A Parallel Approach to Compression and Decompression of Triangle Meshes using the GPU

Most state‐of‐the‐art compression algorithms use complex connectivity traversal and prediction schemes, which are not efficient enough for online compression of large meshes. In this paper we propose a scalable massively parallel approach for compression and decompression of large triangle meshes using the GPU. Our method traverses the input mesh in a parallel breadth‐first manner and encodes the connectivity data similarly to the well known cut‐border machine. Geometry data is compressed using a local prediction strategy. In contrast to the original cut‐border machine, we can additionally handle triangle meshes with inconsistently oriented faces. Our approach is more than one order of magnitude faster than currently used methods and achieves competitive compression rates.     

Efficient Geometry Compression for GPU-based Decoding in Realtime Terrain Rendering

We present a geometry compression scheme for restricted quadtree meshes and use this scheme for the compression of adaptively triangulated digital elevation models (DEMs). A compression factor of 8–9 is achieved by employing a generalized strip representation of quadtree meshes to incrementally encode vertex positions. In combination with adaptive error-controlled triangulation, this allows us to significantly reduce bandwidth requirements in the rendering of large DEMs that have to be paged from disk. The compression scheme is specifically tailored for GPU-based decoding, since it minimizes dependent memory access operations. We can thus trade CPU operations and CPU–GPU data transfer for GPU processing, resulting in twice faster streaming of DEMs from main memory into GPU memory. A novel storage format for decoded DEMs on the GPU facilitates a sustained rendering throughput of about 300 million triangles per second. Due to these properties, the proposed scheme enables scalable rendering with respect to the display resolution independent of the data size. For a maximum screen-space error below 1 pixel it achieves frame rates of over 100 fps, even on high-resolution displays. We validate the efficiency of the proposed method by presenting experimental results on scanned elevation models of several hundred gigabytes.     

A Unified Subdivision Scheme for Polygonal Modeling

Subdivision rules have traditionally been designed to generate smooth surfaces from polygonal meshes. In this paper we propose to employ subdivision rules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesirable properties making them ill suited for polygonal modeling. In this paper we propose a general set of subdivision rules which provides users with more control over the subdivision process. Most existing subdivision schemes are special cases. In particular, we provide subdivision rules which blend approximating spline based schemes with interpolatory ones. Also, we generalize subdivision to allow any number of refinements to be performed in a single step.     

Interactive GPU-based adaptive cartoon-style rendering

In this paper we present a novel real-time cartoon-style rendering approach, which targets very large meshes. Cartoon drawing usually uses a limited number of colors for shading and emphasizes special effects, such as sharp curvature and silhouettes. It also paints the remaining large regions with uniform solid colors. Our approach quantizes light intensity to generate different shadow colors and utilizes multiresolution mesh hierarchy to maintain appropriate levels of detail across various regions of the mesh. To comply with visual requirements, our algorithm exploits graphics hardware programmability to draw smooth silhouette and color boundaries within the vertex and fragment processors. We have adopted a simplification scheme that executes simplification operators without incurring extra simplification operations as a precondition. The real-time refinement of the mesh, which is performed by the graphics processing unit (GPU), dramatically improves image quality and reduces CPU load.     

Wavelet-based progressive compression scheme for triangle meshes: wavemesh

We propose a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression.     

一般多边形网格的几何压缩

提出一个通用的一般多边形网格的几何压缩算法，针对目前三维拓扑压缩算法大都仅适用于三角网格的现状，在巳有算法的基础上，进行了有效的推广，使得对于包含任意边数多边形的网格都可以进行有效的压缩编码；另外，根据多边形网格任一多边形中的各个顶点共面的特性，提出一种顶点坐标压缩方案，该方案与上述拓扑压缩算法有机结合可以显著地减少一般多边形网格数据在网上传输所需的带宽；最后，对编码过程产生的输出流进行流程编码与算术编码相结合的混合压缩编码，从而进一步提高压缩比。     

A Shrink Wrapping Approach to Remeshing Polygonal Surfaces

Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propose a new algorithm for converting a given unstructured triangle mesh into one having subdivision connectivity. The basic idea is to simulate the shrink wrapping process by adapting the deformable surface technique known from image processing. The resulting algorithm generates subdivision connectivity meshes whose base meshes only have a very small number of triangles. The iterative optimization process that distributes the mesh vertices over the given surface geometry guarantees low local distortion of the triangular faces. We show several examples and applications including the progressive transmission of subdivision surfaces.     

Error propagation control in Laplacian mesh compression

Laplacian mesh compression, also known as high‐pass mesh coding, is a popular technique for efficiently storing both static and dynamic triangle meshes that gained further recognition with the advent of perceptual mesh distortion evaluation metrics. Currently, the usual rule of thumb that drives the decision for a mesh compression algorithm is whether or not accuracy in absolute scale is required: Laplacian mesh encoding is chosen when perceptual quality is the main objective, while other techniques provide better results in terms of mechanistic error measures such as mean squared error. In this work, we present a modification of the Laplacian mesh encoding algorithm that preserves its benefits while it substantially reduces the resulting absolute error. Our approach is based on analyzing the reconstruction stage and modifying the quantization of differential coordinates, so that the decoded result stays close to the input even in areas that are distant from anchor points. In our approach, we avoid solving an overdetermined system of linear equations and thus reduce data redundancy, improve conditioning and achieve faster processing. Our approach can be directly applied to both static and dynamic mesh compression and we provide quantitative results comparing our approach with the state of the art methods.     

Taylor Prediction for Mesh Geometry Compression

In this paper, we introduce a new formalism for mesh geometry prediction. We derive a class of smooth linear predictors from a simple approach based on the Taylor expansion of the mesh geometry function. We use this method as a generic way to compute weights for various linear predictors used for mesh compression and compare them with those of existing methods. We show that our scheme is actually equivalent to the Modified Butterfly subdivision scheme used for wavelet mesh compression. We also build new efficient predictors that can be used for connectivity‐driven compression in place of other schemes like Average/Dual Parallelogram Prediction and High Degree Polygon Prediction. The new predictors use the same neighbourhood, but do not make any assumption on mesh anisotropy. In the case of Average Parallelogram Prediction, our new weights improve compression rates from 3% to 18% on our test meshes. For Dual Parallelogram Prediction, our weights are equivalent to those of the previous Freelence approach, that outperforms traditional schemes by 16% on average. Our method effectively shows that these weights are optimal for the class of smooth meshes. Modifying existing schemes to make use of our method is free because only the prediction weights have to be modified in the code.