Structural Lines, TINs, and DEMs

The standard method of building compact triangulated surface approximations to terrain surfaces (TINs) from dense digital elevation models (DEMs) adds points to an initial sparse triangulation or removes points from a dense initial mesh. Instead, we find structural lines to act as the initial skeleton of the triangulation. These lines are based on local curvature of the surface, not on the flow of water. We build TINs from DEMs with points and structural lines. These experiments show that initializing the TIN with structural lines at the correct scale creates a TIN with fewer points given a particular approximation error. Structural lines are especially effective for small numbers of points and correspondingly rougher approximations. Received December 21, 1995; revised September 24, 1999.     

Ordering Points for Incremental TIN Construction from DEMs

The standard method of building compact triangulated surface approximations to terrain surfaces (TINs) from dense digital elevation models (DEMs) adds points to an initial sparse triangulation or removes points from a dense initial mesh. Typically, in each triangle in the current TIN, the worst fitting point, in terms of vertical distance, is selected. The order of insertion of the points is determined by the magnitude of the maximum vertical difference. This measure produces triangulations that minimize the maximum vertical distance between the TIN and the source DEM. Other approximation criteria are often used, however, including the root-mean-squared error or the mean absolute error, both for the vertical difference and normal difference, i.e., the distance in the direction of the normal to the triangular approximation. For these approximation criteria, we still select the worst fit point, but determine the insertion order by various sums of errors over the triangle. Experiments show that using these better evaluation measures significantly reduces the size of the TIN for a given approximation error.     

Robust uniform triangulation algorithm for computer aided design

This paper presents a new robust uniform triangulation algorithm that can be used in CAD/CAM systems to generate and visualize geometry of 3D models. Typically, in CAD/CAM systems 3D geometry consists of 3D surfaces presented by the parametric equations (e.g. surface of revolution, NURBS surfaces) which are defined on a two dimensional domain. Conventional triangulation algorithms (e.g. ear clipping, Voronoi-Delaunay triangulation) do not provide desired quality and high level of accuracy (challenging tasks) for 3D geometry. The approach developed in this paper combines lattice tessellation and conventional triangulation techniques and allows CAD/CAM systems to obtain the required surface quality and accuracy. The algorithm uses a Cartesian lattice to divide the parametric domain into adjacent rectangular cells. These cells are used to generate polygons that are further triangulated to obtain accurate surface representation. The algorithm allows users to control the triangle distribution intensity by adjusting the lattice density. Once triangulated, the 3D model can be used not only for rendering but also in various manufacturing and design applications. The approach presented in this paper can be used to triangulate any parametric surface given in S(u,v) form, e.g. NURBS surfaces, surfaces of revolution, and produces good quality triangulation which can be used in CAD/CAM and computer graphics applications.     

多连通曲面离散点集的3D三角划分算法研究

在对非封闭曲面、简单封闭曲面和多连通封闭曲面的特点进行分析之后,提出了一种多连通封闭曲面离散点集的3D三角划分算法.该算法无须对离散点集所对应的自由曲面进行分片,直接在3D空间根据曲面的形态变化向前逐层推进生成三角网格.算法同时还适用于非封闭曲面和简单封闭曲面两种情形.实验结果表明,该算法的划分效果优良,能够满足曲面重构的需要.     

Object-based delineation of urban tree canopy: assessing change in Oklahoma City, 2006–2013

With a burgeoning global population, the pressures of urbanization are increasingly prevalent. The need to quantify urban greenness remains significant due to environmental impact and its relationship with human well-being. Utilizing 1 m discrete-return airborne lidar-derived digital terrain models (DTMs) and digital surface models (DSMs), aerial imagery, and lidar-imagery fusion, this study assesses vegetation, specifically tree canopy, change within Oklahoma City between 2006 and 2013. Specifically, we (1) identify an accurate object-based image analysis (OBIA) method for the detection of urban vegetation outlines, and (2) apply that method to locate and quantify vegetation change and assess spatial patterns in Oklahoma City between 2006 and 2013. The proposed OBIA approach extracts urban vegetation coverage from aerial imagery and lidar-based models with around 89% accuracy. Regarding vegetation change, Oklahoma City lost 9.69 km² (3.74 mi²) of tree canopy coverage, which accounted for a 2% loss in total greenness.     

Ptex: Per‐Face Texture Mapping for Production Rendering

Explicit parameterization of subdivision surfaces for texture mapping adds significant cost and complexity to film production. Most parameterization methods currently in use require setup effort, and none are completely general. We propose a new texture mapping method for Catmull‐Clark subdivision surfaces that requires no explicit parameterization. Our method, Ptex, stores a separate texture per quad face of the subdivision control mesh, along with a novel per‐face adjacency map, in a single texture file per surface. Ptex uses the adjacency data to perform seamless anisotropic filtering of multi‐resolution textures across surfaces of arbitrary topology. Just as importantly, Ptex requires no manual setup and scales to models of arbitrary mesh complexity and texture detail. Ptex has been successfully used to texture all of the models in an animated theatrical short and is currently being applied to an entire animated feature. Ptex has eliminated UV assignment from our studio and significantly increased the efficiency of our pipeline.     

Evaluation of TanDEM-X 90 m Digital Elevation Model

German Aerospace Center (DLR), EADS Astrium GmbH and Infoterra GmbH alliance came up with the idea of taking DTED-2 (Digital terrain elevation data, level-2) specifications to even higher standard of HRTE-3 (High resolution terrain elevation, level-3) in 2006, as a result TDX (TerraSAR-X, TanDEM-X) constellation was born. The mission was geared to create a rather sensitive, high precision 3 dimensional map of the entire Earth in seamless and very high quality. After Shuttle Radar Topography Mission (SRTM) in 2000 and its derivatives, along with numerous prior and subsequent other similar data, have practically set the standard for defining the topographical surfaces in global scale, the twin satellites acquired all of Earth’s land surfaces numerous times to produce varying resolution digital elevation models (DEM) between 2011 and late 2015. DEMs are widely used in many planning, decision making and engineering related projects. They provide sound backing for mankind’s endeavors. Ground resolution is the most sought after feature of any DEM. Finer resolution is usually associated with a better surface definition. Recently, an entirely new global DEM has been released DLR. The 90 m DEM is the latest variant derived from such an undertaking. This study aimed to examine the overall effectiveness of this alleged new data in four previously surveyed locations and against the performances of finer SRTM 1- and comparable SRTM 3 arc second data. The results showed that TanDEM-X 90 m data overestimated. They seemed to be rather accurate in flat to slightly undulating terrain, but overestimated in broken to treacherous terrain than both SRTMs. Root Mean Square Error was greater in site one and site four, and lower in site two and site three compared to both SRTM 1 and SRTM 3 arc second data.     

一种改进的约束Delaunay三角网构建算法及其在快速立体解译平台中的应用

约束Delaunay三角网在土方量估算、三维表达、地形拟合等方面得到了广泛的应用。本文对传统的无约束三角网生长法进行了扩展,使扩展后的算法可以同时满足外部边界约束及其内部多线串约束。通过对构网过程中的主要判断法则进行优化,提高了算法的效率和鲁棒性。试验表明将本文算法应用于"快速立体解译平台"中的不规则实体体积估算可以取得很好的效果。     

Centroidal Voronoi diagrams for isotropic surface remeshing

This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampling as an initial configuration for building a weighted centroidal Voronoi diagram in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay triangulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother gradation. We demonstrate the versatility of our approach through various remeshing examples.     

Surface deformation models for nonrigid 3D shape recovery

Three-dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here, we introduce an approach to creating such models for deformable 3D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3D deformation models. We show that these models can be used to accurately model a wide range of deforming 3D surfaces from video sequences acquired under realistic conditions.     

Implicit meshes for surface reconstruction

Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiate algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.     

Horizon computation on a hierarchical triangulated terrain model

Hierarchical terrain models describe a topographic surface at different levels of detail, thus providing a multiresolution surface representation as well as a data compression mechanism. We consider the horizon computation problem on a hierarchical polyhedral terrain (in particular, on a hierarchical triangulated irregular network), which involves extracting the horizon of a viewpoint at a given resolution and updating it as the resolution increases. We present an overview of horizon computation algorithms on a nonhierarchical polyhedral terrain. We extend such algorithms to the hierarchical case by describing a method which extracts the terrain edges at a given resolution, and proposing a randomized algorithm for dynamically updating a horizon under insertions and deletions of terain edges     

A real-time terrain visualization algorithm using wavelet-based compression

We propose a real-time terrain visualization algorithm combined with wavelet-based compression. Our approach updates a surface mesh model in real time by using wavelet coefficients and height data decoded from a compressed bitstream. To achieve this, a new mesh approximation method using restricted quadtree triangulation is designed on the basis of wavelet coefficients representing surface complexity. Also, a wavelet-based compression having a multiresolution structure is introduced to handle large terrain data interactively. Simulation results demonstrate that the proposed algorithm is prospective for applications in a network environment where narrow bandwidth and low computational power are usually allowed .     

