Using Discrete Geometry to model PFair scheduling algorithm for Real-Time systems applications

In this paper, we focus on the use of discrete geometry for the sake of real-time modeling and analysis. We consider multiprocessor context, and we determine the geometrical characterization of PFair scheduling algorithms, which are known to be very performant strategies. A feasability test can then be deduced from the geometrical properties

Dynamic Reconstruction of Complex Planar Objects on Irregular Isothetic Grids

International audienceThe vectorization of discrete regular images has been widely developed in many image processing and synthesis applications, where images are considered as a regular static data. Regardless of final application, we have proposed in [14] a reconstruction algorithm of planar graphical elements on irregular isothetic grids. In this paper, we present a dynamic version of this algorithm to control the reconstruction. Indeed, we handle local refinements to update efficiently our complete shape representation. We also illustrate an application of our contribution for interactive approximation of implicit curves by lines, controlling the topology of the reconstruction

Navigation domain representation for interactive multiview imaging

Enabling users to interactively navigate through different viewpoints of a static scene is a new interesting functionality in 3D streaming systems. While it opens exciting perspectives towards rich multimedia applications, it requires the design of novel representations and coding techniques in order to solve the new challenges imposed by interactive navigation. Interactivity clearly brings new design constraints: the encoder is unaware of the exact decoding process, while the decoder has to reconstruct information from incomplete subsets of data since the server can generally not transmit images for all possible viewpoints due to resource constrains. In this paper, we propose a novel multiview data representation that permits to satisfy bandwidth and storage constraints in an interactive multiview streaming system. In particular, we partition the multiview navigation domain into segments, each of which is described by a reference image and some auxiliary information. The auxiliary information enables the client to recreate any viewpoint in the navigation segment via view synthesis. The decoder is then able to navigate freely in the segment without further data request to the server; it requests additional data only when it moves to a different segment. We discuss the benefits of this novel representation in interactive navigation systems and further propose a method to optimize the partitioning of the navigation domain into independent segments, under bandwidth and storage constraints. Experimental results confirm the potential of the proposed representation; namely, our system leads to similar compression performance as classical inter-view coding, while it provides the high level of flexibility that is required for interactive streaming. Hence, our new framework represents a promising solution for 3D data representation in novel interactive multimedia services

The supercover of an m-flat is a discrete analytical object

International audienc

Digital Analytical Geometry: How do I define a digital analytical object?

International audienceThis paper is meant as a short survey on analytically de-ned digital geometric objects. We will start by giving some elements on digitizations and its relations to continuous geometry. We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects. We will end with open problems and challenges for the future

Discrete-Euclidean operations

International audienceIn this paper we study the relationship between the Euclidean and the discrete space. We study discrete operations based on Euclidean functions: the discrete smooth scaling and the discrete-continuous rotation. Conversely, we study Euclidean oper- ations based on discrete functions: the discrete based simplification, the Euclidean- discrete union and the Euclidean-discrete co-refinement. These operations operate partly in the discrete and partly in the continuous space. Especially for the discrete smooth scaling operation, we provide error bounds when different such operations are chained

Voxelization of Free-Form Solids Represented by Catmull-Clark Subdivision Surfaces

www.cs.uky.edu/∼cheng Abstract. A voxelization technique and its applications for objects with arbitrary topology are presented. It converts a free-form object from its continuous geometric representation into a set of voxels that best approximates the geometry of the object. Unlike traditional 3D scan-conversion based methods, our voxelization method is performed by recursively subdividing the 2D parameter space and sampling 3D points from selected 2D parameter space points. Moreover, our voxelization of 3D closed objects is guaranteed to be leak-free when a 3D flooding operation is performed. This is ensured by proving that our voxelization results satisfy the properties of separability, accuracy and minimality.

OpenFab: A programmable pipeline for multimaterial fabrication

Figure 1: Three rhinos, defined and printed using OpenFab. For each print, the same geometry was paired with a different fablet—a shaderlike program which procedurally defines surface detail and material composition throughout the object volume. This produces three unique prints by using displacements, texture mapping, and continuous volumetric material variation as a function of distance from the surface. 3D printing hardware is rapidly scaling up to output continuous mixtures of multiple materials at increasing resolution over ever larger print volumes. This poses an enormous computational challenge: large high-resolution prints comprise trillions of voxels and petabytes of data and simply modeling and describing the input with spatially varying material mixtures at this scale is challenging. Existing 3D printing software is insufficient; in particular, most software is designed to support only a few million primitives, with discrete material choices per object. We present OpenFab, a programmable pipeline for synthesis of multi-material 3D printed objects that is inspired by RenderMan and modern GPU pipelines. The pipeline supports procedural evaluation of geometric detail and material composition, using shader-like fablets, allowing models to be specified easily and efficiently. We describe a streaming architecture for OpenFab; only a small fraction of the final volume is stored in memory and output is fed to the printer with little startup delay. We demonstrate it on a variety of multi-material objects