隐式曲面在三维植物建模中的应用研究综述

分别从BlobTree结构、融合、精确接触造型、具有多项式密度分布的直线骨架卷积曲面和植物表面纹理等方面,介绍并分析了隐式曲面在三维植物建模中的基本思想和关键技术,并对应用隐式曲面得到三维模型的可视化方法进行了总结。最后对这一研究课题进一步的发展趋势进行了讨论。     

Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done essentially using incremental algorithms. Incremental algorithms have the reputation of being efficient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This article describes novel techniques of robust voxelization and visualization of implicit surfaces. First of all our recursive subdivision voxelization algorithm is reviewed. This algorithm was initially inspired by Duff's image space subdivision method. Then, we explain the algorithm to voxelize implicit surfaces defined in spherical or cylindrical coordinates. Next, we show a new technique to produce infinite replications of implicit objects and their voxelization method. Afterward, we comment on the parallelization of our voxelization procedure. Finally we present our voxel visualization algorithm based on point display. Our voxelization algorithms can be used with any data structure, thanks to the fact that a voxel is only stored once the last subdivision level is reached. We emphasize the use of the octree, though, because it is a convenient way to store the discrete model hierarchically. In a hierarchy the discrete model refinement is simple and possible from any previous voxelized scene thanks to the fact that the voxelization algorithms are robust.     

Visualizing nonmanifold and singular implicit surfaces with point clouds

We use octree spatial subdivision to generate point clouds on complex nonmanifold implicit surfaces in order to visualize them. The new spatial subdivision scheme only uses point sampling and an interval exclusion test. The algorithm includes a test for pruning the resulting plotting nodes so that only points in the closest nodes to the surface are used in rendering. This algorithm results in improved image quality compared to the naive use of intervals or affine arithmetic when rendering implicit surfaces, particularly in regions of high curvature. We discuss and compare CPU and GPU versions of the algorithm. We can now render nonmanifold features such as rays, ray-like tubes, cusps, ridges, thin sections that are at arbitrary angles to the octree node edges, and singular points located within plot nodes, all without artifacts. Our previous algorithm could not render these without severe aliasing. The algorithm can render the self-intersection curves of implicit surfaces by exploiting the fact that surfaces are singular where they self-intersect. It can also render the intersection curves of two implicit surfaces. We present new image space and object space algorithms for rendering these intersection curves as contours on one of the surfaces. These algorithms are better at rendering high curvature contours than our previous algorithms. To demonstrate the robustness of the node pruning algorithm we render a number of complex implicit surfaces such as high order polynomial surfaces and Gaussian curvature surfaces. We also compare the algorithm with ray casting interms of speed and image quality. For the surfaces presented here, the point clouds can be computed in seconds to minutes on atypical Intel based PC. Once this is done, the surfaces can be rendered at much higher frame rates to allow some degree of interactive visualization.     

Diffusion equations over arbitrary triangulated surfaces for filtering and texture applications

In computer graphics, triangular mesh representations of surfaces have become very popular. Compared with parametric and implicit forms of surfaces, triangular mesh surfaces have many advantages, such as easy to render, convenient to store and the ability to model geometric objects with arbitrary topology. In this paper, we are interested in data processing over triangular mesh surfaces through PDEs (partial differential equations). We study several diffusion equations over triangular mesh surfaces, and present corresponding numerical schemes to solve them. Our methods work for triangular mesh surfaces with arbitrary geometry (the angles of each triangle are arbitrary) and topology (open meshes or closed meshes of arbitrary genus). Besides the flexibility, our methods are efficient due to the implicit/semi-implicit time discretization. We finally apply our methods to several filtering and texture applications such as image processing, texture generating and regularization of harmonic maps over triangular mesh surfaces. The results demonstrate the flexibility and effectiveness of our methods.     

复杂表面小尺度凝结现象真实感仿真

凝结是自然界中很常见的一种现象,其真实感仿真对虚拟现实、影视特效及游戏娱乐等领域都有重要的意义.针对传统的基于物理的仿真方法难以保持凝结小尺度液滴细节的问题,提出一种基于光滑粒子流体动力学与自适应流体隐式粒子法耦合的仿真方法.首先基于光滑粒子流体动力学离散建模空气的热传导,并辅以相对湿度模型和露点描述相变过程;然后结合基于八叉树的自适应背景网格和流体隐式粒子法仿真凝结液滴,突出了小尺度液滴高精度的细节;最后引入表面张力、黏附力与阻力,逼真地仿真了复杂固体表面上液滴的运动.实验结果表明,该方法可以真实、高效地反映复杂固体表面的凝结现象.     

