Stylized Image Triangulation

The art of representing images with triangles is known as image triangulation, which purposefully uses abstraction and simplification to guide the viewer's attention. The manual creation of image triangulations is tedious and thus several tools have been developed in the past that assist in the placement of vertices by means of image feature detection and subsequent Delaunay triangulation. In this paper, we formulate the image triangulation process as an optimization problem. We provide an interactive system that optimizes the vertex locations of an image triangulation to reduce the root mean squared approximation error. Along the way, the triangulation is incrementally refined by splitting triangles until certain refinement criteria are met. Thereby, the calculation of the energy gradients is expensive and thus we propose an efficient rasterization‐based GPU implementation. To ensure that artists have control over details, the system offers a number of direct and indirect editing tools that split, collapse and re‐triangulate selected parts of the image. For final display, we provide a set of rendering styles, including constant colours, linear gradients, tonal art maps and textures. Finally, we demonstrate temporal coherence for animations and compare our method with existing image triangulation tools.     

Skeletonization based on error reduction

The accuracy of a non-pixel-based skeletonization method is largely dependent on the contour information chosen as input. When using a Constrained Delaunay Triangulation to construct an object's skeleton, a number of contour pixels must be chosen as a basis for triangulation. This paper presents a new method of selecting these contour pixels. A new method for measuring skeletonization error is proposed, which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image. The goal of the proposed algorithm is to reduce this error to an acceptable level, whilst retaining the superior efficiencies of previous non-pixel-based techniques. Experimental results show that the proposed method is adept at following the medial axis of an image, and is capable of producing a skeleton that is confirmed by a human's perception of the image. It is also computationally efficient and robust against noise.     

Text region extraction in a document image based on the Delaunay tessellation

In this paper, Delaunay triangulation is applied for the extraction of text areas in a document image. By representing the location of connected components in a document image with their centroids, the page structure is described as a set of points in two-dimensional space. When imposing Delaunay triangulation on these points, the text regions in the Delaunay triangulation will have distinguishing triangular features from image and drawing regions. For analysis, the Delaunay triangles are divided into four classes. The study reveals that specific triangles in text areas can be clustered together and identified as text body. Using this method, text regions in a document image containing fragments can also be recognized accurately. Experiments show the method is also very efficient.     

约束Delaunay三角剖分中强行嵌入约束边的多对角线交换算法

在不允许改变原有点集的场合,实现约束Ｄｅｌａｕｎａｙ 三角剖分的一种有效算法是：将边界点与内点一起进行标准Ｄｅｌａｕｎａｙ 三角剖分,然后强行嵌入不在剖分中的约束边,最后删除域外三角形．其中,任意一条待嵌入约束边所经三角形构成的多边形区域称为该约束边的影响域,影响域内部的每条边称为对角线．文中对一般形状影响域中对角线的可交换性进行了研究,并在此基础上,结合对已有算法的分析和借鉴,提出并证明了两种强行嵌入约束边的多对角线交换算法,即递减算法与循环算法．其中的循环算法具有编程简单和运算速度快的特点     

基于近平面合并的三角网格简化算法

提出一种基于近平面合并的三角网格简化算法,针对三维重建MarchingCubes算法中产生的大量三角片进行简化。首先依据近平面判断条件将近似共面的三角形合并成一个大的多边形,然后按相应的准则将其重新进行三角化得到更少的三角形面片,以达到简化的目的。该算法在最大化的保留图像细节的前提下,精简了三角片的数目,提高了重建后图像绘制和传输的速率,节省了存储空间和处理时间。     

Direct generation of extended STL file from unorganized point data

An extended STL file format is presented in this paper. Differing with existing solutions, it proposes a new format to produce and store triangles. The format uses a cluster unit composed of several triangles. The main advantages of the format are that it contains both geometry and topological information and has improved storage capability. Direct generation of the extended STL from the scanned data has a great advantage in that it can reduce the time and error in modeling process. In order to obtain the format from unorganized point cloud, a new triangulation algorithm was introduced. The algorithm is based on reconstructing the relative Delaunay triangulation of the sample points on the surface. Other advantages of the extended STL format were also presented in this paper.     

