Automatic generation of high-quality fully-hexahedral meshes remains a challenging problem in engineering applications. In this paper, a PolyCube hexahedral mesh generation method based on line-surface hybrid skeleton and shape decomposition is proposed. Compared to existing methods, the proposed approach is of higher computational efficiency and capable of generating hexahedral meshes with better quality and more flexible structures. The method consists of three main stages: First, the skeleton of the input model is decomposed structurally and geometrically to produce a high-quality partitioning of the model. Next, a minimum-volume oriented bounding box is constructed for each sub-region so as to setup a local frame that minimizes the alignment cost of all bounding boxes with respect to this frame. Finally, the aligned bounding boxes are combined to form a multi-cube structure from which the hexahedral mesh is extracted, fitted back to the input mesh and optimized. We have tested our method on a wide range of models. Compared to existing hexahedral mesh generation techniques, our approach can produce fully-hexahedral meshes with simpler singularity structures and higher element quality.高质量的全六面体网格自动生成是工程应用中的一项挑战性工作。提出了一种基于线面混合骨架与形状分解的PolyCube六面体网格生成算法，较现有算法计算效率更高，能生成质量更高、结构更灵活的六面体网格。首先，对输入模型的骨架进行结构分解与几何分解，进而生成输入模型的高质量区域分解；然后，计算每个子区域的最小体积有向包围盒，同时计算一个局部标架，使得所有的包围盒对齐于该标架的旋转代价最小；最后，由组合对齐的包围盒生成多立方体结构，从中提取六面体网格，并将其拟合回输入网格并进行质量优化。不同模型的测试结果表明，与现有的六面体网格生成算法相比，所提算法能生成奇异结构更简单、单元质量更高的六面体网格。
The rapid development of the 3D animation, film and television production, and gaming industries has accumulated massive amounts of high-precision 3D human motion data, making efficient management and intelligent retrieval a serious challenge. In response to the two major bottlenecks in current cross modal retrieval research-insufficient modeling of the association between human motion and text semantics and high computational costs, this paper proposes a differentiable hash cross modal retrieval framework based on attention fusion. It innovatively constructs a dual channel Transformer framework to achieve feature extraction of motion capture data and natural language, captures fine-grained spatiotemporal correlations between motion sequences and text descriptions with learnable cross modal attention mechanisms, and designs an end-to-end hash encoding optimization strategy to compress high-dimensional features into compact binary streams. Experiments have shown that this method significantly improves the accuracy and efficiency of bidirectional motion text retrieval on commonly used datasets. Compared to the baseline model, the sum of recall rates has increased by 2.6 times, providing an efficient solution for motion data reuse in fields such as digital entertainment.随着三维动画、影视制作及游戏产业的快速发展，海量高精度三维人体运动数据不断积累，数据的高效管理与智能检索面临重大挑战。针对当前在跨模态检索研究中存在的人体运动与文本语义关联性建模不足及计算成本过高这两大瓶颈，提出一种基于注意力机制的可微分哈希跨模态检索框架，构建的双通道Transformer架构实现了对运动数据的捕捉与自然语言特征的提取，以可学习的跨模态注意力机制捕捉运动序列与文本描述间的细粒度时空关联，并通过设计端到端的哈希编码优化策略将高维特征压缩为紧凑的二进制码流。在常用数据集上实现了运动-文本双向检索精度与效率的显著提升，召回率总和较基线模型提升了2.6倍，为数字娱乐等领域的运动数据复用提供了高效解决方案。
Although existing quadrilateral mesh generation algorithms can generate high-quality quadrilateral meshes, due to insufficient control over singular points, they may lead to a large number of singular points in the mesh, which affects subsequent numerical analysis. To overcome this problem, a local optimization method for quadrilateral meshes guided by frame fields is proposed. Under the premise of keeping the number of discrete boundary segments unchanged, the internal mesh topology is adjusted to reduce the number of singular points. Firstly, the local mesh regions to be optimized are identified according to the singular point density. Then, a high-quality frame field for each region is generated. Using its streamline information, edge pairs are matched through dynamic programming, and the ideal connection paths between edge pairs are determined by combining graph search algorithms. Finally, the mesh topology of the concerned region is optimized through chord adjustment operations. Experimental results show that the proposed method effectively reduces singularities and improves overall mesh quality, confirming its practical effectiveness.