Computer Aided Geometric Design最新文献_第3页

A dynamic arrangement framework for automatic tooth alignment based on orthodontic rules 基于正畸规则的牙齿自动对齐动态排列框架

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-30 DOI: 10.1016/j.cagd.2025.102436

Yeying Fan , Guangshun Wei , Weijie Liu , Chuanxiang Yang , Chuanyun Fu , Wenping Wang , Yuanfeng Zhou

Automatically achieving functionally and aesthetically aligned teeth is a critical task in computer-aided orthodontic treatment. However, existing expert rule-based approaches still require manual intervention and focus solely on occlusion functionality. Meanwhile, data-driven methods rely on large paired datasets of pre- and post-treatment cases, making it challenging to address issues such as missing teeth or collisions effectively. To alleviate these problems, this paper proposes a novel framework DyOrthoAlign that translates the automatic tooth alignment into a dynamic arrangement process based on orthodontic rules. Our DyOrthoAlign consists of two stages. We first construct the ideal dental occlusion curve based on tooth anatomical features. Then, we arrange each tooth along the ideal occlusion curve in a specific order and a series of decisions. The dynamic arrangement process continues until all the teeth are arranged, resulting in the final ideal tooth arrangement. Extensive qualitative and quantitative experiments validate our framework can produce ideal tooth alignment and offer significant practical value for personalized and efficient orthodontic treatment.

在计算机辅助正畸治疗中，自动实现牙齿功能和美观对齐是一项关键任务。然而，现有的基于专家规则的方法仍然需要人工干预，并且只关注遮挡功能。同时，数据驱动的方法依赖于治疗前和治疗后病例的大型成对数据集，这使得有效解决缺牙或碰撞等问题具有挑战性。为了解决这些问题，本文提出了一种新的框架DyOrthoAlign，将牙齿自动对准转化为基于正畸规则的动态排列过程。我们的DyOrthoAlign包含两个阶段。首先根据牙齿的解剖特征构建理想牙合曲线。然后，我们将每颗牙齿沿着理想的咬合曲线以特定的顺序和一系列的决定排列。动态排列过程一直持续到所有的齿都排列整齐，从而得到最终理想的齿排。大量的定性和定量实验验证了我们的框架可以产生理想的牙齿排列，为个性化和高效的正畸治疗提供了重要的实用价值。

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引用次数: 0

Projection-driven grid-BSP tree for real-time trimming on GPU 投影驱动的网格- bsp树在GPU上的实时修剪

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-30 DOI: 10.1016/j.cagd.2025.102451

Jiaming Zhu , Yang Lu , Ruicheng Xiong , Cong Chen , Ligang Liu

In Computer Aided Design (CAD), trimmed non-uniform rational B-spline (NURBS) is the industrial standard to represent the shapes of models. Trimming, the process of removing unnecessary portions of a surface, remains a major performance bottleneck in the recent CAD model rendering methods based on real-time surface tessellation. In this paper, we identify the core reasons for the inefficiency in existing real-time trimming methods, and present a new trimming method that incurs nearly no cost in the state-of-the-art NURBS surface rendering pipeline. Our approach begins with building a projection-driven grid-bsp-tree with a fixed depth of two and leaf nodes containing only one single curve segment, effectively minimizing the overall cost of tree traversal and ray-curve intersections. Additionally, we reduce the cost of trimming tests by approximating trimming curves into poly-lines while keeping the storage consumption at a minimum, where the quality of the approximation is measured by a novel on-surface error metric. Compared with existing works, our method achieves consistent error control for across the entire model using a more reasonable error metric while requiring less memory. Compared to the previous kd-tree-based method, our method achieves a 70% speedup, reducing the trimming process to just 5% of the total rendering time, effectively eliminating it as a major performance bottleneck. Due to its superior performance, our method provides significant advantages for rendering large-scale CAD models.

