Curvature estimation scheme for triangle meshes using biquadratic Bézier patches

When dealing with triangle meshes, it is often important to compute curvature information for the purposes of feature recognition, segmentation, or shape analysis. Since a triangle mesh is a piecewise linear surface, curvature has to be estimated. Several different schemes have been proposed, both discrete and continuous, i.e. based on fitting surfaces locally. This paper compares commonly used discrete and continuous curvature estimation schemes. We also present a novel method which uses biquadratic Bézier patches as a local surface fitting technique.     

A new construction of smooth surfaces from triangle meshes using parametric pseudo-manifolds

We introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate the effectiveness of our manifold-based construction with a few concrete examples.     

Displaced subdivision surfaces of animated meshes

This paper proposes a novel technique for converting a given animated mesh into a series of displaced subdivision surfaces. Instead of independently converting each mesh frame in the animated mesh, our technique produces displaced subdivision surfaces that share the same topology of the control mesh and a single displacement map. We first propose a conversion framework that enables sharing the same control mesh topology and a single displacement map among frames, and then present the details of the components in the framework. Each component is specifically designed to minimize the shape conversion errors that can be caused by enforcing a single displacement map. The resulting displaced subdivision surfaces have a compact representation, while reproducing the details of the original animated mesh. The representation can also be used for efficient rendering on modern graphics hardware that supports accelerated rendering of subdivision surfaces.     

Volume rendering by adaptive refinement

Volume rendering is a technique for visualizing sampled scalar functions of three spatial dimensions by computing 2D projections of a colored semi-transparent gel. This paper presents a volume-rendering algorithm, in which image quality is adaptively refined over time. An initial image is generated by casting a small number of rays into the data, less than one ray per pixel, and interpolating between the resulting colors. Subsequent images are generated by alternately casting more rays and interpolating. The usefulness of these rays is maximized by distributing them according to measures of local image complexity. Examples from two applications are given: molecular graphics and medical imaging.     

Local refinement of three-dimensional finite element meshes

Mesh refinement is an important tool for editing finite element meshes in order to increase the accuracy of the solution. Refinement is performed in an iterative procedure in which a solution is found, error estimates are calculated, and elements in regions of high error are refined. This process is repeated until the desired accuracy is obtained.Much research has been done on mesh refinement. Research has been focused on two-dimensional meshes and three-dimensional tetrahedral meshes ([1] Ning et al. (1993) Finite Elements in Analysis and Design, 13, 299–318; [2] Rivara, M. (1991) Journal of Computational and Applied Mathematics 36, 79–89; [3] Kallinderis; Vijayar (1993) AIAA Journal,31, 8, 1440–1447; [4] Finite Element Meshes in Analysis and Design,20, 47–70). Some research has been done on three-dimensional hexahedral meshes ([5] Schneiders; Debye (1995) Proceedings IMA Workshop on Modelling, Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations). However, little if any research has been conducted on a refinement algorithm that is general enough to be used with a mesh composed of any three-dimensional element (hexahedra, wedges, pyramids, and/or retrahedra) or any combination of three-dimensional elements (for example, a mesh composed of part hexahedra and part wedges). This paper presents an algorithm for refinement of three-dimensional finite element meshes that is general enough to refine a mesh composed of any combination of the standard three-dimensional element types.     

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accuracy.     

Virtual stereo content rendering technology review for light-field display

Light field display (LFD) is considered as a promising technology to reconstruct the light rays’ distribution of the real 3D scene, which approximates the original light field of target displayed objects with all depth cues in human vision including binocular disparity, motion parallax, color hint and correct occlusion relationship. Currently, computer-generated content is widely used for the LFD system, therefore rich 3D content can be provided. This paper firstly introduces applications of light field technologies in display system. Additionally, virtual stereo content rendering techniques and their application scenes are thoroughly combed and pointed out its pros and cons. Moreover, according to the different characteristics of light field system, the coding and correction algorithms in virtual stereo content rendering techniques are reviewed. Through the above discussion, there are still many problems in the existing rendering techniques for LFD. New rendering algorithms should be introduced to solve the real-time light-field rendering problem for large-scale virtual scenes.     

