High-quality rendering of quartic spline surfaces on the GPU

We present a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct in the sense that since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-Bézier techniques) for Phong illumination on the GPU. Inaccurate shading and artifacts appearing for triangular tesselated surfaces are completely avoided. Level of detail is automatic since all computations are done on a per fragment basis. We compare three different (quasi-) interpolating schemes for uniformly sampled gridded data, which differ in the smoothness and the approximation properties of the splines. The results show that our hardware based renderer leads to visualizations (including texturing, multiple light sources, environment mapping, etc.) of highest quality.     

Efficient skeleton-guided displaced subdivision surfaces

Displacement mapping is a computer graphics technique that uses scalar offsets along normals on a base surface to represent and render a model with highly geometric details. The technique natively compresses the model and saves memory I/O. A subdivision surface is the ideal base surface, due to its good geometric properties, such as arbitrary topology, global smoothness, and multi-resolution via hardware tessellation, among others. Two of the main challenges in displacement mapping representation are constructing the base surface faithfully and generating displacement maps efficiently. In this paper, we propose an efficient skeleton-guided displaced subdivision surfaces method. The construction of the base mesh is guided by a sketched skeleton. To make the shape of the base surface fit the input model well, we develop an efficient progressive GPU-based subdivision fitting method. Finally, a GPU-based raycasting method is proposed to sample the input model and generate the displacement maps. The experimental results demonstrate that the proposed method can efficiently generate a high-quality displacement mapping representation. Compared with the traditional displaced subdivision surface method, the proposed method is more suitable for the modern rendering pipeline and has higher efficiency.     

Fractional Reyes‐Style Adaptive Tessellation for Continuous Level of Detail

In this paper we present a fractional parametric splitting scheme for Reyes‐style adaptive tessellation. Our parallel algorithm generates crack‐free tessellation from a parametric surface, which is also free of sudden temporal changes under animation. Continuous level of detail is not addressed by existing Reyes‐style methods, since these aim to produce subpixel‐sized micropolygons, where topology changes are no longer noticeable. Using our method, rendering pipelines that use larger triangles, thus sensitive to geometric popping, may also benefit from the quality of the split‐dice tessellation stages of Reyes. We demonstrate results on a real‐time GPU implementation, going beyond the limited quality and resolution of the hardware tessellation unit. In contrast to previous split‐dice methods, our split stage is compatible with the fractional hardware tessellation scheme that has been designed for continuous level of detail.     

Adaptive mesh subdivision for efficient light baking

Light baking has long been a popular technique for real-time rendering. It usually precomputes and bakes the global lighting effects as vertex attributes or textures. Vertex baking requires less memory but can cause artifacts for large triangles. Texture baking can avoid this and generate a high-quality visual effect in real-time rendering. However, it requires significant memory consumption, which may limit the real-time performance and usage. To address this problem, we propose an adaptive mesh subdivision algorithm for memory-efficient light baking, including a fast triangle subdivision level determination method and an optimized solution to calculate vertex colors. Only the subdivided mesh is required during the real-time rendering. Therefore, memory requirements can be significantly reduced while keeping the visual effect. Besides, the subdivision level is allowed to be intuitively controlled by users with a specified parameter. Our algorithm can be easily implemented on commodity graphics hardware and integrated in existing real-time applications such as online preview systems.     

屏幕空间自适应的地形Tessellation绘制

为了在大规模真实感地形渲染中利用GPU硬件加速的Tessellation技术,在对地形Tessellation原理分析的基础上,提出一种屏幕空间自适应的地形Tessellation绘制算法,实现了在GPU内部对地形模型的三角形自适应细分。该算法采用Tile和Patch的形式对地形数据进行分层组织,在CPU和GPU上分别以Tile和Patch为基础实现地形LOD(level of detail)的自适应简化;提出在Hull Shader上基于Patch边界的细分系数计算模型,确保了Patch细分时的无缝连接;给出了Domain Shader上置换贴图的处理过程,以实现细分顶点的高程纹理映射;并且采用了两级视锥体裁剪机制,减少了渲染数据的冗余量。实验结果表明,该算法具有较好的屏幕空间自适应性和渲染性能,能够在输入粗糙网格的基础上,渲染输出高分辨率几何细节特征的地形模型。     