在计算机辅助设计（CAD）中，裁剪非均匀有理b样条（NURBS）是表示模型形状的工业标准。修剪，即去除表面不必要部分的过程，仍然是当前基于实时曲面镶嵌的CAD模型绘制方法的主要性能瓶颈。在本文中，我们确定了现有实时切边方法效率低下的核心原因，并提出了一种新的切边方法，该方法在最先进的NURBS表面渲染管道中几乎没有成本。我们的方法首先构建一个投影驱动的grid-bsp-tree，其固定深度为两个，叶子节点仅包含一个单一的曲线段，有效地减少了树遍历和光线曲线相交的总成本。此外，我们通过将切边曲线近似为多线段来降低切边测试的成本，同时将存储消耗保持在最小，其中近似值的质量是通过一种新的表面误差度量来测量的。与已有的方法相比，该方法使用更合理的误差度量实现了对整个模型的一致性误差控制，同时需要更少的内存。与之前基于kd树的方法相比，我们的方法实现了70%的加速，将修剪过程减少到总渲染时间的5%，有效地消除了它作为主要性能瓶颈的影响。由于其优越的性能，我们的方法为绘制大规模CAD模型提供了显着的优势。

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引用次数: 0

Computing the intersection of two ellipsoids based on a fast algebraic topology determination strategy 基于快速代数拓扑确定策略的两个椭球相交计算

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-29 DOI: 10.1016/j.cagd.2025.102442

Xiao Chu , Kai Li , Xiaohong Jia , Jieyin Yang , Jiarui Kang

Ellipsoids serve as the most commonly used geometric primitives and bounding volumes in computer-aided design and computer graphics, where an efficient and topologically stable intersection algorithm between two ellipsoids is highly required. Although there has been extensive research on intersections of two general quadrics, ellipsoids have their own specialty in both algebra and geometry which guides to new possibilities to break the bottleneck in intersection computation. In this paper, we use a topology-determination-based strategy in computing the intersection of ellipsoids. Firstly, the topology of the intersection curve is quickly determined using some algebraic discriminants without computing any point on the intersection curve; then an octree strategy is applied to efficiently compute at least one point on each intersection branch; finally, by tracing the branch, we get the complete intersection loci. Plenty of examples show that our algorithm is topologically stable when facing challenging cases including multi-branches, small loops, singular or tangent intersections, and is more efficient compared with existing algorithms.

椭球体是计算机辅助设计和计算机图形学中最常用的几何基元和边界体，这对椭球体间高效且拓扑稳定的相交算法提出了很高的要求。虽然对于两种一般二次曲面的相交已经有了大量的研究，但椭球体在代数和几何上都有自己的特点，这为突破相交计算的瓶颈提供了新的可能性。在本文中，我们使用基于拓扑确定的策略来计算椭球的交点。首先，在不计算交点的情况下，利用代数判别式快速确定交点曲线的拓扑结构；然后采用八叉树策略，在每个交点分支上高效地计算出至少一个点；最后，通过对分支的跟踪，得到完整的交点轨迹。大量的算例表明，该算法在面对多分支、小环路、奇异或切交等复杂情况时拓扑稳定，比现有算法效率更高。

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引用次数: 0

Physics and geometry-augmented neural implicit surfaces for rigid bodies 刚体的物理和几何增强神经隐式曲面

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-29 DOI: 10.1016/j.cagd.2025.102437

Yuanmu Xu , Guanli Hou , Jiangbei Hu , Tenglong Ren , Xiaokun Wang , Yalan Zhang , Xiaojuan Ban , Chen Qian , Fei Hou , Ying He

This paper tackles the challenges of physics-based simulation of rigid bodies in neural rendering, with a focus on 3D model representation and collision handling. We propose Physics and Geometry-Augmented Neural Implicit Surfaces (PGA-NeuS), a novel approach that combines neural implicit surfaces with a differentiable physics solver. In the pre-processing stage, PGA-NeuS reconstructs static scene and object geometry from multi-view images using signed distance fields (SDFs). For dynamic scenes captured in monocular videos, these SDFs, along with the initial position and orientation of moving rigid bodies, are fed into a differentiable rigid body solver to optimize physical parameters, such as initial velocity and friction coefficients. Subsequently, PGA-NeuS leverages color loss, physics loss, and object mask supervision to iteratively refine the neural implicit surface, ensuring the target object's alignment with the predicted motion sequence. We evaluate PGA-NeuS on five real-world scenes, demonstrating its ability to accurately reconstruct realistic motion sequences and estimate physical parameters such as position and velocity. Dataset and source code are available at https://github.com/Raining00/PGA-NeuS.

