基于能量模型的曲面展开通用算法

文中提出了一个基于能量模型的曲面展开通用算法,解决了复杂曲面的展开问题,将一个三维曲面展平为与之相对应的二维片,在计算机辅助设计、制造及计算机图形学中的纹理映射等方面都有应用,首先,采用三角片模型来表达一个曲面,然后建立一个基于能量的模型将三维曲面展开为二维片,在这一过程中,曲面展开的局部精度较易控制,因此,较之以前的方法,此方法能更有效地解决CAD/CAM中的曲面展开问题。     

Computing minimal distances on polyhedral surfaces

The authors implement an algorithm that finds minimal (geodesic) distances on a three-dimensional polyhedral surface. The algorithm is intrinsically parallel, in as much as it deals with all nodes simultaneously, and is simple to implement. Although exponential in complexity, it can be used with a companion gradient-descent surface-flattening algorithm that produces an optimal flattening of a polyhedral surface. Together, these two algorithms have made it possible to obtain accurate flattening of biological surfaces consisting of several thousand triangular faces (monkey visual cortex) by providing a characterization of the distance geometry of these surfaces. The authors propose this approach as a pragmatic solution to characterizing the surface geometry of the complex polyhedral surfaces which are encountered in the cortex of vertebrates     

三维鞋样交互设计方法研究

提出了一种在三角网格鞋楦模型上生成三维帮样曲线的离散表示及其交互编辑修改方法。基于改进的能量模型对鞋楦曲面的选择区域进行展平,利用展平过程建立的三维帮面与展平后二维帮面间的拓扑对应关系,实现鞋样曲线在三维空间与二维展平空间的实时关联;所生成的二维帮样曲线以3次非均匀B-spline表示,并以DXF格式输出,便于其他程序调用。算例结果显示,本文方法具有交互性好、实时直观的优点,能够满足基于楦型的帮样交互设计要求。     

Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening

We propose a new method to compute planar triangulations of faceted surfaces for surface parameterization. In contrast to previous approaches that define the flattening problem as a mapping of the three-dimensional node locations to the plane, our method defines the flattening problem as a constrained optimization problem in terms of angles (only). After applying a scaling that derives from the ‘curvature’ at a node, we minimize the relative deformation of the angles in the plane with respect to their counterparts in the three-dimensional surface. This approach makes the method more stable and robust than previous approaches, which used node locations in their formulations. The new method can handle any manifold surface for which a connected, valid, two-dimensional parameterization exists, including surfaces with large curvature gradients. It does not require the boundary of the flat two-dimensional domain to be prede-fined or convex. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.     

3D Topology Preserving Flows for Viewpoint-Based Cortical Unfolding

We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface with respect to a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. The third is a method that dramatically improves the computational speed of the 3D topology preservation approach by creating a tree structure of the 3D surface and using a recursion technique. Experiments results show that the proposed approach can successfully unfold highly convoluted surfaces such as the cortex while preserving their topology during the evolution.     

Freeform surface flattening based on fitting a woven mesh model

This paper presents a robust and efficient surface flattening approach based on fitting a woven-like mesh model on a 3D freeform surface. The fitting algorithm is based on tendon node mapping (TNM) and diagonal node mapping (DNM), where TNM determines the position of a new node on the surface along the warp or weft direction and DNM locates a node along the diagonal direction. During the 3D fitting process, strain energy of the woven model is released by a diffusion process that minimizes the deformation between the resultant 2D pattern and the given surface. Nodes mapping and movement in the proposed approach are based on the discrete geodesic curve generation algorithm, so no parametric surface or pre-parameterization is required. After fitting the woven model onto the given surface, a continuous planar coordinate mapping is established between the 3D surface and its counterpart in the plane, based on the idea of geodesic interpolation of the mappings of the nodes in the woven model. The proposed approach accommodates surfaces with darts, which are commonly utilized in clothing industry to reduce the stretch of surface forming and flattening. Both isotropic and anisotropic materials are supported.     

Pattern flattening for orthotropic materials

In many applications it is necessary to define good-fitting 2D flattened patterns for user-defined regions of a larger 3D surface. This paper describes the major stages involved in pattern flattening and illustrates the process with examples. In generating 2D patterns, some distortion is inevitably involved if the target 3D surface is not developable. For situations where distortion is required, it can be quantified in terms of the energy that must be imparted to the 2D flattening in localised areas so that it takes-up the original 3D region of the surface. An orthotropic strain model is adopted to convert the strain values to energy values. Starting with a bi-parametric definition of a large 3D surface, an arbitrary defined region is specified by the user in terms of a contiguous series of cubic curves lying on the bi-parametric plane. To extract the 3D region, a polygon list is generated to represent the surface. The triangulation process is based on a ‘marching front’ algorithm. A process is described which then flattens this polygon list and performs an energy minimisation analysis every time the process attempts to flatten an over-constrained triangle. Further consideration is made of seam insertion in the 3D surface definition and of adaptively modifying the triangulation process so that more triangles are used in areas of high-energy concentration. Examples are also presented to illustrate the sensitivity of the strain profiles to the fabric grain direction when the pattern is applied to the 3D surface.     