基于混合子分方法的曲面网格顶点与法向插值

顶点位置和法向插值是参数曲面造型的重要内容,文中基于混合子分方法生成三次B样条控制网格,使得相应的三次B样条曲面插值初始网格中指定的顶点,并通过引入插值模板的概念,把法向的插值转化为对模板的旋转变换,使得曲面在不改变2插值顶点的情况下插值法向,最后得到一张C^2连续的插值指定顶点和法向的曲面,与传统的逐片Bezier或Coons曲面片构造方法相比,此方法更为简洁且具有更高的连续阶,而且易于推广到高阶B样条和任意拓扑情形,具有较强的实用性。     

Tessellation‐Independent Smooth Shadow Boundaries

We propose an efficient and light‐weight solution for rendering smooth shadow boundaries that do not reveal the tessellation of the shadow‐casting geometry. Our algorithm reconstructs the smooth contours of the underlying mesh and then extrudes shadow volumes from the smooth silhouettes to render the shadows. For this purpose we propose an improved silhouette reconstruction using the vertex normals of the underlying smooth mesh. Then our method subdivides the silhouette loops until the contours are sufficiently smooth and project to smooth shadow boundaries. This approach decouples the shadow smoothness from the tessellation of the geometry and can be used to maintain equally high shadow quality for multiple LOD levels. It causes only a minimal change to the fill rate, which is the well‐known bottleneck of shadow volumes, and hence has only small overhead.     

The floating column algorithm for shaded, parallel display offunction surfaces without patches

The floating column algorithm is a new method for the shaded rendering of function surfaces. Derived from the monochromatic floating horizon algorithm, it uses the partial derivatives of the function to compute surface normals, thus enabling intensity or normal-interpolation shading. Current rendering methods require tiling the surface with patches, so higher-resolution patching is required for zoom-in views, interactive modification or time-varying surfaces. The new algorithm requires no patching and uses only constant space, so it can be implemented on graphics cards and hand-held devices. Each pixel column is displayed independently of the others, and this "independent column mode" makes the algorithm inherently parallel in the image space, so it is suitable for multiprocessor workstations and clusters and it is scalable in the resolution size. Furthermore, the sampling frequency of the surface can be controlled locally, matching local surface features, distance or artifact elimination requirements. Space-efficient super-sampling for anti-aliasing is also possible. The new algorithm, which allows orthogonal and perspective projections, produces pixel-wide strips which can be displayed in software or hardware. Various extensions are described, including shadows and texture mapping. These properties, together with the algorithm's parallelism, make it potentially useful for the real-time display of functionally-defined textured terrains and the animated display of time-varying surfaces     

Subdivision-Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPU

Subdivision surfaces have become an invaluable asset in production environments. While progress over the last years has allowed the use of graphics hardware to meet performance demands during animation and rendering, high-performance is limited to immutable mesh connectivity scenarios. Motivated by recent progress in mesh data structures, we show how the complete Catmull-Clark subdivision scheme can be abstracted in the language of linear algebra. While this high-level formulation allows for a fully parallel implementation with significant performance gains, the underlying algebraic operations require further specialization for modern parallel hardware. Integrating domain knowledge about the mesh matrix data structure, we replace costly general linear algebra operations like matrix-matrix multiplication by specialized kernels. By further considering innate properties of Catmull-Clark subdivision, like the quad-only structure after refinement, we achieve an additional order of magnitude in performance and significantly reduce memory footprints. Our approach can be adapted seamlessly for different use cases, such as regular subdivision of dynamic meshes, fast evaluation for immutable topology and feature-adaptive subdivision for efficient rendering of animated models. In this way, patchwork solutions are avoided in favor of a streamlined solution with consistent performance gains throughout the production pipeline. The versatility of the sparse matrix linear algebra abstraction underlying our work is further demonstrated by extension to other schemes such as and Loop subdivision.     