Generalized Stochastic Sampling Method for Visualization and Investigation of Implicit Surfaces

Recently we proposed the stochastic sampling method (SSM), which can numerically generate sample points on complicated implicit surfaces quickly and uniformly. In this paper we generalize the method in two aspects: (1) We introduce two kinds of boundary conditions, so that we can sample a finite part of an open surface spreading infinitely. (2) We generalize the stochastic differential equation used in the SSM, so that its solutions can satisfy plural constraint conditions simultaneously. The first generalization enables us to visualize cut views of open surfaces. The second generalization enables us to visualize intersections of static and moving implicit surfaces, which leads to detailed investigation of intersections and other interesting applications such as visualization of contour maps.     

Lines of curvature for polyp detection in virtual colonoscopy

Computer-aided diagnosis (CAD) is a helpful addition to laborious visual inspection for preselection of suspected colonic polyps in virtual colonoscopy. Most of the previous work on automatic polyp detection makes use of indicators based on the scalar curvature of the colon wall and can result in many false-positive detections. Our work tries to reduce the number of false-positive detections in the preselection of polyp candidates. Polyp surface shape can be characterized and visualized using lines of curvature. In this paper, we describe techniques for generating and rendering lines of curvature on surfaces and we show that these lines can be used as part of a polyp detection approach. We have adapted existing approaches on explicit triangular surface meshes, and developed a new algorithm on implicit surfaces embedded in 3D volume data. The visualization of shaded colonic surfaces can be enhanced by rendering the derived lines of curvature on these surfaces. Features strongly correlated with true-positive detections were calculated on lines of curvature and used for the polyp candidate selection. We studied the performance of these features on 5 data sets that included 331 pre-detected candidates, of which 50 sites were true polyps. The winding angle had a significant discriminating power for true-positive detections, which was demonstrated by a Wilcoxon rank sum test with p < 0.001. The median winding angle and inter-quartile range (IQR) for true polyps were 7.817 and 6.770 - 9.288 compared to 2.954 and 1.995 - 3.749 for false-positive detections.     

Robust creation of implicit surfaces from polygonal meshes

Implicit surfaces are used for a number of tasks in computer graphics, including modeling soft or organic objects, morphing, collision detection, and constructive solid geometry. Although operating on implicit surfaces is usually straightforward, creating them is not. We introduce a practical method for creating implicit surfaces from polygonal models that produces high-quality results for complex surfaces. Whereas much previous work in implicit surfaces has been done with primitives such as "blobbies," we use implicit surfaces based on a variational interpolation technique (the three-dimensional generalization of thin-plate interpolation). Given a polygonal mesh, we convert the data to a volumetric representation to use as a guide for creating the implicit surface iteratively. We begin by seeding the surface with a number of constraint points through which the surface must pass. Iteratively, additional constraints are added; the resulting surfaces are evaluated, and the errors guide the placement of subsequent constraints. We have applied our method successfully to a variety of polygonal meshes and consider it to be robust     

Large steps in GPU-based deformable bodies simulation

The interactive deformation and visualization of volumetric objects is still a challenging problem for many application areas. We present a novel integrated system which implements physically-based deformation and volume visualization of tetrahedral meshes on modern graphics hardware by exploiting the last features of vertex and fragment shaders.We achieve fast and stable deformation of tetrahedral meshes by means of a GPU-based implicit solver and present a hardware-based single-pass raycaster for deformed tetrahedral meshes. Thus, direct visualization of the inner structures of the deformed mesh is possible, while keeping the data on the graphics hardware throughout the entire simulation.     

基于偏微分方程的隐式曲面光顺方法

提出隐式曲面的光顺问题．针对该问题，给出刻画隐式曲面光顺程度的能量模型，并将能量解释为关于隐函数的泛函．基于变分原理，构造出隐函数关于时间的偏微分方程。通过求解该方程得到隐函数序列，使得光顺能量逐渐变小，从而达到光顺隐式曲面的目的．另外．针对光顺问题提出的其它约束条件，如尽可能保持面积不变，保持原有的形状特征等，对模型进行修正．最后，给出方程的实用解法及实验结果。并作简单讨论．实验结果表明该方法通用、灵活、有效，而且程序易于实现．