Defining and rendering of textured objects through the use of exponential functions

We present a method for modeling and rendering various surface textures by actually defining them over the entire three-dimensional space. Once this is done any surface representable by an implicit function can be rendered. We do not do any volume rendering; instead the surfaces are ray traced directly. The implicit functions used to define various surfaces are taken to be exponential functions with exponents with large magnitudes. Use of such functions allows us to define even such surfaces as the surface (entire) of a rectangular solid or a truncated cone as precisely as we want. It also allows us to model complex surfaces through piecewise modeling and blending of different analytical surfaces. Even for simple surfaces, it allows us to calculate the ray-surface points of intersection and the normals at those points very precisely because of the large relative variation of the implicit functional density in the entire three-dimensional space. Both regular and stochastic textures can be modeled and rendered. A complete methodology together with several examples is presented.     

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.     

面向三维模型轻量化的自私羊群优化算法研究

针对传统三维仿真模型优化的费时、费力、占用大量内存以及渲染时的画面丢帧、报错等问题,提出一种基于自私羊群智能优化的三维模型轻量化方法3DL-SHO,在确保三维数据准确性的基础上,降低冗余类型、减少场景的数据量、加快模型的优化速度,同时利用3DMax脚本语言MAXScript实现了轻量化处理方法,方便烘焙。通过对BIM系统以及电厂三维仿真系统的几种智能优化算法的对比实验证明,采用该方法可快速执行所有3DMax批量化操作,显著提高了建模和优化的效率。     

A Stationary SVBRDF Material Modeling Method Based on Discrete Microsurface

Microfacet theory is commonly used to build reflectance models for surfaces. While traditional microfacet‐based models assume that the distribution of a surface's microstructure is continuous, recent studies indicate that some surfaces with tiny, discrete and stochastic facets exhibit glittering visual effects, while some surfaces with structured features exhibit anisotropic specular reflection. Accordingly, this paper proposes an efficient and stationary method of surface material modeling to process both glittery and non‐glittery surfaces in a consistent way. Our method comprises two steps: in the preprocessing step, we take a fixed‐size sample normal map as input, then organize 4D microfacet trees in position and normal space for arbitrary‐sized surfaces; we also cluster microfacets into 4D K‐lobes via the adaptive k‐means method. In the rendering step, moreover, surface normals can be efficiently evaluated using pre‐clustered microfacets. Our method is able to efficiently render any structured, discrete and continuous micro‐surfaces using a precisely reconstructed surface NDF. Our method is both faster and uses less memory compared to the state‐of‐the‐art glittery surface modeling works.     

Inverse Displacement Mapping in the General Case

Inverse Displacement Mapping is a form of displacement mapping which allows the ray tracing of displacement mapped surfaces. The technique performs all calculations in the inverse (parametric) space of the surface thus avoiding the need to explicitly model the complex three dimensional geometry. This produces a compact and general algorithm, Only when the solution, in parametric space, has been determined is it transformed back to 3D space. The algorithm works by projecting the ray into the parametric space of the surface. This ray is then split into a series of segments, each of which can be efficiently handled to calculate the intersection points. The algorithm presented here has been used to ray trace displacement mapped objects from a variety of underlying surface types.     

Computational surface flattening: a voxel-based approach

A voxel-based method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxel-based calculation of the minimal geodesic distances between points on the surface and finding a configuration of points in 2D that has Euclidean distances as close as possible to these distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multidimensional scaling (MDS) for finding the 2D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown     

Surface modeling with polynomial splines over hierarchical T-meshes

Computer graphics and computer-aided design communities prefer piecewise spline patches to represent surfaces. But keeping the smoothness between the adjacent patches is a challenging task. In this paper, we present a method for stitching several surface patches, which is a key step in complicated surface modeling, with polynomial splines over hierarchical T-meshes (PHT-spline for short). The method is simple and can be easily applied to complex surface modeling. With the method, spline surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parameterization is obtained, where only small sized linear systems of equations are involved.     

基于柱坐标B样条活动曲面模型的3D分割方法

基于长轴和短轴系列核磁共振图像重建3D左心室内外表面是提取左心室基本形态参数以及左心室运动分析的基础.提出了柱坐标B样条主动表面(CBAS)模型,将其用于3D分割左心室内外膜表面. CBAS模型的等参曲线网格由B-snake模型组成,根据短轴、长轴成像平面在3D空间中的位置关系,网格中的节点在两幅短轴及长轴图像上寻找对应的边缘点,节点间的采样点则在单一的短轴或长轴图像上获得图像能量.首先利用改进的模糊Hough变换确定短轴图像中左心室心肌内外轮廓的大致位置,其次用其构建柱坐标B样条主动曲面模型的初始表面.对左心室表面的分割过程在柱坐标下进行,使得模型在SA图像及LA图像上形状的改变能够统一为一个参数的变化,减小了模型的复杂度.最后通过与手工分割结果的线性回归分析证明了方法的准确性.     

