Nelson L. Max

Optical models for direct volume rendering

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. >

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

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 function is interpolated between values defined at the vertices, and the polyhedra are sorted in depth before compositing. For n tetrahedra comprising a Delaunay triangulation, this sorting can always be done in O(n) time. Since a Delaunay triangulation can be efficiently computed for scattered data points, this provides a method for visualizing such data sets. The integrals for opacity and visible intensity along a ray through a convex polyhedron are computed analytically, and this computation is coherent across the polyhedrons projected area.

Bidirectional reflection functions from surface bump maps

The Torrance-Sparrow model for calculating bidirectional reflection functions contains a geometrical attenuation factor to account for shadowing and occlusions in a hypothetical distribution of grooves on a rough surface. Using an efficient table-based method for determining the shadows and occlusions, we calculate the geometric attenuation factor for surfaces defined by a specific table of bump heights.Diffuse and glossy specular reflection of the environment can be handled in a unified manner by using an integral of the bidirectional reflection function times the environmental illumination, over the hemisphere of solid angle above a surface. We present a method of estimating the integral, by expanding the bidirectional reflection coefficient in spherical harmonics, and show how the coefficients in this expansion can be determined efficiently by reorganizing our geometric attenuation calculation.

Texture splats for 3D scalar and vector field visualization

Volume visualization is becoming an important tool for understanding large 3D data sets. A popular technique for volume rendering is known as splatting. With new hardware architectures offering substantial improvements in the performance of rendering texture mapped objects, we present textured splats. An ideal reconstruction function for 3D signals is developed which can be used as a texture map for a splat. Extensions to the basic splatting technique are then developed to additionally represent vector fields.<<ETX>>

A contract based system for large data visualization

VisIt is a richly featured visualization tool that is used to visualize some of the largest simulations ever run. The scale of these simulations requires that optimizations are incorporated into every operation VisIt performs. But the set of applicable optimizations that VisIt can perform is dependent on the types of operations being done. Complicating the issue, VisIt has a plugin capability that allows new, unforeseen components to be added, making it even harder to determine which optimizations can be applied. We introduce the concept of a contract to the standard data flow network design. This contract enables each component of the data flow network to modify the set of optimizations used. In addition, the contract allows for new components to be accommodated gracefully within VisIts data flow network system.

Weights for computing vertex normals from facet normals

Abstract I propose a new equation to estimate the normal at a vertex of a polygonal approximation to a smooth surface, as a weighted sum of the normals to the facets surrounding the vertex. The equation accounts for the difference in size of these facets by assigning larger weights for smaller facets. When tested on random cubic polynomial surfaces, the equation is superior to other popular weighting methods.

Horizon mapping: shadows for bump-mapped surfaces

Bump mapping produces realistic shading by perturbing normal vectors to a surface, but does not show the shadows that the bumps cast on nearby parts of the same surface. In this paper, these shadows are found from precomputed tables of horizon angles, listing, for each position entry, the elevation of the horizon in a sampled collection of directions. These tables are made for bumps on a standard flat surface, and then a transformation is developed so that the same tables can be used for an arbitrary curved parametrized surface patch. This necessitates a new method for scaling the bump size to the patch size. Incremental calculations can be used in a scan line algorithm for polygonal surface approximations. The errors in the bump shadows are discussed, as well as their anti-aliasing. (An earlier version of this article appeared as Max [10].)

Sorting and hardware assisted rendering for volume visualization

We present some techniques for volume rendering unstructured data. Interpolation between vertex colors and opacities is performed using hardware assisted texture mapping, and color is integrated for use with a volume rendering system. We also present an O(n{sup 2}) method for sorting n arbitrarily shaped convex polyhedra prior to visualization. It generalizes the Newell, Newell and Sancha sort for polygons to 3-D volume elements.

Smooth transitions between bump rendering algorithms

A method is described for switching smoothly between rendering algorithms as required by the amount of visible surface detail. The result will be more realism with less computation for displaying objects whose surface detail can be described by one or more bump maps. The three rendering algorithms considered are a BRDF, bump mapping, and displacement mapping. The bump mapping has been modified to make it consistent with the other two. For a given viewpoint, one of these algorithms will show a better trade-off between quality, computation time, and aliasing than the other two. The decision as to which algorithm is appropriate is a function of distance, viewing angle, and the frequency of bumps in the bump map.

Flow volumes for interactive vector field visualization

Flow volumes are the volumetric equivalent of stream lines. They provide more information about the vector field being visualized than do stream lines or ribbons. Presented is an efficient method for producing flow volumes, composed of transparently rendered tetrahedra, for use in an interactive system. The problems of rendering, subdivision, sorting, composing artifacts, and user interaction are dealt with. Efficiency comes from rendering only the volume of the smoke, and using hardware texturing and compositing.<<ETX>>