本文解决了神经渲染中基于物理的刚体模拟的挑战，重点是3D模型表示和碰撞处理。我们提出了物理和几何增强神经隐式曲面（PGA-NeuS），这是一种将神经隐式曲面与可微物理求解器相结合的新方法。在预处理阶段，PGA-NeuS使用符号距离场（sdf）从多视图图像中重建静态场景和物体几何形状。对于单目视频中捕获的动态场景，这些sdf与运动刚体的初始位置和方向一起被馈送到可微刚体求解器中，以优化物理参数，如初始速度和摩擦系数。随后，PGA-NeuS利用颜色损失、物理损失和对象掩码监督来迭代地改进神经隐式表面，确保目标对象与预测的运动序列对齐。我们在五个真实场景中对PGA-NeuS进行了评估，证明了它能够准确地重建真实的运动序列并估计位置和速度等物理参数。数据集和源代码可从https://github.com/Raining00/PGA-NeuS获得。

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引用次数: 0

Weingarten surface approximation by curvature diagram transformation 曲率图变换的维因加滕曲面近似

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-28 DOI: 10.1016/j.cagd.2025.102438

Fei Huang , Caigui Jiang , Yong-Liang Yang

Weingarten surfaces are characterized by a functional relation between their principal curvatures. Such a specialty makes them suitable for building surface paneling in architectural applications, as the curvature relation implies approximate local congruence on the surface thus the molds for paneling can be largely reused. In this work, we aim at a novel task of Weingarten surface approximation. Given a surface mesh with arbitrary topology, we optimize its shape to make it as Weingarten as possible. We devise a curvature-based optimization approach based on the fact that the 2D principal curvature plots of a Weingarten surface comprise a group of 1D curves that encode the curvature relations. Our approach alternatively performs two steps. The first step transforms the principal curvature plots from a 2D region to 1D curves in order to explore the curvature relations. The second step deforms the shape such that its curvatures conform to the corresponding transformed curvature plots. We demonstrate the effectiveness of our work on a variety of shapes with different topologies. Hopefully our work would bring inspiration on the study of general Weingarten surfaces with arbitrary topology and curvature relation.

温加滕曲面的特征是其主曲率之间的函数关系。这种特性使它们适合于建筑应用中的建筑表面镶板，因为曲率关系意味着表面上的近似局部同余，因此镶板模具可以大量重复使用。在这项工作中，我们的目标是一个新的任务Weingarten曲面逼近。给定一个具有任意拓扑结构的表面网格，我们优化其形状以使其尽可能符合Weingarten。基于Weingarten曲面的二维主曲率图由一组编码曲率关系的一维曲线组成这一事实，我们设计了一种基于曲率的优化方法。我们的方法执行两个步骤。第一步将主曲率图从二维区域转换为一维曲线，以探索曲率关系。第二步对形状进行变形，使其曲率符合相应的变换曲率图。我们展示了我们在具有不同拓扑的各种形状上的工作的有效性。希望我们的工作能对具有任意拓扑和曲率关系的一般Weingarten曲面的研究带来启示。

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引用次数: 0

Efficient neural RGB-D indoor scene reconstruction based on normal features 基于正常特征的高效神经RGB-D室内场景重建

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-25 DOI: 10.1016/j.cagd.2025.102452

Xiaoqun Wu, Xin Liu, Yumeng Cao, Haisheng Li

Reconstructing large-scale indoor scenes from 2D images to 3D models presents substantial challenges, particularly in handling texture-less regions and extensive scene sizes with both accuracy and efficiency. This paper introduces a novel method for efficient and high-quality geometric reconstruction of indoor scenes using RGB-D images. Our approach integrates normal features as prior information into the RGB-D data and employs a truncated signed distance function (TSDF) to represent scene surfaces. Combined with multi-resolution hash encoding, the proposed method achieves both high reconstruction quality and computational efficiency. Specifically, we estimate normal vectors from RGB images as feature priors to guide surface fitting. To address the inaccuracies of normal estimation in regions with small objects or complex geometric details, we incorporate depth information to better constrain the surface fitting process. Additionally, multi-resolution hash encoding is used to stratify sampling points, enabling rapid feature lookups via hash functions. Experimental results demonstrate that the proposed method significantly outperforms existing approaches in terms of both reconstruction quality and computational efficiency.