一个利用法矢的散乱点三角剖分算法

曲面上散乱点的三角剖分在曲面重建中发挥着重要作用,借助于曲面上的法矢信息和三维Delaunay三角剖分算法,该文给出了一种新的散乱点三角剖分算法,输入一组散乱点以及所在曲面S在这些散乱点处的一致定向的法矢信息,该算法将产生一张插值散乱点的三角网格曲面M,并且曲面M可以近似地看成是曲面S的三角剖分,算法的主要步骤分为两步：首先通过曲面S的一致定向的法矢信息,在曲面S的同一侧添加辅助点,利用这些辅助点来剔除Delaunay三角剖分中产生的不需要的三角片;然后将剩余的三角片连接成一张完整的网格曲面,与基于中轴的三角剖分算法相比,该文算法需要更少和更简单的计算,与局部三角剖分算法相比,该文算法可以更有效地避免重建后的曲面产生自交,该文的算法可用于任意拓扑的光滑曲面重建。     

基于三角剖分的形状检索算法

提出了一种基于三角剖分的形状检索改进算法.算法的基本思想是:先对图像进行边界跟踪和角点检测;然后寻找初始角点在边界跟踪中的对应点,并对找到对应点的角点按对应点在边界跟踪中的顺序进行排序;再对排序后的角点进行德洛内三角剖分,得到能表示目标真实形状的三角形序列;最后计算三角形序列的角度直方图作为形状特征进行相似性匹配.实验结果表明,该算法有较高的效率和检索精度.     

一种基于逐点插入Delaunay三角剖分生成Voronoi图的算法

采用改进的逐点插入算法生成Voronoi图。该算法在逐点插入的过程中生成凸壳,进而生成Delaunay三角剖分。在生成Voronoi图的实现过程中,通过遍历三角形的边顶点快速识别相关的三角形组,进而生成Voronoi图。试验结果表明,该算法能实现,成功生成Voronoi图。     

约束数据域的Delaunay三角剖分算法研究及应用

研究了一种约束Delaunay三角网生成算法,它充分利用分治算法与生长算法的优点,对离散点、构网中实时生成的边及三角形采用分块进行网格索引,有效地减少了搜索目标点、边及三角形的时间,从而提高了构网速度,并将该算法用于地面模型的构建中,实现了地形三维可视化。     

曲率约束的隐式曲面三角网格化

提出一种有效的隐式曲面三角网格化算法。从隐式曲面上的一个种子点开始,生成网格的边界作为扩张多边形,且该多边形最小角对应的顶点为扩张点,计算从扩张点处欲生成的三角网格,为了防止新生成的三角网格和已经存在的三角网格重叠,要进行冲突检测。在隐式曲面三角网格化的过程中,扩张多边形是不断变化的,需要重复上述步骤,直至没有扩张多边形时结束。该算法分别应用于解析隐式曲面和变分隐式曲面的三角网格化。实验结果表明,该算法不需要重新网格化的步骤,生成的三角网格具有较高的质量,且三角网格随曲率适应性变化,因此说明了该算法的有效性。     

基于均匀网格的Delaunay三角网算法在随机聚合网屏中的应用

Delaunay三角网一直是一个重要而有意义的研究课题，并具有极其广泛的用途。经过20多年来的研究，它的生成算法已趋于成熟。为了满足印刷、印染系统中随机聚合网屏生成的实时性需要，将一种将的算法引处到FM网屏技术中，并首先简要介绍了Delaunay三角网的牧场考及生成算法的分类；然后主要介绍了一种基于均匀网格的Delaunay三角网生成算法在随机聚合网屏中的应用；最后给出了算法的正确性证明。经测试，该算法的运算速度相当快，具有接近于线性的时间复杂性，能够满足排版印刷、印染系统中随机聚合网屏生成的需要。     