A vision-aided reverse engineering approach to reconstructing free-form surfaces

A vision-aided reverse engineering approach (VAREA) has been developed to reconstruct least-square free-form surface models from physical models, with a coordinate measurement machine (CMM) equipped with a touch-triggered probe and a computer vision system. The VAREA integrates computer vision, surface data digitization and surface modelling into a single process. Two main steps are applied in this innovative approach. The initial vision-driven surface triangulation process (IVSTP) generates a triangular patch by using stereo image detection and a constrained Delaunay triangulation method. The adaptive model-based digitizing process is then used to refine the surface reconstruction and to control accuracy to within user-specified tolerances. As a result, a least-squares bicubic B-spline surface model with the controlled accuracy of digitization can be obtained for further application in product design and manufacturing processes. More than 85% reduction has been achieved in the time required to construct free-form surfaces using this approach, as compared with traditional manual methods with CMM. Therefore, product design lead time can be significantly reduced.     

由任意形状轮廓线重建三维表面的方法研究

由一组二维轮廓线重建出物体的三维表面是医学数据可视化的一种主要绘制方式。当轮廓线比较复杂,例如当遇到非凸轮廓或相邻层轮廓线相差过大时,常用的三角化拼接方法就会失败。文章提出一种新的轮廓拼接方法能够处理任意形状的轮廓线。该方法的基本思想是对轮廓线进行凹凸性层次分析,然后将相邻轮廓线从外到内逐层拼接,从而构成一个三角化的物体表面。实验结果表明,该算法对于手动勾画和自动提取的轮廓线都可以给出较好的重建效果。     

第四代地理信息系统研究中的尺度转换数字模型

分析了空间插值模型,数字地面模型和它们与地理信息系统集成的研究进展,存在的缺陷和需要解决的理论问题,论述了建立基于曲面论和遥感反演方法数字模型及实现其与地理信息系统有效集成的必要性和可行性。     

Parallax Walls: Light fields from occlusion on height fields

We introduce a simple, inexpensively manufacturable, height field surface geometry that, when appropriately painted, can produce diffuse reflections under ambient lighting approximating a target light field. We demonstrate a light field basis analysis of these surfaces which allows us to formulate the problem as a gamut-mapping, and propose a perceptually motivated metric for bringing complex light fields into gamut while preserving their structure. We show resultant surfaces displaying physical light fields, animations, HDR exposure stacks, and scene relighting.     

Segmentation of multi-material CT data of mechanical parts for extracting boundary surfaces

We introduce a method for segmentation of materials segmented in volumetric models of mechanical parts created by X-ray CT scanning for the purpose of generating their boundary surfaces. When the volumetric model is composed of two materials, one for the object and the other for the background (Air), these boundary surfaces can be extracted as isosurfaces using a surface contouring method. For a volumetric model composed of more than two materials, we need to classify the voxel types into segments by material and then use a surface contouring method that can deal with both CT values and material types. Here we propose a method for precisely classifying the volumetric model into its component materials using a modified and combined method of two well-known algorithms in image segmentation, region growing and Graph-cut. We then apply our non-manifold iso-contouring method to generate triangulated mesh surfaces. In addition, we demonstrate the effectiveness of our method by constructing high-quality triangular mesh models of the segmented parts.     

Terrain Reconstruction from Contours by Skeleton Construction

Generating terrain models from contour input is still an important process. Most methods have been unsatisfactory, as they either do not preserve the form of minor ridges and valleys, or else they are poor at modeling slopes. A method is described here, based on curve extraction and generalization techniques, that is guaranteed to preserve the topological relationships between curve segments. The skeleton, or Medial Axis Transform, can be extracted from the Voronoi diagram of a well-sampled contour map and used to extract additional points that eliminate cases of flat triangles in a triangulation. Elevation estimates may be made at these points. Based on this approach it is possible to make reasonable estimates of slopes for terrain models, and to extract meaningful intermediate points for triangulated irregular networks (TINs).