Results 11  20
of
42
Centroidal Voronoi Tesselation of Line Segments and Graphs
"... Figure 1: Starting from a mesh (A) and a template skeleton (B), our method fits the skeleton to the mesh (C) and outputs a segmentation (D). Our main contribution is an extension of Centroidal Voronoi Tesselation to line segments, using approximated Voronoi Diagrams of segments (E). Segment Voronoi ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Figure 1: Starting from a mesh (A) and a template skeleton (B), our method fits the skeleton to the mesh (C) and outputs a segmentation (D). Our main contribution is an extension of Centroidal Voronoi Tesselation to line segments, using approximated Voronoi Diagrams of segments (E). Segment Voronoi cells (colors) are approximated by the union of sampled point’s Voronoi cells (thin lines, right half of D). Clipped 3D Voronoi cells are accurately computed, at a subfacet precision (F). Centroidal Voronoi Tesselation (CVT) of points has many applications in geometry processing, including remeshing and segmentation to name but a few. In this paper, we propose a new extension of CVT, generalized to graphs. Given a graph and a 3D polygonal surface, our method optimizes the placement of the vertices of the graph in such a way that the graph segments best approximate the shape of the surface. We formulate the computation of CVT for graphs as a continuous variational problem, and present a simple approximated method to solve this problem. Our method is robust in the sense that it is independent of degeneracies in the input mesh, such as skinny triangles, Tjunctions, small gaps or multiple connected components. We present some applications, to skeleton fitting and to shape segmentation.
Clipping Using Homogeneous Coordinates
 Proceedings of SIGGRAPH ’78
, 1978
"... Clipping is the process of determining how much of a given line segment lies within the boundaries of the display screen. Homogeneous coordinates are a convenient mathematical device for representing and transforming objects. The space represented by homogeneous coordinates is not, however, a simple ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Clipping is the process of determining how much of a given line segment lies within the boundaries of the display screen. Homogeneous coordinates are a convenient mathematical device for representing and transforming objects. The space represented by homogeneous coordinates is not, however, a simple Euclidean 3space. It is, in fact, analagous to a topological shape called a "projective plane". The clipping problem is usually solved without consideration for the differences between Euclidean space and the space represented by homogeneous coordinates. For some constructions, this leads to errors in picture generation which show up as lines marked invisible when they should be visible. This paper will examine these cases and present techniques for correctly clipping the line segments. 1.
Parallel Rendering Techniques for Multiprocessor Systems
 Comenius University Bratislava
, 1994
"... This paper presents the stateoftheart parallel rendering techniques for interpolation shading, raytracing and radiosity. In addition the most sophisticated parallel architectures for real time rendering are introduced. The new Virtual Walls concept especially designed for asyncronously distribute ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
This paper presents the stateoftheart parallel rendering techniques for interpolation shading, raytracing and radiosity. In addition the most sophisticated parallel architectures for real time rendering are introduced. The new Virtual Walls concept especially designed for asyncronously distributed multiprocessor systems is presented by the author. It describes new distributed rendering techniques based on spatial subdivision and has already been implemented on massively parallel transputer systems and on networks of workstations. Keywords: Parallel, Rendering, Raytracing, Radiosity. 1 Introduction Parallel rendering techniques is a field whose time has come. Until recently for the most it was an cumbersome specialty involving complicated and expensive hardware. In addition the programmers of distributed software had to begin to think parallel. In the last few years, however, there has been a steady and sometimes even spectacular reduction in the hardware price/performance ratio an...
ThreeDimensional Computer Graphics: A CoordinateFree Approach
, 1992
"... Data Type ............ 14 2.4 The Simple Graphics Package .............. 19 2.4.1 TwoDimensional Windowing and Viewporting 19 2.5 TwoDimensional Line Clipping ............. 23 2.5.1 CohenSutherland Line Clipping ........ 25 2.5.2 The Clipping Divider .............. 27 2.6 Windowing and Viewportin ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Data Type ............ 14 2.4 The Simple Graphics Package .............. 19 2.4.1 TwoDimensional Windowing and Viewporting 19 2.5 TwoDimensional Line Clipping ............. 23 2.5.1 CohenSutherland Line Clipping ........ 25 2.5.2 The Clipping Divider .............. 27 2.6 Windowing and Viewporting Revisited ......... 28 CHAPTER 3. Coordinatefree Geometric Programming I 31 3.1 Problems with the Coordinatebased Approach .... 31 3.2 Aftinc Spaces ....................... 33 3.3 Euclidean Geometry ................... 42 3.3.1 The Inner Product ................ 43 3.4 Frames ........................... 44 3.5 *Matrix Representations of Points and Vectors .... 49 3.6 Aftinc Transformations .................. 51 3.7 *Matrix Representations of Aftinc Transformations . . 58 3.8 Ambiguity Revisited ................... 60 3.9 CoordinateFree Line Clipping ............. 62 3.10 A Brief Review of Linear Algebra ............ 67 CHAPTER 4. ThreeDimensional Wireframe Viewing 69 4.1
Texel Programs for RandomAccess Antialiased Vector Graphics
, 2007
"... We encode a broad class of vector graphics in a randomly accessible format. Our approach is to create a coarse grid in which eacch cell contains a teexel program — a locally speciialized descriptioon of the graphics primitives ove erlapping the ceell. These texxel programs are intterpreted at runti ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We encode a broad class of vector graphics in a randomly accessible format. Our approach is to create a coarse grid in which eacch cell contains a teexel program — a locally speciialized descriptioon of the graphics primitives ove erlapping the ceell. These texxel programs are intterpreted at runti ime within a proogrammable pixxel shader. Advanttages include coherent lowba andwidth memory access, efficient interprimitive antialiasing, and the ability to maap general vector grraphics (including strokes) onto arbitrary surfacees. We present a faast construction algorithm, and demonstrate thhe space and time efficiency of the representation on many practical examples.
Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration
"... This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvatureadapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by computing a Centroidal Voronoi Tessellation (CVT), i.e. the minimizer of a C 2 objective function that depends on the coordinates at the vertices (quantization noise power). Optimizing this objective function requires to compute the intersection between the (higher dimensional) Voronoi cells and the surface (Restricted Voronoi Diagram). The method overcomes the dfactorial cost of computing a Voronoi diagram of dimension d by directly computing the restricted Voronoi cells with a new algorithm that can be easily parallelized (Vorpaline: Voronoi Parallel Linear Enumeration). The method is demonstrated with several examples comprising CAD and scanned meshes.
SMOOTHNESSINCREASING ACCURACYCONSERVING (SIAC) POSTPROCESSING FOR DISCONTINUOUS GALERKIN SOLUTIONS OVER STRUCTURED TRIANGULAR MESHES ∗
, 1899
"... Abstract. Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothnessincreasing accuracyconserving (SIAC) filtering. Howeve ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothnessincreasing accuracyconserving (SIAC) filtering. However, it is a computationally complex task to perform this in an efficient manner, which becomes an even greater issue considering nonquadrilateral mesh structures. In this paper, we present an extension of this SIAC filter to structured triangular meshes. The basic theoretical assumption in the previous implementations of the postprocessor limits the use to numerical solutions solved over a quadrilateral mesh. However, this assumption is restrictive, which in turn complicates the application of this postprocessing technique to general tessellations. Additionally, moving from quadrilateral meshes to triangulated ones introduces more complexity in the calculations as the number of integrations required increases. In this paper, we extend the current theoretical results to variable coefficient hyperbolic equations over structured triangular meshes and demonstrate the effectiveness of the application of this postprocessor to structured triangular meshes as well as exploring the effect of using inexact quadrature. We show that there is a direct theoretical extension to structured triangular meshes for hyperbolic equations with bounded variable coefficients. This is a challenging first step toward implementing SIAC filters for unstructured tessellations. We show that by using the usual Bspline implementation, we are able to improve on the order of accuracy as well as decrease the magnitude of the errors. These results are valid regardless of whether exact or inexact integration is used. The results here demonstrate that it is still possible, both theoretically and computationally, to improve to 2k+1 over the DG solution itself for structured triangular meshes.
An efficient algorithm for line clipping by convex polygon
 Computer & Graphics
, 1993
"... AbstractA new line clipping algorithm against convex window based on a new approach for intersection detection is presented. Theoretical comparisons with CyrusBeck's algorithm are shown together with experimental results obtained by simulations. The main advantage of the presented algorithm is th ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
AbstractA new line clipping algorithm against convex window based on a new approach for intersection detection is presented. Theoretical comparisons with CyrusBeck's algorithm are shown together with experimental results obtained by simulations. The main advantage of the presented algorithm is the substantial acceleration of the line clipping problem solution and that edges can be oriented clockwise or anticlockwise. I.
Sense and sidedness in the graphics pipeline via a passage through a separable space
 THE VISUAL COMPUTER
, 2009
"... Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean spa ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean space. This is a weak foundation for computer graphics. An instructor is at a loss: one day entering the classroom and invoking the established and venerable theory of projective geometry while asserting that projective spaces are not separable, and then entering the classroom the following week to tell the students that the standard graphics pipeline performs clipping not in Euclidean, but in projective space—precisely the operation (deciding sidedness, which depends on separability) that was deemed nonsensical. But there is no need to present Blinn and Newell’s algorithm [4, 24]—the crucial clipping step in the graphics pipeline and, perhaps, the most original knowledge a student learns in a fourthyear computer graphics class—as a clever trick that just works. Jorge Stolfi described in 1991 oriented projective geometry. By declaring the two vectors (x, y, z, w) T and (−x, −y, −z, −w) T distinct, Blinn and Newell were already unknowingly working in oriented projective space. This paper presents the graphics pipeline on this stronger foundation.
An improved observation model for superresolution under affine motion
 IEEE Trans. Image Process
, 2006
"... Abstract — Superresolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higherresolution images. We propose an original observation model devoted to the case of non isometric interframe motion as required, for instance, in the context of airborne imaging ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract — Superresolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higherresolution images. We propose an original observation model devoted to the case of non isometric interframe motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for non isometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by rowbyrow or columnbycolumn 1D affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions. Index Terms — SuperResolution, affine motion, multipass interpolation, bspline, L2 approximation, projection, inverse problems,