从2D图像到3D模型重建大规模室内场景提出了巨大的挑战，特别是在处理无纹理区域和具有准确性和效率的广泛场景尺寸方面。本文介绍了一种利用RGB-D图像对室内场景进行高效、高质量几何重建的新方法。我们的方法将常规特征作为先验信息集成到RGB-D数据中，并使用截断符号距离函数（TSDF）来表示场景表面。结合多分辨率哈希编码，该方法具有较高的重建质量和计算效率。具体来说，我们从RGB图像中估计法向量作为特征先验来指导表面拟合。为了解决在具有小目标或复杂几何细节的区域中正态估计的不准确性，我们结合了深度信息来更好地约束表面拟合过程。此外，多分辨率哈希编码用于分层采样点，通过哈希函数实现快速特征查找。实验结果表明，该方法在重建质量和计算效率方面都明显优于现有方法。

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引用次数: 0

What smooth surfaces can be constructed from total degree 2 splines? 2次样条曲线可以构造出什么样的光滑曲面？

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-25 DOI: 10.1016/j.cagd.2025.102435

Jörg Peters, Kȩstutis Karčiauskas

On a planar Euclidean domain, Powell-Sabin splines form a rich space of

C^{1}

polynomials of total degree 2, i.e. with constant second derivatives. However, when the domain has a different structure because the genus of the surface is not 1, building curved free-form surfaces solely with total degree quadratic polynomials, with each piece defined over a flat, straight-edge domain triangle, meets with obstructions. By pinpointing these obstructions, the limitations of modeling with quadratics are made precise, the allowable

C^{1}

free-form constructions are characterized and their necessary shape-deficiency is demonstrated.

在平面欧几里得域上，Powell-Sabin样条形成了一个总次为2的C1多项式的丰富空间，即二阶导数为常数的空间。然而，当由于曲面的格不为1而使该域具有不同的结构时，仅用总次二次多项式构建弯曲的自由曲面，并且每一块都定义在一个平坦的直边域三角形上，就会遇到阻碍。通过对这些障碍的精确定位，明确了二次曲面建模的局限性，对允许的C1自由形式结构进行了表征，并证明了它们必要的形状缺陷。

引用次数: 0

Feature-preserving point cloud filtering via mixture family manifold 基于混合族流形的特征保持点云滤波

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-25 DOI: 10.1016/j.cagd.2025.102453

Peng Du, Xingce Wang, Yaohui Fang, Xudong Ru, Haichuan Zhao, Zhongke Wu

Filtering noisy point cloud of complex models while effectively preserving geometric features, especially fine-scale features, presents the main challenge. In this paper, we propose a non-learning, feature-preserving point cloud filtering method from the novel perspective of mixture family manifold, which does not require normal estimation and does not depend on the distribution of the input data. Our novel perspective refers to formulate a potential function regularization term, related to Shannon entropy, within the mixture family manifold parameterized by the mixture weights. This regularization constrains the parameter estimation in the point cloud filtering model inspired by the Gaussian Mixture Model (GMM), avoiding the use of purely distance-based isotropic weights. Our method effectively removes noise while preserving geometric details. Experimental results on both synthetic and scanned data demonstrate that our approach outperforms the selected state-of-the-art methods, including those that roughly utilize normal information for point cloud filtering.

在有效保留几何特征，特别是精细尺度特征的同时，对复杂模型的噪声点云进行滤波是目前面临的主要挑战。本文从混合族流形的新角度提出了一种不需要正态估计且不依赖于输入数据分布的非学习、特征保持的点云滤波方法。我们的新观点是在由混合权重参数化的混合族流形中建立一个与香农熵相关的势函数正则化项。这种正则化约束了受高斯混合模型（GMM）启发的点云滤波模型中的参数估计，避免了纯粹基于距离的各向同性权重的使用。我们的方法在保留几何细节的同时有效地去噪。合成数据和扫描数据的实验结果表明，我们的方法优于所选的最先进的方法，包括那些大致利用正常信息进行点云过滤的方法。

引用次数: 0

Transfinite barycentric coordinates for arbitrary planar domains 任意平面域的超有限质心坐标

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-23 DOI: 10.1016/j.cagd.2025.102433