Efficient view-dependent refinement of 3D meshes using sqrt{3}-subdivision

In this paper we introduce an efficient view-dependent refinement technique well suited to adaptive visualization of 3D triangle meshes on a graphic terminal. Our main goal is the design of fast and robust, smooth surface reconstruction from coarse meshes. We demonstrate that the sqrt{3}-subdivision operator recently introduced by Kobbelt offers many benefits, including view-dependent refinement, removal of polygonal aspect and a highly tunable level of detail adaptation. In particular, we propose a new data structure that requires neither edges nor hierarchies for efficient and reversible view-dependent refinement. Results on various 3D meshes illustrate the relevance of the technique.     

A selective rendering method for data visualization

Selective visualization is a solution for visualizing data of large size and dimensionality. In this paper a new method is proposed for effectively rendering certain chosen parts among the full set of data in terms of a colour buffer, referred to as the virtual plane, for storing intermediate results. By this method, scientists may concentrate their attention on the contents of data in which they are interested. Besides, the method could be easily integrated with all the current direct volume rendering techniques, especially progressive refinement methods and selective methods. Copyright © 1999 John Wiley & Sons, Ltd.     

Efficient rendering of animated characters through optimized per‐joint impostors

In this paper, we present a new impostor‐based representation for 3D animated characters supporting real‐time rendering of thousands of agents. We maximize rendering performance by using a collection of pre‐computed impostors sampled from a discrete set of view directions. Our approach differs from previous work on view‐dependent impostors in that we use per‐joint rather than per‐character impostors. Our characters are animated by applying the joint rotations directly to the impostors, instead of choosing a single impostor for the whole character from a set of pre‐defined poses. This offers more flexibility in terms of animation clips, as our representation supports any arbitrary pose, and thus, the agent behavior is not constrained to a small collection of pre‐defined clips. Because our impostors are intended to be valid for any pose, a key issue is to define a proper boundary for each impostor to minimize image artifacts while animating the agents. We pose this problem as a variational optimization problem and provide an efficient algorithm for computing a discrete solution as a pre‐process. To the best of our knowledge, this is the first time a crowd rendering algorithm encompassing image‐based performance, small graphics processing unit footprint, and animation independence is proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

GPU-based rendering for deformable translucent objects

In this paper we introduce an approximate image-space approach for real-time rendering of deformable translucent models by flattening the geometry and lighting information of objects into textures to calculate multi-scattering in texture spaces. We decompose the process into two stages, called the gathering and scattering corresponding to the computations for incident and exident irradiance respectively. We derive a simplified illumination model for the gathering of the incident irradiance, which is amenable for deformable models using two auxiliary textures. In the scattering stage, we adopt two modes for efficient accomplishment of the view-dependent scattering. Our approach is implemented by fully exploiting the capabilities of graphics processing units (GPUs). It achieves visually plausible results and real-time frame rates for deformable models on commodity desktop PCs.     

A double layer method for constructing signed distance fields from triangle meshes

A new algorithm is proposed for constructing signed distance fields (SDF) from triangle meshes. In our approach, both the internal and external distance fields for the triangle mesh are computed first. Then the desired SDF is computed directly from these two distance fields. As only points are used to generate the distance fields, some complicated operations, such as the computation of the distance from a point to a triangle, are avoided. Our algorithm is in a very simple form and is straightforward to parallelize. Actually, we have implemented it by use of the OpenCL API and a CPU-to-GPU speedup ratio of 10–40 is obtained. Further, this method is validated by our numerical results.     

Delphi: geometry-based connectivity prediction in triangle mesh compression

Delphi is a new geometry-guided predictive scheme for compressing the connectivity of triangle meshes. Both compression and decompression algorithms traverse the mesh using the EdgeBreaker state machine. However, instead of encoding the EdgeBreaker clers symbols that capture connectivity explicitly, they estimate the location of the unknown vertex, v , of the next triangle. If the predicted location lies sufficiently close to the nearest vertex, w , on the boundary of the previously traversed portion of the mesh, then Delphi estimates that v coincides with w . When the guess is correct, a single confirmation bit is encoded. Otherwise, additional bits are used to encode the rectification of that prediction. When v coincides with a previously visited vertex that is not adjacent to the parent triangle (EdgeBreaker S case), the offset, which identifies the vertex v , must be encoded, mimicking the cut-border machine compression proposed by Gumhold and Strasser. On models where 97% of Delphi predictions are correct, the connectivity is compressed down to 0.19 bits per triangle. Compression rates decrease with the frequency of wrong predictors, but remains below 1.50 bits per triangle for all models tested.     

Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance

A new approach to the merging of Finite Element (FE) triangle meshes is proposed. Not only it takes into account the geometric aspects, but it also considers the way the semantic information possibly associated to the groups of entities (nodes, faces) can be maintained. Such high level modification capabilities are of major importance in all the engineering activities requiring fast modifications of meshes without going back to the CAD model. This is especially true in the context of industrial maintenance where the engineers often have to solve critical problems in very short time. Indeed, in this case, the product is already designed, the CAD models are not necessarily available and the FE models might be tuned. Thus, the product behaviour has to be studied and improved during its exploitation while prototyping directly several alternate solutions. Such a framework also finds interest in the preliminary design phases where alternative solutions have to be simulated. The algorithm first removes the intersecting faces in an n-ring neighbourhood so that the filling of the created holes produces triangles whose sizes smoothly evolve according to the possibly heterogeneous sizes of the surrounding triangles. The hole-filling algorithm is driven by an aspect ratio factor which ensures that the produced triangulation fits well the FE requirements. It is also constrained by the boundaries of the groups of entities gathering together the simulation semantic. The filled areas are then deformed to blend smoothly with the surroundings meshes.     

View-dependent pruning for real-time rendering of trees

The main problem in the real-time rendering of vegetation is the massive amount of primitives to be rendered. These primitives are needed to fully describe the geometry of the plants. However, some of them are not visible depending on the location of the viewer. This work focuses on this fact to interactively reduce the amount of geometry needed to represent the foliage through a view-dependent multiresolution scheme. Following a camera-dependent criterion, the less visible parts of the foliage are detected in real time, and rendered with a decreased level of detail for improving efficiency. This fact considerably reduces the extraction and the visualization time of the geometry that represents the foliage. The novelty of the presented method is that its design is oriented to being efficient on massively parallel architectures, such as the graphics processing unit. Moreover, we introduce a new management system for efficiently handling level of detail objects in order to improve performance for forest scenes.     

面向三角网格的自适应细分

细分曲面存在的一个问题是随着细分次数的增多,网格的面片数迅速增长,巨大的数据量使得细分后的模难以进行其它处理。针对这个问题,该文利用控制点的局部信息提出了一种基于Loop模式的自适应细分算法,利用该算法可避免在相对光滑处再细分,与正常细分相比,既大大减少了数据量,提高了模型的处理速度,又达到了对模型进行细分的目的。     

Obtuse triangle suppression in anisotropic meshes

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy.     

A hybrid approach to feature segmentation of triangle meshes

Segmentation of a polygonal mesh is a method of breaking the mesh down into ‘meaningful’ connected subsets of meshes called regions or features. Several methods have been proposed in the past and they are either vertex based or edge based. The vertex method used here is based on the watershed segmentation scheme which appears prominently in the image segmentation literature and was later applied to the 3D segmentation problem [9] and [10]. Its main drawback is that it is a vertex based method and no hard boundaries (edges) are created for the features or regions. Edge based methods rely on the dihedral angle between polygon faces to determine if the common edge should be classified as a Feature Edge. However, this method results in many disconnected edges and thereby incomplete feature loops.We propose a hybrid method which takes advantage of both methods mentioned earlier and create regions with complete feature loops. Satisfactory results have been achieved for both CAD parts as well as other laser scanned objects such as bones and ceramic vessels.     

GPU-based rendering of point-sampled water surfaces

Particle-based simulations are widely used to simulate fluids. We present a real-time rendering method for the results of particle-based simulations of water. Traditional approaches to visualize the results of particle-based simulations construct water surfaces that are usually represented by polygons. To construct water surfaces from the results of particle-based simulations, a density function is assigned to each particle and a density field is computed by accumulating the values of the density functions of all particles. However, the computation of the density field is time consuming. To address this problem, we propose an efficient calculation of density field using a graphics processing unit (GPU). We present a rendering method for water surfaces sampled by points. The use of the GPU permits efficient simulation of optical effects, such as refraction, reflection, and caustics.