Parallel Rendering and Animation of Subdivision Surfaces on the Cell BE Processor

In this work we propose a parallel graphics pipeline for real-time interactive editing, processing and rendering of smooth surface primitives on the Cell BE. Our approach integrates a special patch-based geometry shader for subdivision surface targeting high-performance single-chip multi-core platforms. We describe a combination of algorithmic, architectural and back-end optimizations that enable us to render smooth subdivision surfaces in real-time and to dynamically deform 3D models represented by subdivision surfaces.     

基于GPU的视点相关自适应细分

利用GPU的强大浮点数计算能力和并行处理能力,提出一种完全基于GPU的视点相关自适应细分内核进行快速细分计算的方法.在GPU中,依次实现视点相关的面片细分深度值计算、基于基函数表的细分表面顶点求值、细分表面绘制等核心步骤,无须与CPU端系统内存进行几何数据交换.视点相关的自适应细分准则在表面绘制精度保持不变的情况下,有效地降低了细分表面的细分深度和细分的计算量,在此基础上完全基于GPU的细分框架使得曲面细分具有快速高效的特点.该方法还可以在局部重要细节用较大深度值进行实时自适应细分,以逼近极限曲面.     

面向移动终端的三角网格逆细分压缩算法

针对移动用户的实时显示需求,提出一种基于逆细分的三角网格压缩算法.通过改进逆Butterfly简化算法,采用逆改版Loop模式,将细密的三角网格简化生成由稀疏的基网格和一系列偏移量组成的渐进网格;然后,通过设计偏移量小波树,将渐进网格进行嵌入式零树编码压缩.实验结果表明:该算法与以往方法相比,在获得较高压缩比的同时,运行速度较快.适用于几何模型的网络渐进传输和在移动终端上的3D图形实时渲染.     

Adaptive Ray‐bundle Tracing with Memory Usage Prediction: Efficient Global Illumination in Large Scenes

This paper proposes an adaptive rendering technique for ray‐bundle tracing. Ray‐bundle tracing can be done by per‐pixel linked‐list construction on a GPU rasterization pipeline. This rasterization based approach offers significant benefits for the efficient generation of light maps (e.g., hardware acceleration, tessellation, and recycling of shaders used in real‐time graphics). However, it is inapplicable to large and complex scenes due to the limited capacity of the GPU memory because it requires a high‐resolution frame buffer and high‐capacity node buffer for the linked‐lists. In addition, memory overflow can potentially occur on the per‐pixel linked‐list since the memory usage of the lists is usually unknown before the rendering process. We introduce an adaptive tiling technique with memory usage prediction. Our method uses an appropriately tiled frame buffer, thus eliminating almost all of the overflow risks thanks to our adaptive tile subdivision scheme. Using this technique, we are able to render high‐quality light maps of large and complex scenes which cannot be computed using previous ray‐bundle based methods.     

Bounded Radiosity – Illumination on General Surfaces and Clusters

Traditionally, Radiosity algorithms have been restricted to scenes made from planar patches. Most algorithms for computing form factors and the subdivision criterion for hierarchical methods implicitly assume planar patches. In this paper, we present a new radiosity algorithm that is solely based on simple geometric information about surface elements, namely their bounding boxes and cone of normals. Using this information allows to compute efficient error bounds that can be used for the subdivision oracle and for computing the energy transfer. Due to the simple interface to geometric objects, our algorithm not only allows for computing illumination on general curved surfaces, but it can also be directly applied to a hieararchy of clusters. Several examples demonstrate the advantages of the new approach.     

Detecting and reconstructing subdivision connectivity

inverse subdivision algorithms , with linear time and space complexity, to detect and reconstruct uniform Loop, Catmull–Clark, and Doo–Sabin subdivision structure in irregular triangular, quadrilateral, and polygonal meshes. We consider two main applications for these algorithms. The first one is to enable interactive modeling systems that support uniform subdivision surfaces to use popular interchange file formats which do not preserve the subdivision structure, such as VRML, without loss of information. The second application is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Our Loop inverse subdivision algorithm is based on global connectivity properties of the covering mesh, a concept motivated by the covering surface from Algebraic Topology. Although the same approach can be used for other subdivision schemes, such as Catmull–Clark, we present a Catmull–Clark inverse subdivision algorithm based on a much simpler graph-coloring algorithm and a Doo–Sabin inverse subdivision algorithm based on properties of the dual mesh. Straightforward extensions of these approaches to other popular uniform subdivision schemes are also discussed. Published online: 3 July 2002     

