design subtask, designer and design knowledge are studied in terms of the match method between design knowledge and designer. A two-step match method is proposed after their contents are analyzed. Finally a prototype system based on knowledge management and driven by workflow is developed and an example for eddy current retarder design is given