Volume Rendering–Mathematical Foundations and Algorithmic Aspects

In this paper various algorithms for rendering gaseous phenomena are reviewed. In computer graphics such algorithms are used to model natural scenes containing clouds, fog, ames and so on. On the other hand displaying three dimensional scalar datasets as cloudy objects has become an important technique in scienti c visualization. Our emphasis is on this latter subject of so-called direct volume rendering. All algorithms will be discussed within the framework of linear transport theory. The equation of transfer is derived. This equation is suitable to describe the radiation eld in a participating medium where absorption, emission, and scattering of light can occur. Almost all volume rendering algorithms can beshown to solve special cases of the equation of transfer. Related problems like the mapping from data values to model parameters or possible parallelization strategies will be discussed as well.

1993

In this paper various algorithms for rendering gaseous phenomena are reviewed. In computer graphics such algorithms are used to model natural scenes containing clouds, fog, flames and so on. On the other hand displaying three dimensional scalar datasets as cloudy objects has become an important technique in scientific visualization. Our emphasis is on this latter subject of so-called direct volume rendering. All algorithms will be discussed within the framework of linear transport theory. The equation of transfer is derived. This equation is suitable to describe the radiation field in a participating medium where absorption, emission, and scattering of light can occur. Almost all volume rendering algorithms can be shown to solve special cases of the equation of transfer. Related problems like the mapping from data values to model parameters or possible parallelization strategies will be discussed as well.

IEEE Transactions on Visualization and Computer Graphics, 1995

This tutorial survey paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, and/or scattering material. They are, in order of increasing realism, absorption only, emission only, emission and absorption combined, single scattering of external illumination without shadows, single scattering with shadows, and multiple scattering. For each model I give the physical assumptions, describe the applications for which it is appropriate, derive the differential or integral equations for light transport, present calculations methods for solving them, and show output images for a data set representing a cloud. Special attention is given to calculation methods for the multiple scattering model.

1993

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 de nition 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.

Applied Optics, 1998

We discuss the representation of aerosol-scattering properties, boundary information, and the use of these results in line-of-sight rendering applications for visualization of a modeled atmosphere based on a discrete ordinates three-dimensional radiative-transport method. The outputs of the radiativetransfer model provide spatial and angular distributions of limiting path radiance, given an input density distribution and external illumination conditions. We discuss the determination of the direct attenuated radiance, integrated path radiance, and background radiance for each pixel in the rendered scene. Orthographic and perspective projection approaches for displaying these results are described, and sample images are shown.

1996

Abstract Traditional volume rendering is computationally expensive and can therefore only be performed at low frame rates. In recent years algorithms have been developed that are speci cally tailored towards the use of graphics hardware for volume rendering. On systems equipped with the appropriate hardware, these algorithms are capable of rendering volumes at interactive rates. Unfortunately, existing algorithms rely on advanced graphics features like texture mapping, which are not available on contemporary lowend systems.

ACM Siggraph Computer Graphics, 1984

This paper presents new algorithms to trace objects represented by densities within a volume grid, e.g. clouds, fog, flames, dust, particle systems. We develop the light scattering equations, discuss previous methods of solution, and present a new approximate solution to the full three-dimensional radiative scattering problem suitable for use in computer graphics. Additionally we review dynamical models for clouds used to make an animated movie.

2020

Each discrete element of an heterogeneous volume grid is often referred to as a voxel. A scalar value ρ , indicates the density of matter per unit volume. Transfer functions are used in volume rendering to map voxel densities with different appearance properties. The default transfer functions used for each data set appearing in our paper are shown in Figure 1. The absorption and scattering coefficients, respectively μa and μs, describe the probability of either absorbing or scattering radiance energy. The extinction coefficient μt = μa + μs indicates the combined probability of either event happening per unit distance. The behavior of these events might also be affected by the incident or outgoing direction of radiance. Moreover, voxels can contribute by adding new energy to the light path.

Computer Graphics Forum, 2009

Volumetric rendering is widely used to examine 3D scalar fields from scanners and direct numerical simulation datasets. One key aspect of volumetric rendering is the ability to provide shading cues to aid in understanding structure contained in the datasets. While shading models that reproduce natural lighting conditions have been shown to better convey depth information and spatial relationships, they traditionally require considerable (pre-)computation. In this paper, we propose a novel shading model for interactive direct volume rendering that provides perceptual cues similar to that of ambient occlusion, for both solid and transparent surface-like features. An image space occlusion factor is derived from the radiative transport equation based on a specialized phase function. Our method does not rely on any precomputation and thus allows for interactive explorations of volumetric data sets via on-the-fly editing of the shading model parameters or (multi-dimensional) transfer functions. Unlike ambient occlusion methods, modifications to the volume, such as clipping planes or changes to the transfer function, are incorporated into the resulting occlusion-based shading. Figure 1: From left to right: a) Visible male data set with occlusion of solid and transparent materials (3.4 FPS, 996 slices) b) CT scan of an engine block where a clipping plane was used to show the exhaust port (13.3 FPS, 679 slices) c) Bonsai data set of which complex features are exposed by our ambient occlusion approximation (4.

ACM Siggraph Computer Graphics, 1988

A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.