Shape aware normal interpolation for curved surface shading from polyhedral approximation

Independent interpolation of local surface patches and local normal patches is an efficient way for fast rendering of smooth curved surfaces from rough polyhedral meshes. However, the independently interpolating normals may deviate greatly from the analytical normals of local interpolating surfaces, and the normal deviation may cause severe rendering defects when the surface is shaded using the interpolating normals. In this paper we propose two novel normal interpolation schemes along with interpolation of cubic Bézier triangles for rendering curved surfaces from rough triangular meshes. Firstly, the interpolating normal is computed by a Gregory normal patch to each Bézier triangle by a new definition of quadratic normal functions along cubic space curves. Secondly, the interpolating normal is obtained by blending side-vertex normal functions along side-vertex parametric curves of the interpolating Bézier surface. The normal patches by these two methods can not only interpolate given normals at vertices or boundaries of a triangle but also match the shape of the local interpolating surface very well. As a result, more realistic shading results are obtained by either of the two new normal interpolation schemes than by the traditional quadratic normal interpolation method for rendering rough triangular meshes.     

Projected tetrahedra revisited: a barycentric formulation applied to digital radiograph reconstruction using higher-order attenuation functions

This paper presents a novel method for volume rendering of unstructured grids. Previously, we introduced an algorithm for perspective-correct interpolation of barycentric coordinates and computing polynomial attenuation integrals for a projected tetrahedron using graphics hardware. In this paper, we enhance the algorithm by providing a simple and efficient method to compute the projected shape (silhouette) and tessellation of a tetrahedron, in perspective and orthographic projection models. Our tessellation algorithm is published for the first time. Compared with works of other groups on rendering unstructured grids, the main contributions of this work are: 1) A new algorithm for finding the silhouette of a projected tetrahedron. 2) A method for interpolating barycentric coordinates and thickness on the faces of the tetrahedron. 3) Visualizing higher-order attenuation functions using GPU without preintegration. 4) Capability of applying shape deformations to a rendered tetrahedral mesh without significant performance loss. Our visualization model is independent of depth-sorting of the cells. We present imaging and timing results of our implementation, and an application in time-critical "2D-3D" deformable registration of anatomical models. We discuss the impact of using higher-order functions on quality and performance.     

基于硬件细分的层次细节地形渲染算法

针对顶点着色器细分地形网格需要额外生成模板、计算细分层次复杂的不足,提出了一种利用细分着色器进行地形网格细分的层次细节(LOD)地形渲染算法。利用分块四叉树组织建立地形粗糙网格的分层结构,以LOD判别函数对活动地形块进行筛选;提出了在细分控制着色器中基于视点三维连续距离的细分因子计算方法,并针对外部细分因子进行处理消除了裂缝;实现在细分计算着色器上的置换贴图,对精细网格的高度分量进行位移。而且将四叉树结构存储至顶点缓冲区,减少中央处理器(CPU)与图形处理器(GPU)的资源交换;引入细分队列加速细分过程。实验证明,该算法具有平滑的细节层次过渡和良好的细分效果,能够有效提高GPU利用率和地形渲染效率。     

Efficient direct rendering of deforming surfaces via shared subdivision trees

In this paper, we present a subdivision-based approach to rasterize implicit surfaces embedded in volumetric Bézier patches undergoing a nonlinear deformation. Subdividing a given patch into simpler patches to perform the surface rasterization task is numerically robust, and allows guaranteeing visual accuracy even in the presence of geometric degeneracies. However, due to its memory requirements and slow convergence rates, subdivision is challenging to be used in an interactive environment. Unlike previous methods employing subdivision, our approach is based on the idea where for a given patch only one subdivision tree is maintained and shared among pixels. Furthermore, as the geometry of the object changes from frame to frame, a flexible data structure is proposed to manage the geometrically varying Bézier patches. The resulting algorithm is general and maps well to parallel computing platforms such as CUDA. We demonstrate on a variety of representative graphics and visualization examples that our GPU scheme scales well and achieves up to real-time performance on consumer-level graphics cards by guaranteeing visual accuracy.