一种基于Delaunay三角化的手写体文字细化方法

为了对手写体文字进行快速准确的识别，基于Delaunay三角化方法，提出了一种新的文字图象细化算法，该算法首先通过对文字图象边界的近似多边形进行Delaunay三角化，同时把其分成一系列保持拓扑关系的三角形，然后根据三角形的类型生成不同的局部骨架；最后连接生成整文字图象的骨架，由于该算法充分利用了图象的全局和局部信息，因此具有速度快，效果好等优点。     

Delaunay三角剖分算法优化的实现

文章分析Delaunay三角剖分算法各种优缺点,提出了具体的优化思想。详细介绍了Delaunay三角剖分算法优化的设计步骤及实现的具体流程。通过VisualStudio．Net中的C＋＋编程验证了算法的有效性,并对该算法的时间复杂度进行了分析。     

Bezier曲面的适应性细分和三角形化的四叉树方法

计算机生成具有浓淡的参数曲面的方法之一是先对曲面进行适应性细分,并对所得到的曲面细分三角形化,得到曲面的三角形网表示,从而可以对每个三角形施行通常的浓淡处理算法。本文介绍了适应性细分双三次Bezier曲面的方法及曲面细分的四叉树表示,在此基础上给出了一个将曲面细分三角形化的算法。该算法防止了由于适应性细分而可能产生的曲面上的裂缝。     

基于Delaunay三角网的模型拼合算法研究

模型拼合在地理建模、铁(公)路路线三维设计等领域应用十分广泛，研究如何快速高效地获得拼合模型的算法很有必要。基于Delaunay三角网模型的拼合算法，提出了一种快速获取模型拼合交线的方法和快速搜索交线范围内三角形的算法，采取拼合交线入网及初始D-三角网的裁剪2个关键步骤来实现D-三角网模型拼合。对模型拼合的整个过程进行了详细的阐述，采用VC^ 6．O语言实现了算法，并利用实验数据对算法进行测试，验证了算法的正确性与可行性。     

一种基于ROAM的大型DEM实时剖分算法

采用ROAM算法实现大型DEM的实时多分辨率三角网。利用帧一致性,提出双树参考剖分模式,实现顶点数据和三角形误差数据的高效重用,使得算法运行在外存模式,内存中只保留需要的少量数据。对三角形剖分误差进行预计算,改进了误差计算方法,生成多分辨率误差树,将传统的误差计算简化为误差读取,提高了误差数据获取速度以及三角网对DEM表达的精度。实验表明,算法实现了较高的实时剖分速度,适合大型DEM的多分辨率表达。     

Direct quad-dominant meshing of point cloud via global parameterization

In this paper, we present a new algorithm for quad-dominant meshing of unorganized point clouds based on periodic global parameterization. Our meshing method is guided by principal directions so as to preserve the intrinsic geometric properties. We use local Delaunay triangulation to smooth the initial principal directions and adapt the global parameterization to point clouds. By optimizing the fairness measure we can find the two scalar functions whose gradients best align with the guided principal directions. To handle the redundant vertices in the iso-lines due to overlapped triangles, an approach is specially designed to clean the iso-lines. Our approach is fully automatic and applicable to a surface of arbitrary genus. We also show an application of our method in curve skeleton extraction from incomplete point cloud data.     

Delaunay triangulation using a uniform grid

An algorithm for triangulating 2-D data points that is based on a uniform grid structure and a triangulation strategy that builds triangles in a circular fashion is discussed. The triangulation strategy lets the algorithm eliminate points from the internal data structure and decreases the time used to find points to form triangles, given an edge. The algorithm has a tested linear time complexity that significantly improves on that of other methods. As a by-product, the algorithm produces the convex hull of the data set at no extra cost. Two ways to compute the convex hull using the algorithm are presented. The first is based on the edge list and the second is based on the grid structure     

High-quality 2D mesh generation without obtuse and small angles

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles.