Volumetric rendering is widely used to examine 3D scalar fields from CT/MRI scanners and numerical simulation datasets. One key aspect of volumetric rendering is the ability to provide perceptual cues to aid in understanding structure contained in the data. 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, a shading model for interactive direct volume rendering is proposed that provides perceptual cues similar to those 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. The 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 while modifications to the volume via clipping planes are incorporated into the resulting occlusion-based shading.

a) 6.1 FPS (b) 3.8 FPS (c) 3.8 FPS (d) 3.8 FPS Figure 1: The backpack data set with 512 × 512 × 373 voxels rendered a) with Phong shading only; and b) with depth of field with α = 30.9 • focused on the spray can in the foreground, c) on the wires behind it and d) on the boxes with the other spray can in the background. In each image 1469 slices were taken and gradients were estimated on the fly. AbstractIn this paper, a method for interactive direct volume rendering is proposed for computing depth of field effects, which previously were shown to aid observers in depth and size perception of synthetically generated images. The presented technique extends those benefits to volume rendering visualizations of 3D scalar fields from CT/MRI scanners or numerical simulations. It is based on incremental filtering and as such does not depend on any precomputation, thus allowing interactive explorations of volumetric data sets via on-the-fly editing of the shading model parameters or (multi-dimensional) transfer functions.

Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. As they provide a generic means of solving a wide variety of problems, numerical methods are most often used to solve the air-light integral even under simplifying assumptions. In this paper, we present a novel analytical approach to single scattering from isotropic point light sources in homogeneous media. We derive the first closed-form solution to the air-light integral in isotropic media and extend this formulation to anisotropic phase functions. The technique relies neither on pre-computation nor on storage, and we provide a practical implementation allowing for an explicit control on the accuracy of the solutions. Finally, we demonstrate its quantitative and qualitative benefits over both previous numerical and analytical approaches.

Due to the intricate nature of the equation governing light transport in participating media, accurately and efficiently simulating radiative energy transfer remains very challenging in spite of its broad range of applications. As an alternative to traditional numerical estimation methods such as ray-marching and volume-slicing, a few analytical approaches to solving single scattering have been proposed but current techniques are limited to the assumption of isotropy, rely on simplifying approximations and/or require substantial numerical precomputation and storage. In this paper, we present the very first closed-form solution to the air-light integral in homogeneous media for general 1-D anisotropic phase functions and punctual light sources. By addressing an open problem in the overall light transport literature, this novel theoretical result enables the analytical computation of exact solutions to complex scattering phenomena while achieving semi-interactive performance on graphics hardware for several common scattering modes.

Understanding fluid flow is a difficult problem and of increasing importance as computational fluid dynamics (CFD) produces an abundance of simulation data. Experimental flow analysis has employed techniques such as shadowgraph, interferometry, and schlieren imaging for centuries, which allow empirical observation of inhomogeneous flows. Shadowgraphs provide an intuitive way of looking at small changes in flow dynamics through caustic effects while schlieren cutoffs introduce an intensity gradation for observing large scale directional changes in the flow. Interferometry tracks changes in phase-shift resulting in bands appearing. The combination of these shading effects provides an informative global analysis of overall fluid flow. Computational solutions for these methods have proven too complex until recently due to the fundamental physical interaction of light refracting through the flow field. In this paper, we introduce a novel method to simulate the refraction of light to generate synthetic shadowgraph, schlieren and interferometry images of time-varying scalar fields derived from computational fluid dynamics data. Our method computes physically accurate schlieren and shadowgraph images at interactive rates by utilizing a combination of GPGPU programming, acceleration methods, and data-dependent probabilistic schlieren cutoffs. Applications of our method to multifield data and custom application-dependent color filter creation are explored. Results comparing this method to previous schlieren approximations are finally presented.