Qingjun Chang, Kai Hormann

Generalized barycentric coordinates provide a simple way of interpolating data given at the vertices of a polygon or polyhedron, with widespread applications in computer graphics, geometry processing, and other fields. Transfinite barycentric coordinates, also known as barycentric kernels, extend this idea to curved domains and can be used to interpolate continuous data given on the boundary of such domains. We present a novel framework for defining non-negative barycentric kernels over arbitrary bounded planar domains. This framework is inspired by the construction of a transfinite version of maximum likelihood coordinates and can be used to define a variety of barycentric kernels, including a simple pseudo-harmonic kernel and a non-negative variant of the mean value kernel. Moreover, we propose a novel barycentric kernel which yields transfinite interpolants that are similar to harmonic interpolants. We tested our new kernel for domains and boundary data described by closed uniform quadratic splines and in particular for image deformation. The results indicate that our method has several advantages over alternative approaches.

广义重心坐标是对多边形或多面体顶点上的数据进行内插的一种简单方法，在计算机制图、几何处理和其他领域有着广泛的应用。无穷重心坐标也称为重心核，它将这一理念扩展到了曲面域，可用于插值曲面域边界上的连续数据。我们提出了一个新框架，用于定义任意有界平面域上的非负重心核。该框架的灵感来自于最大似然坐标的无穷版本的构建，可用于定义各种重心核，包括简单的伪谐波核和均值核的非负变体。此外，我们还提出了一种新的重心核，它能产生类似于谐波插值的无穷插值。我们对封闭均匀二次样条描述的域和边界数据，特别是图像变形测试了我们的新核。结果表明，与其他方法相比，我们的方法具有多项优势。

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引用次数: 0

MTSegNet: Manifold Transformer for 3D shape segmentation MTSegNet：用于3D形状分割的歧管变压器

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-04-22 DOI: 10.1016/j.cagd.2025.102440

Zhenyu Shu , Zhichao Zhang , Yiming Zhao , Teng Wu

The semantic segmentation of 3D meshes is a critical component of 3D shape analysis, which involves assigning semantic labels to each face of a 3D mesh. Despite its significance, current methods often struggle to capture manifold information in 3D meshes, a fundamental characteristic distinguishing them from other representation forms of 3D data, like 3D point clouds or 3D voxels, resulting in suboptimal segmentation outcomes. In this paper, we propose a novel Transformer-based approach, Manifold Transformer (MTSegNet), for 3D mesh semantic segmentation, which effectively learns manifold information. By using hierarchical Transformers, MTSegNet can capture both local and global features of 3D meshes, while reducing the computational complexity and memory consumption. To further improve the performance of our method, we design an effective input-generating algorithm that serializes input data into multiple sequences of tokens that represent the geometry and topology of 3D meshes. This algorithm preserves the structural information and spatial relations of 3D meshes, while enabling the use of standard Transformer architectures. The proposed method is evaluated on four benchmark datasets: PSB, COSEG, ShapeNetCore, and HumanBody, and it achieves state-of-the-art results on all datasets, outperforming the previous methods.

三维网格的语义分割是三维形状分析的一个重要组成部分，它涉及到为三维网格的每个面分配语义标签。尽管具有重要意义，但目前的方法往往难以捕获3D网格中的流形信息，这是将它们与3D数据的其他表示形式（如3D点云或3D体素）区分开来的基本特征，导致分割结果不理想。在本文中，我们提出了一种新的基于变压器的三维网格语义分割方法，流形变压器（MTSegNet），它可以有效地学习流形信息。通过使用分层变压器，MTSegNet可以同时捕获3D网格的局部和全局特征，同时降低计算复杂度和内存消耗。为了进一步提高我们的方法的性能，我们设计了一个有效的输入生成算法，该算法将输入数据序列化为多个表示3D网格几何和拓扑的令牌序列。该算法保留了三维网格的结构信息和空间关系，同时能够使用标准的Transformer架构。在PSB、COSEG、ShapeNetCore和HumanBody四个基准数据集上对该方法进行了评估，结果表明该方法在所有数据集上都取得了最先进的结果，优于之前的方法。

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引用次数: 0