径向基函数网络的隐式曲面方法

将径向基函数网络与隐式曲面构造原理相结合,提出一种构造隐式曲面的方法．首先以描述物体曲面的隐式函数为基础构造三元显式函数,然后用径向基函数网络逼近显式函数,最后从神经网络的仿真超曲面得到描述物体的封闭曲面;并证明了在理论上此等值面可以以任意精度逼近物体曲面．该方法具有光滑度高、稳定性好,尤其适用少量采样点情形等特点．实验表明,它具有很强的造型能力．     

基于径向基函数的单级插值隐式曲面重构

研究基于径向基函数单级插值隐式曲面重构问题．探讨基于标准紧支撑径向基函数和变形径向基函数插值的参数求解过程。实验结果表明,该方法能有效地构造隐式曲面。并且插值过程相当快。     

基于径向基函数的三角网格曲面孔洞修补算法

提出一种对三角网格曲面中孔洞的修补算法,在对孔洞多边形进行填补后,使用径向基函数建立孔洞曲面的隐式方程,然后把新增加的三角片顶点映射到曲面上．由于在修补时不仅考虑了对孔洞多边形的三角划分问题,还考虑了孔洞周围的几何信息,使得修补后的孔洞曲面与原始曲面光滑地融为一体,尤其对曲率变化较剧烈部位处的孔洞取得了理想的修补效果．     

点法约束下厄米径向基隐式自由光学曲面的光滑构造EI北大核心CSCD

自由曲面因其具有更高自由度成为光学设计与制造的重要工具,二次支撑包络曲面因具有内在可积性成为自由曲面光学设计的主流方法之一,但其通常是不光滑的,需要进一步求解其光滑包络面以满足加工要求.以二次支撑曲面上的采样型值点和对应单位法向量作为约束条件,利用基于厄米径向基的隐式曲面方法成功地生成了投射均匀方斑的光滑自由光学曲面;进一步在型值点细分插值和支撑子面规模2个方面优化了点法约束条件.与已有曲面重建算法相比较,所提算法具有更小的点法误差和更好的光束整形效果.     

基于径向基函数网络的隐式曲线

将径向基函数网络与隐式曲线构造原理相结合,提出了构造隐式曲线的新方法,即首先由约束点构造神经网络的输入与输出,把描述物体边界曲线的隐式函数转化为显式函数,然后用径向基函数网络对此显式函数进行逼近,最后由神经网络的仿真曲面得到物体边界的拟合曲线.实验表明,基于径向基函数网络的隐式曲线具有很强的物体边界描述能力和缺损修复能 力.     

基于拓扑不变性的GSRBF隐式曲面重建

为提高大规模点云曲面重建的精度和效率,提出一种基于拓扑不变性的全局支撑的径向基函数(GSRBF)隐式曲面重建算法。结合Hausdorff算法,根据点云的主曲率和高斯曲率引入一个临界值,防止提取特征点时产生较大误差,构造特征点点云拓扑同胚的拓扑结构;引入八叉树网格划分法进行点云拓扑关系的构造,通过构造与模型控制网格拓扑同胚的拓扑结构来重建曲面的拓扑;构造基函数确定特征点的影响范围,将其归一化得到曲面拓扑上的单位分解,复合单位分解与特征点得到隐式曲面。实验结果表明,该算法适用于任意拓扑的曲面重建,具有较高的精度和效率。     

使用局部支撑径向基函数的隐式曲线曲面几何迭代算法

由散乱数据稳定重构曲线曲面,在变分拟插值方法的基础之上,提出了使用局部支撑径向基函数的隐式几何迭代算法.首先,根据给定数据点的法向构造隐式函数的非零约束,构造计算隐函数系数的迭代格式,并讨论其收敛性;然后,在此基础上引入加速因子,对隐式迭代算法进行加速,同时讨论了加速算法的收敛性;最后,为了降低迭代过程空间和时间的复杂度,给出了一种加速算法的改进版本.数值实验表明,使用局部支撑径向基函数的隐式几何迭代算法对曲线曲面重构是有效的,并对部分信息缺失、非均匀分布、带噪声采样数据的重构也达到了较好的效果,且实现简单,易于并行.     

