We present a simple stochastic system for non-periodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, large expanses of non-periodic texture (or patterns or geometry) can be created as needed very efficiently at runtime. Wang Tiles

Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated non-linear optimization to compute a tangent frame and the (commonly overlooked) fact that the normal to this tangent frame is not the surface normal. An alternative definition of Point Set Surfaces, inspired by the MLS projection, is the implicit surface version of Adamson & Alexa. We use this surface definition to show how to compute exact surface normals and present simple, efficient projection operators. The exact normal computation also allows computing orthogonal projections. Categories and Subject Descriptors (according to ACM CCS): G.1.2 [Numerical Analysis]: Approximation of surfaces and contours I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations

In this paper we present a novel framework for direct volume rendering using a splatting approach based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter combining a reconstruction with a low-pass kernel. Because of the similarity to Heckbert’s EWA (elliptical weighted average) filter for texture mapping we call our technique EWA volume splatting. It provides high image quality without aliasing artifacts or excessive blurring even with non-spherical kernels. Hence it is suitable for regular, rectilinear, and irregular volume data sets. Moreover, our framework introduces a novel approach to compute the footprint function. It facilitates efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in reconstructing surface and volume data.

Current surface-based methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend on the underlying surface representation and hence are affected neither by its complexity nor by its quality aspects. However, while analogously to surfacebased methods high quality deformations can be derived from variational optimization, the major drawback lies in the computation and evaluation, which is considerably more expensive for volumetric space deformations. In this paper we present techniques which allow us to use triharmonic radial basis functions for real-time freeform shape editing. An incremental least-squares method enables us to approximately solve the involved linear systems in a robust and efficient manner and by precomputing a special set of deformation basis functions we are able to significantly reduce the per-frame costs. Moreover, evaluating these linear basis functions on the GPU finally allows us to deform highly complex polygon meshes or point-based models at a rate of 30M vertices or 13M splats per second, respectively. 1.

We present the 3D Video Recorder, a system capable of recording, processing, and playing three–dimensional video from multiple points of view. We first record 2D video streams from several synchronized digital video cameras and store pre-processed images to disk. An off-line processing stage converts these images into a time–varying three– dimensional hierarchical point–based data structure and stores this 3D video to disk. We show how we can trade–off 3D video quality with processing performance and devise efficient compression and coding schemes for our novel 3D video representation. A typical sequence is encoded at less than 7 megabit per second at a frame rate of 8.5 frames per second. The 3D video player decodes and renders 3D videos from hard–disk in real–time, providing interaction features known from common video cassette recorders, like variable–speed forward and reverse, and slow motion. 3D video playback can be enhanced with novel 3D video effects such as freeze–and–rotate and arbitrary scaling. The player builds upon point–based rendering techniques and is thus capable of rendering high–quality images in real–time. Finally, we demonstrate the 3D Video Recorder on multiple real–life video sequences. 1

Abstract. We present a novel point rendering primitive, called Differential Point (DP), that captures the local differential geometry in the vicinity of a sampled point. This is a more general point representation that, for the cost of a few additional bytes, packs much more information per point than the traditional point-based models. This information is used to efficiently render the surface as a collection of local neighborhoods. The advantages to this representation are manyfold: (1) it delivers a significant reduction in the number of point primitives that represent a surface (2) it achieves robust hardware accelerated per-pixel shading – even with no connectivity information (3) it offers a novel point-based simplification technique that has a convenient and intuitive interface for the user to efficiently resolve the speed versus quality tradeoff. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splatbased approach. Visual appearances being similar, DPs are about two times faster and require about � � less disk space in comparison to splatting primitives.

The increasing popularity of points as rendering primitives has led to a variety of different rendering algorithms, and the different implementations compare like apples to oranges. In this paper, we revisit and compare a number of recently developed point-based rendering implementations within a common testbed. Also we briefly summarize a few proposed hierarchical multiresolution point data structures and discuss their advantages. Based on a common viewdependent level-of-detail (LOD) rendering framework, we then examine different hardware accelerated point rendering algorithms. Experimental results are given with respect to performance timing and rendering quality for the different approaches. Additionally, we also compare the point-based rendering techniques to a basic triangle mesh approach.

Point-based rendering is a compact and efficient means of displaying complex geometry. Our goal is to enable flexible point-based rendering, permitting local image refinement, required for example when zooming into very complex scenes, and efficient shadow computations. We use hierarchical packed point representations, based on recursive grid data structures. Such compact structures are particularly well adapted to devices with limited memory and display resolution, such as PDA’s. To achieve flexible rendering we store intermediate attributes such as normals and colors at internal nodes of the hierarchy. We examine the memory and computation tradeoffs involved in the type of structure used, and find that tri-grids (3x3x3 hierarchical grids) are a suitable compromise for many cases. We show implementations of our method on PC and on a PDA, for octrees and tri-grids. The PDA version can render objects sampled by 1.3 million points at 2.1 frames per second. 1

We present a hardware-accelerated adaptive EWA (elliptical weighted average) volume splatting algorithm. EWA splatting combines a Gaussian reconstruction kernel with a low-pass image filter for high image quality without aliasing artifacts or excessive blurring. We introduce a novel adaptive filtering scheme to reduce the computational cost of EWA splatting. We show how this algorithm can be efficiently implemented on modern graphics processing units (GPUs). Our implementation includes interactive classification and fast lighting. To accelerate the rendering we store splat geometry and 3D volume data locally in GPU memory. We present results for several rectilinear volume datasets that demonstrate the high image quality and interactive rendering speed of our method.

We present efficient data structures and caching schemes to accelerate ray-surface intersections for deforming point-sampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compared to existing techniques. Starting from a tight bounding sphere hierarchy for the undeformed object, we use a lazy updating scheme to adapt the hierarchy to the deformed surface in each animation step. In addition, we achieve a significant speedup for ray-surface intersections by caching per-ray intersection points. We also present a technique for rendering sharp edges and corners in point-sampled models by introducing a novel surface clipping algorithm.