Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, free-form deformation and displacement mapping. We present a versatile and complete free-form shape modeling framework for point-sampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, point-sampled surfaces can easily be re-structured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on point-sampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.

In the last years point-based rendering has been shown to offer the potential to outperform traditional triangle based rendering both in speed and visual quality when it comes to processing highly complex models. Existing surface splatting techniques achieve superior visual quality by proper filtering but they are still limited in rendering speed. On the other hand the increasing availability and programmability of graphics hardware lead to the developement of very efficient hardware-accelerated rendering methods. However, since no filtered splats are used, these approaches trade visual quality for rendering speed.

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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

the geometry into frequency space by computing the Manifold Harmonic Transform (MHT). C: Apply the frequency space filter on the transformed geometry. D: Transform back into geometric space by computing the inverse MHT. We present a new method to convert the geometry of a mesh into frequency space. The eigenfunctions of the Laplace-Beltrami operator are used to define Fourier-like function basis and transform. Since this generalizes the classical Spherical Harmonics to arbitrary manifolds, the basis functions will be called Manifold Harmonics. It is well known that the eigenvectors of the discrete Laplacian define such a function basis. However, important theoretical and practical problems hinder us from using this idea directly. From the theoretical point of view, the combinatorial graph Laplacian does not take the geometry into account. The discrete Laplacian (cotan weights) does not have this limitation, but its eigenvectors are not orthogonal. From the practical point of view, computing even just a few eigenvectors is currently impossible for meshes with more than a few thousand vertices. In this paper, we address both issues. On the theoretical side, we show how the FEM (Finite Element Modeling) formulation defines a function basis which is both geometry-aware and orthogonal. On the practical side, we propose a band-by-band spectrum computation algorithm and an out-of-core implementation that can compute thousands of eigenvectors for meshes with up to a million vertices. Finally, we demonstrate some applications of our method to interactive convolution geometry filtering and interactive shading design.

We present a novel algorithm for accurate, high quality point rendering, which is based on the formulation of splatting using homogeneous coordinates. In contrast to previous methods, this leads to perspective correct splat shapes, avoiding artifacts such as holes caused by the affine approximation of the perspective projection. Further, our algorithm implements the EWA resampling filter, hence providing high image quality with anisotropic texture filtering. We also present an extension of our rendering primitive that facilitates the display of sharp edges and corners. Finally, we describe an efficient implementation of the entire point rendering pipeline using vertex and fragment programs of current GPUs.

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.

Within the field of computer graphics and visualization, it is often necessary to visualize polygonal models with large number of polygons. Display quality is mandatory, but it is also desirable to have the ability to rapidly update the display in order to facilitate interactive use. Point based rendering methods have been shown effective for this task. Building on this paradigm we introduce the PMR system which uses a hierarchy both in points and triangles for rendering. This hierarchy is fundamentally different from the ones used in existing methods. It is based on the feature geometry in the object space rather than its projection in the screen space. This provides certain advantages over the existing methods.

Abstract—We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry in the vicinity of that 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 geometries. To use the hardware acceleration, the DPs are quantized into 256 different types and each sampled point is approximated by the closest quantized DP and is rendered as a normal-mapped rectangle. The advantages to this representation are: 1) The surface can be represented more sparsely compared to other point primitives, 2) it achieves a robust hardware accelerated per-pixel shading—even with no connectivity information, and 3) it offers a novel point-based simplification technique that factors in the complexity of the local geometry. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splat-based approach. Visual appearances being similar, DPs are about two times faster and require about 75 percent less disk space in comparison to splatting primitives. Index Terms—Differential geometry, simplification, point sample rendering, per-pixel shading. æ

We propose a scheme for modeling point sample geometry with statistical analysis. In our scheme we depart from the current schemes that deterministically represent the attributes of each point sample. We show how the statistical analysis of a densely sampled point model can be used to improve the geometry bandwidth bottleneck and to do randomized rendering without sacrificing visual realism. We first carry out a hierarchical principal component analysis (PCA) of the model. This stage partitions the model into compact local geometries by exploiting local coherence. Our scheme handles vertex coordinates, normals, and color. The input model is reconstructed and rendered using a probability distribution derived from the PCA analysis. We demonstrate the benefits of this approach in all stages of the graphics pipeline: (1) orders of magnitude improvement in the storage and transmission complexity of point geometry, (2) direct rendering from compressed data, and (3) view-dependent randomized rendering.