现有的四边形网格生成方法由于对奇异点控制不足，所生成的网格存在大量奇异点，影响后续数值分析。为此，提出一种基于标架场引导的四边形网格局部优化方法，在保持边界离散段数不变的前提下，通过调整内部网格拓扑结构，减少奇异点数量。首先，根据奇异点密度识别待优化区域。然后，生成该区域的高质量标架场，利用其流线信息，通过动态规划匹配边对，并结合图搜索算法确定边对间的理想连接路径。最后，通过弦调整操作优化待优化区域的网格拓扑结构。实例结果表明，四边形网格的奇异点数量得到有效减少，网格质量有所提升，验证了方法的有效性。
Point-normal (PN) subdivision algorithms are generalizations of linear subdivision algorithms. PN subdivision adjusts the shape of subdivided curves and surfaces using control vertices and control normals while maintaining the same convergence and continuity order as linear subdivision curves/surfaces. In this paper, a sufficient condition for local quasi-interpolation of PN subdivision curves/surfaces is proposed based on their circle-preserving/sphere-preserving properties. Then geometric interpolation algorithms for PN-B spline subdivision curves and PN-Catmull-Clark subdivision surfaces are given. The control vertices and normals of the interpolating PN-B spline curves and PN-Catmull-Clark surfaces can be directly computed from given points, normals, and curvatures. The free parameters in the control vertices and normals are determined by establishing and optimizing a Dirichlet energy function. Numerical experiments demonstrate the effectiveness of the proposed method for curve and surface modeling.点法向（PN）细分算法是线性细分算法的推广，利用控制顶点和控制法向调整细分曲线和细分曲面的形状，具有与其对应的线性细分算法相同的收敛性和连续阶。基于PN细分算法的保圆/保球面性质，给出了一种PN细分曲线和细分曲面局部拟插值的充分条件，并利用该条件提出了一种PN-B样条细分曲线和PN-Catmull-Clark细分曲面几何插值算法。PN-B样条细分曲线和PN-Catmull-Clark细分曲面的控制顶点和控制法向可由给定插值点的位置、法向和曲率直接计算得到，控制顶点和控制法向中的自由参数可通过建立和优化Dirichlet能量函数选取。数值实验验证了法向调整、曲率约束及局部点位置变化对曲线和曲面几何形态的调控作用。
To investigate the relationship between spline representation and geometric representation, the geometric shape of the 4th-order non-uniform algebraic triangular B spline (NUAT-B spline) is exploited. By separating the NUAT-B spline basis functions into algebraic polynomial splines and trigonometric polynomial splines, and deriving the geometric features of each part respectively, it is concluded that any 4th-order NUAT-B spline curve describes the trajectory of a point that rotates around the center of a series of ellipses in sequence, while the center of the ellipses translates along a series of straight lines in sequence. The ellipses and straight lines change at the parameter nodes of the spline. Moreover, the explicit expressions of the endpoints of these straight lines, the semi-major and semi-minor axes of the ellipses, and the foci in terms of the control vertices of the spline curve are demonstated. Further, an algorithm for converting between the NUAT-B spline form and the geometric form is designed. The correctness of the algorithm is verified through experiments, and it is shown that the helix and cycloid can precisely adjust the control vertices through geometric features such as the radius of the circle, thereby changing the geometric shape in real time.为探究样条表示与几何表示之间的关系，考虑4阶非均匀代数三角B（NUAT-B）样条曲线的几何形状。将NUAT-B样条基函数分离为代数多项式样条和三角多项式样条两部分，分别推导每一部分的几何特征，得到任意一条可描述一个点的轨迹的4阶NUAT-B样条曲线，该点沿着一系列椭圆轨道绕椭圆中心旋转，同时椭圆中心沿着一系列直线平移，椭圆和直线在样条的参数节点处发生变化。并且，给出这些直线的端点、椭圆的长短半轴和焦点关于样条曲线控制顶点的显式表达。进一步，设计了NUAT-B样条形式与几何形式的相互转换算法，并用实验检验算法的正确性。实验结果表明，圆柱螺线和摆线可通过圆半径等几何特征精确调节控制顶点，实时改变几何形状。
