Analysis and design of Hermite subdivision schemes

Published online: 14 May 2002     

一种对称非均匀细分曲面算法

为了得到能更好应用于CAD系统的细分曲面造型方法,提出一种基于B-样条的对称非均匀细分算法,其中的思想和均匀Lane-Riesenfeld节点插入算法相似。基于B-样条的节点插入算法,以Blossoming为工具,计算出细分后的新控制顶点。细分后得到的极限曲面由张量积样条曲面组成,在奇异点达到2C连续。与传统的细分曲面算法相比,该细分曲面算法具有良好的局部支撑性,大大降低了算法的复杂度,而且该算法是对称的,不用考虑定向问题。     

General triangular midpoint subdivision

In this paper, we introduce triangular subdivision operators which are composed of a refinement operator and several averaging operators, where the refinement operator splits each triangle uniformly into four congruent triangles and in each averaging operation, every vertex will be replaced by a convex combination of itself and its neighboring vertices. These operators form an infinite class of triangular subdivision schemes including Loop's algorithm with a restricted parameter range and the midpoint schemes for triangular meshes. We analyze the smoothness of the resulting subdivision surfaces at their regular and extraordinary points by generalizing an established technique for analyzing midpoint subdivision on quadrilateral meshes. General triangular midpoint subdivision surfaces are smooth at all regular points and they are also smooth at extraordinary points under certain conditions. We show some general triangular subdivision surfaces and compare them with Loop subdivision surfaces.     

应用剖分遥感影像模板快速提取作物种植面积

全球剖分理论为全球海量遥感影像数据的组织管理和多尺度遥感影像的作物提取和识别提供新的解决思路．结合基于地图分幅扩展的全球剖分模型及其剖分面片的几何特征,阐述剖分遥感影像模板的概念模型和数据模型,提出利用剖分遥感影像模板来提取作物种植面积的处理流程．并给出不同尺度范围提取作物面积适宜选取的剖分级别和影像分辨率。采用高分辨率遥感影像初步尝试对河南省许昌地区小麦种植面积进行提取,通用遥感影像处理软件相比,其精度和速度都有一定的提高．     

Point-augmented biquadratic C1 subdivision surfaces

Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented and the polar bi-2 subdivision are complemented by a new Primal Bi-2 Subdivision scheme. All surfaces are $C^1$ and can be combined.     

基于.Net的选择型工具小窗口在系统开发中的应用

以地区选择为例,阐述了在弹出的小窗口中,利用TreeView控件完成复杂数据获取的一些技术和技巧,并借此推广,完成更多复杂数据的获取。     

基于ATmega128的步进电机细分驱动技术

本文根据合成电流矢量恒幅均匀旋转法,利用AVR高档8位单片机ATmega128的16位PWM模块产生双PWM信号,结合双全桥功率驱动芯片L298N来实现二相混合式步进电机的细分驱动,给出了细分驱动的硬件设计原理图以及相应的软件控制流程图。实验结果表明:该细分驱动器具有控制精度高、低频运行平滑度稳定、并且根据具体应用场合要求有细分数可调等特点。     

Adaptive triangular-mesh reconstruction by mean-curvature-based refinement from point clouds using a moving parabolic approximation

We use a moving parabolic approximation (MPA) to reconstruct a triangular mesh that approximates the underlying surface of a point cloud from closed objects. First, an efficient strategy is presented for constructing a hierarchical grid with adaptive resolution and generating an initial mesh from point clouds. By implementing the MPA algorithm, we can estimate the differential quantities of the underlying surface, and subsequently, we can obtain the local quadratic approximants of the squared distance function for any point in the vicinity of the target shape. Thus, second, we adapt the mesh to the target shape by an optimization procedure that minimizes a quadratic function at each step. With the objective of determining the geometrical features of the target surface, we refine the approximating mesh selectively for the non-flat regions by comparing the estimated curvature from the point clouds and the estimated curvatures computed from the current mesh. Finally, we present various examples that demonstrate the robustness of our method and show that the resulting reconstructions preserve geometric details.     

Ternary butterfly subdivision

This paper presents an interpolating ternary butterfly subdivision scheme for triangular meshes based on a 1–9 splitting operator. The regular rules are derived from a C² interpolating subdivision curve, and the irregular rules are established through the Fourier analysis of the regular case. By analyzing the eigenstructures and characteristic maps, we show that the subdivision surfaces generated by this scheme is C¹ continuous up to valence 100. In addition, the curvature of regular region is bounded. Finally we demonstrate the visual quality of our subdivision scheme with several examples.     

Adjustable speed surface subdivision

We introduce a non-uniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio σ:1−σ, where σ(0,1). We call σ the speed of the non-uniform subdivision and verify C¹ continuity of the limit surface. For σ=1/2, the Catmull–Clark limit surface is recovered. Other speeds are useful to vary the relative width of the polynomial spline rings generated from extraordinary nodes.