基于三维激光扫描的物体重构建模

物体拍摄环境具有测量数据量大、物体外轮廓信息复杂等特点,采用当前方法能够获得物体精确的三维点云数据,但缺乏颜色和纹理信息,导致物体重构精度不高,真实感较差;为此,提出一种基于三维激光扫描的物体重构建模方法;该方法通过三维激光扫描技术获取物体点云数据,采用显式的欧拉积分方法对物体整个三维曲面进行平滑,依据三角生长法进行物体三维空间三角划分,将物体网格顶点向球面进行映射,由此构造物体三角网格模型,通过迭代最近点算法对物体非同步点云数据初步匹配结果进行精确配准,利用最近点搜索算法将经多视图立体视觉算法优化后的物体颜色信息和三维点云数据坐标相融合;实验结果表明,所提方法可以快速精确地建立物体三维重构模型,验证了所提方法的可行性。     

Multidimensional illumination functions for visualization of complex 3D environments

This paper presents a new view-independent, energy equilibrium method for determining the light distributed in a complex 3D environment consisting of surfaces with general reflectance properties. The method does not depend on discretization of directions or discretization of surfaces to differential elements. Hence, it is a significant improvement over the earlier complete view-independent method which is computationally intractable for complex environments or the hybrid methods which include an extended view-dependent ray tracing second pass. The new method is based on an efficient data structure of order O(N²) called the spherical cover. The spherical cover elegantly captures the complex multidimensional directional nature of light distributed over surfaces. Subdivision techniques based on range estimation of various parameters using interval-arithmetic-like methods are next described for efficiently computing the spherical cover for a given 3D environment. Using the spherical cover, light is progressively propagated through the environment until energy equilibrium is reached. Complexity analysis of the propagation step is carried out to show that the method is computationally tractable. The paper also includes a comprehensive review of earlier rendering techniques viewed from the point of view of capturing the multidimensional nature of light distribution over surfaces.     

基于变分水平集的三维模型复杂孔洞修复*

针对三维模型重建后存在大量复杂孔洞的问题,提出一种孔洞修补算法。首先构造符号距离函数,孔洞所在曲面用静态符号距离函数的零水平集表达,另一动态符号距离函数表示初始曲面;借助隐式曲面上的变分水平集,引入全局凸优化能量模型,通过对其极小化诱导,从而将提取孔洞边缘的问题转化为维体上隐式曲面的演化过程;最后以提取到的孔洞边缘曲面作为初始观察面,通过卷积和合成两个交替的步骤进行体素扩散完成孔洞修补。实验表明该算法能够有效恢复复杂孔洞区域的显著几何特征,且适用于含有网格较多的模型的孔洞修复。     

Generating seamless surfaces for transport and dispersion modeling in GIS

A standard use of triangulation in GIS is to model terrain surface using TIN. In many simulation models of physical phenomena, triangulation is often used to depict the entire spatial domain, which may include buildings, landmarks and other surface objects in addition to the terrain surface. Creating a seamless surface of complex building structures together with the terrain is challenging and existing approaches are laborious, time-consuming and error-prone. We propose an efficient and robust procedure using computational geometry techniques to derive triangulated building surfaces from 2D polygon data with a height attribute. We also propose a new method to merge the resultant building surfaces with the triangulated terrain surface to produce a seamless surface for the entire study area. Using Oklahoma City data, we demonstrate the proposed method. The resultant surface is used as the input data for a simulated transport and dispersion event in Oklahoma City. The proposed method can produce the seamless surface data to be used for various types of physical models in a fraction of the time required by previous methods.     

A Mobile Robotic Measurement System for Large-scale Complex Components Based on Optical Scanning and Visual Tracking

Large-scale components with complex curved surfaces are the foundation of aerospace, energy, and transportation fields, while full-field 3D measurements along with accuracy analyses are critical to control manufacturing quality. Most of the existing measurement methodologies rely on manual inspection, and the accuracy and efficiency are unsatisfactory. This paper introduces an integrated mobile robotic measurement system for the accurate and automatic 3D measurement of large-scale components with complex curved surfaces. The measurement system is composed of a mobile manipulator, a fringe projection scanner and a stereo vision system, and it can provide accurate noncontact 3D measurements of large-scale complex components. By proposing a hand-eye calibration method and scanning pose tracking method based on a stereo vision system, the local point clouds obtained by scanning along with the movement of the mobile robot around the component can be accurately unified into a common reference frame. The proposed measuring system and method are verified by measuring and reconstructing the whole surface of a wind turbine blade model with a length of 2.8 m. The accuracy evaluation proves the effectiveness of the proposed system and method.