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 the paper provides the physical assumptions, describes the applications for which it is appropriate, derives the differential or integral equations for light transport, presents calculation methods for solving them, and shows output images for a data set representing a cloud. Special attention is given to calculation methods for the multiple scattering model. >

Optical models for direct volume rendering

A new and easy-to-implement method for direct volume rendering that uses 3D texture maps for acceleration, and incorporates directional lighting, is described. The implementation, called Voltx, produces high-quality images at nearly interactive speeds on workstations with hardware support for three-dimensional texture maps. Previously reported methods did not incorporate a light model, and did not address issues of multiple texture maps for large volumes. Our research shows that these extensions impact performance by about a factor of ten. Voltx supports orthographic, perspective, and stereo views. This paper describes the theory and implementation of this technique, and compares it to the shear-warp factorization approach. A rectilinear data set is converted into a three-dimensional texture map containing color and opacity information. Quantized normal vectors and a lookup table provide efficiency. A new tesselation of the sphere is described, which serves as the basis for normal-vector quantization. A new gradient-based shading criterion is described, in which the gradient magnitude is interpreted in the context of the field-data value and the material classification parameters, and not in isolation. In the rendering phase, the texture map is applied to a stack of parallel planes, which effectively cut the texture into many slabs. The slabs are composited to form an image.

/pdf/direct-volume-rendering-with-shading-via-three-dimensional-rc936emieo.pdf

Direct volume rendering with shading via three-dimensional textures

Direct volume rendering offers the opportunity to visualize all of a three-dimensional sample volume in one image. However, processing such images can be very expensive and good quality high-resolution images are far from interactive. Projection approaches to direct volume rendering process the volume region by region as opposed to ray-casting methods that process it ray by ray. Projection approaches have generated interest because they use coherence to provide greater speed than ray casting and generate the image in a layered, informative fashion. This paper discusses two topics: First, it introduces a projection approach for directly rendering rectilinear, parallel-projected sample volumes that takes advantage of coherence across cells and the identical shape of their projection. Second, it considers the repercussions of various methods of integration in depth and interpolation across the scan plane. Some of these methods take advantage of Gouraud-shading hardware, with advantages in speed but potential disadvantages in image quality.

A coherent projection approach for direct volume rendering

A visibility-ordering of a set of objects from some viewpoint is an ordering such that if object a obstructs object b, then b precedes a in the ordering. An algorithm is presented that generates a visibility-ordering of an acyclic convex set of meshed convex polyhedra. This algorithm takes time linear in the size of the mesh. Modifications to this algorithm and/or preprocessing techniques are described that permit nonconvex cells nonconvex meshes (meshes with cavities and/or voids), meshes with cycles, and sets of disconnected meshes to be ordered. Visibility-ordering of polyhedra is applicable to scientific visualization, particularly direct volume rendering. It is shown how the ordering algorithms can be used for domain decomposition of finite element meshes for parallel processing, and how the data structures used by these algorithms can be used to solve the spatial point location problem. The effects of cyclically obstructing polyhedra are discussed and methods for their elimination are described, including the use of the Delaunay triangulation. Methods for converting nonconvex meshes into convex meshes are described.

http://www0.cs.ucl.ac.uk/research/vr/Projects/VLF/vlfpapers/p103-williams__vis_ordering.pdf

Visibility-ordering meshed polyhedra

Volume visualization is a method of extracting meaningful information from volumetric data using interactive graphics and imaging. It is concerned with volume data representation, modeling, manipulation, and rendering. Volume data are 3D (possibly time-varying) entities that may have information inside them, may not consist of tangible surfaces and edges, or may be too voluminous to be represented geometrically. They are obtained by sampling, simulation, or modeling techniques. When volumetric data are visualized using a surface-rendering technique, a dimension of information is essentially lost. In response to this, volume rendering techniques were developed that attempt to capture the entire 3D data in a single 2D image. Volume rendering conveys more information than surface-rendered images but at the cost of increased algorithm complexity and consequently increased rendering times. To improve interactivity in volume rendering, many optimization methods both for software and graphics-accelerator implementations as well as several special-purpose volume rendering machines have been developed.

/pdf/7-overview-of-volume-rendering-3uaii3coqa.pdf

7 – Overview of Volume Rendering

We present an algorithm for compositing a combination of density clouds and contour surfaces used to represent a scalar function on a 3-D volume subdivided into convex polyhedra. The scalar functio...

Area and volume coherence for efficient visualization of 3D scalar functions

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Area and volume coherence for efficient visualization of 3D scalar functions