利用径向基函数重建飞机表面的Cp值曲面

利用风洞实验获得的复杂飞机表面上部分散乱点的Ｃｐ值,重建出整张曲面上的Ｃｐ值是气动力学分析中的一个难题。该文提出一种新的重建Ｃｐ值曲面方法,先将形状复杂的飞机表面转化为与其拓扑等价的规则曲面,再利用径向基函数对这些散乱点的值进行光滑插值加密计算重建出全局值。通过大量标准函数测试以及实际应用证明,该方法简单、准确、有效。     

测量点集的简化及其隐式曲面重建误差分析

基于测量点集的模型重建是逆向工程中的关键环节,为提高模型重建精度和重建效率、保证为模型重建提供必需的信息,简化测量点集、分析重建误差是十分必要的。首先实现了一种测量点集的快速简化算法,然后提出了采用紧支撑径向基函数建立简化后点集的隐式曲面方程,从而实现重建误差分析的方法。实例结果表明,本文简化算法效率较高、效果良好,运用隐式曲面实现的重建误差分析为简化测量点集提供了误差依据。     

径向基函数神经网络曲面数据破损修补

本文针对工业零件设计中曲面数据的破损问题,提出了一种基于径向基函数(RBF)神经网络的数据修补方法。阐述了数据修补方法的原理,设计了网络结构和训练算法,运用K均值算法实现隐层节点的中心初始化。通过两种曲面的数据进行训练,并对此两种曲面数据破损进行修补,结果表明,本文提出的曲面数据破损修补方法是有效的。     

Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit vol-ume model which fits the data points and normal constraints. Compared with variational implicit sur-faces,we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs,the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.     

Implicit Fitting Using Radial Basis Functions with Ellipsoid Constraint

Implicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non‐algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted to a given data set is often unbounded, multiple sheeted, and disconnected when a high degree polynomial is used, whereas a low degree polynomial is too simple to represent general shapes. Recently, there has been increasing interest in non‐algebraic implicit surface fitting. In these techniques, one popular way of representing an implicit surface has been the use of radial basis functions. This type of implicit surface can represent various shapes to a high level of accuracy. In this paper, we present an implicit surface fitting algorithm using radial basis functions with an ellipsoid constraint. This method does not need to build interior and exterior layers for the given data set or to use information on surface normal but still can fit the data accurately. Furthermore, the fitted shape can still capture the main features of the object when the data sets are extremely sparse. The algorithm involves solving a simple general eigen‐system and a computation of the inverse or psedo‐inverse of a matrix, which is straightforward to implement.     

利用隐式曲面创建实体的多分辨率表示

最近 ,对隐式曲面的研究取得了一些新进展 ,研究者可以通过对一个点集的插值来得到隐式曲面 ,插值过程只需要求解一个简单的线性系统即可 .采用基于包围球的层次结构对原始点集进行不同尺度的采样 ,使用采样后的点集来构造隐式曲面 ,从而得到实体的不同尺度的表示形式 .与基于多边形网格的表示形式相比 ,作者探讨了利用插值型隐式曲面来创建多尺度表示的一些优点     

Approximate implicitization of parametric surfaces by using compactly supported radial basis functions

In this paper, a new approach is proposed to solve the approximate implicitization of parametric surfaces. It is primarily based on multivariate interpolation of scattered data by using compactly supported radial basis functions. Experimental results are provided to illustrate the proposed method is flexible and effective.     

Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and Boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will extend the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We describe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations. We call this structure the BlobTree . Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree . The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems.     

基于RBF的点模型布尔运算

由已有模型构造新的模型是数字娱乐领域的重要造型方法,提出了一种基于RBF（径向基函数）的点模型布尔运算方法。该方法首先将输入点模型进行空间八叉树划分,然后采用RBF将点模型隐式化生成隐函数表示的符号距离场,最后通过隐式曲面的布尔运算方法剔除多余的点,得到需要的新点模型。对点模型进行空间八叉树划分加速了点模型的RBF隐式化过程。该方法可由多个简单的点模型快速构造出复杂的点模型。