An efficient parametric algorithm for octree traversal

An octree is a well known hierarchical spatial structure which is widely used in Computer Graphics algorithms. One of the most frequent operations is the computation of the octree voxels intersected by a straight line. This has a number of applications, such as ray-object intersection tests speed-up and visualisation of hierarchical density models by ray-casting. Several methods have been proposed to achieve this goal, which differ in the order in which intersected voxels are visited. In this paper we introduce a new top-down parametric method. The main difference with previously proposed methods is related to descent movements, that is, the selection of a child sub-voxel from the current one. This selection, as the algorithm, is based on the parameter of the ray and comprises simple comparisons. The resulting algorithm is easy to implement, and efficient when compared to other related top-down and bottom-up algorithms for octrees. Finally, a comparison with Kelvin’s method for binary trees is presented

Direct volume rendering of unstructured grids

This paper investigates three categories of algorithms for direct volume rendering of unstructured grids, which are image-space, object-space, and hybrid methods. We propose three new algorithms. Cell Projection algorithm, which falls into object-space category, is capable of rendering non-convex meshes through a simple yet efficient sorting schema that exploits both image and object space coherencies. Existing hybrid methods use object-then-image traversal order that enforces the processing of each cell. Thus, these algorithms perform redundant operations and do not support early ray termination. We propose a hybrid method, called Span-Buffer Ray Casting (SBRC), that can support early ray termination discarding redundant operations by employing image-then-object traversal order. Another hybrid method, called Koyamada-SBRC (K-SBRC), is proposed with the motivation of refining image-space and hybrid methods to extract the best features of them. This method is developed by blending SBRC approach with Koyamada's algorithm, which is an efficient image-space algorithm. All proposed algorithms are capable of handling acyclic non-convex meshes and generating images of acceptable quality. SBRC and K-SBRC algorithms have the additional capabilities of rendering cyclic meshes and supporting early ray termination. The proposed algorithms and Koyamada's algorithm are implemented and experimented in a common framework for analyzing their relative performance. © 2003 Elsevier Science Ltd. All rights reserved

Progressive refinement rendering of implicit surfaces

The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting

VolumeEVM: A new surface/volume integrated model

Volume visualization is a very active research area in the field of scien-tific visualization. The Extreme Vertices Model (EVM) has proven to be a complete intermediate model to visualize and manipulate volume data using a surface rendering approach. However, the ability to integrate the advantages of surface rendering approach with the superiority in visual exploration of the volume rendering would actually produce a very complete visualization and edition system for volume data. Therefore, we decided to define an enhanced EVM-based model which incorporates the volumetric information required to achieved a nearly direct volume visualization technique. Thus, VolumeEVM was designed maintaining the same EVM-based data structure plus a sorted list of density values corresponding to the EVM-based VoIs interior voxels. A function which relates interior voxels of the EVM with the set of densities was mandatory to be defined. This report presents the definition of this new surface/volume integrated model based on the well known EVM encoding and propose implementations of the main software-based direct volume rendering techniques through the proposed model.Postprint (published version

An Overview of Rendering from Volume Data --- including Surface and Volume Rendering

Volume rendering is a title often ambiguously used in science. One meaning often quoted is: `to render any three volume dimensional data set'; however, within this categorisation `surface rendering'' is contained. Surface rendering is a technique for visualising a geometric representation of a surface from a three dimensional volume data set. A more correct definition of Volume Rendering would only incorporate the direct visualisation of volumes, without the use of intermediate surface geometry representations. Hence we state: `Volume Rendering is the Direct Visualisation of any three dimensional Volume data set; without the use of an intermediate geometric representation for isosurfaces'; `Surface Rendering is the Visualisation of a surface, from a geometric approximation of an isosurface, within a Volume data set'; where an isosurface is a surface formed from a cross connection of data points, within a volume, of equal value or density. This paper is an overview of both Surface Rendering and Volume Rendering techniques. Surface Rendering mainly consists of contouring lines over data points and triangulations between contours. Volume rendering methods consist of ray casting techniques that allow the ray to be cast from the viewing plane into the object and the transparency, opacity and colour calculated for each cell; the rays are often cast until an opaque object is `hit' or the ray exits the volume

A progressive refinement approach for the visualisation of implicit surfaces

Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting

Interactive Visualization of the Largest Radioastronomy Cubes

3D visualization is an important data analysis and knowledge discovery tool, however, interactive visualization of large 3D astronomical datasets poses a challenge for many existing data visualization packages. We present a solution to interactively visualize larger-than-memory 3D astronomical data cubes by utilizing a heterogeneous cluster of CPUs and GPUs. The system partitions the data volume into smaller sub-volumes that are distributed over the rendering workstations. A GPU-based ray casting volume rendering is performed to generate images for each sub-volume, which are composited to generate the whole volume output, and returned to the user. Datasets including the HI Parkes All Sky Survey (HIPASS - 12 GB) southern sky and the Galactic All Sky Survey (GASS - 26 GB) data cubes were used to demonstrate our framework's performance. The framework can render the GASS data cube with a maximum render time < 0.3 second with 1024 x 1024 pixels output resolution using 3 rendering workstations and 8 GPUs. Our framework will scale to visualize larger datasets, even of Terabyte order, if proper hardware infrastructure is available.Comment: 15 pages, 12 figures, Accepted New Astronomy July 201

Topological correction of hypertextured implicit surfaces for ray casting

Hypertextures are a useful modelling tool in that they can add three-dimensional detail to the surface of otherwise smooth objects. Hypertextures can be rendered as implicit surfaces, resulting in objects with a complex but well defined boundary. However, representing a hypertexture as an implicit surface often results in many small parts being detached from the main surface, turning an object into a disconnected set. Depending on the context, this can detract from the realism in a scene where one usually does not expect a solid object to have clouds of smaller objects floating around it. We present a topology correction technique, integrated in a ray casting algorithm for hypertextured implicit surfaces, that detects and removes all the surface components that have become disconnected from the main surface. Our method works with implicit surfaces that are C2 continuous and uses Morse theory to find the critical points of the surface. The method follows the separatrix lines joining the critical points to isolate disconnected components