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Physics-based Transparency Visualization for Smoke in 3D Rendering

This document explores the interactions of light and smoke, focusing on the absorption, emission, and scattering of light within volumetric rendering. It delves into the application of the Radiation Transport Equation and Beer-Lambert Law in computing smoke transparency, providing a framework for visualizing smoke phenomena effectively. The study highlights the Fire Dynamics Simulator (FDS) for calculating obscurations and presents techniques for optimizing smoke rendering by adjusting view distances dynamically. Ultimately, it aims to enhance the realism and efficiency of smoke visualization in computational environments.

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Physics-based Transparency Visualization for Smoke in 3D Rendering

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  1. Light/Smoke interactions absorption out-scattering emission in-scattering Volume Rendering Equation – Radiation Transport Equation Beer-Lambert law Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) 3D smoke display using transparency 3D smoke display using transparency 3D smoke display using transparency 3D smoke display using transparency Side view (between two slices) Front view Side view (between two slices) Front view Side view (between two slices) Front view Side view (between two slices) Front view

  2. Beer’s law I/I0=exp(-stDx) Orient planes to be most perpendicular to line of sight DX Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  3. 3D Smoke Dxdistance between adjacent grid planes Sisoot density aiopacity • FDS computes a for each grid node • Smokeview combines a’s using the video card Dx ai = 1 - exp(-ksiDx) S1 Si SN Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  4. 3D SmokeCorrecting a FDS computed: a Smokeview computed: Solve for exp(-ks): Skipping Frames Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  5. Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  6. 3D Smoke Problems can occur for large grids (DX small) ai = 1 - exp(-ksiDx) - Beer’s law a < 1/256 =0 More refined grids  smaller Dx smaller a  increased error Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  7. Dx Observer Background Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  8. x0 Convert temperature and density within each ray to color and opacity xi Ci ai Ti Si xN Image plane Combine colors and opacities to form one color and opacity Cast rays through each image plane pixel Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

  9. Ci Ci+1 C0 CN background ti ti+1 observer x0 xi xi+1 xN Dx t=t1t2 C=t2C1+C2 x0 D xN t1 t2 C1 C2 x0 D D xN Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency Using Transparency to Visualize Smoke Physics-based computation of smoke transparency • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • FDS computes and compresses obscurations, a, (using Dx between adjacent grid planes)at each grid node using soot density data, si, and Beer’s law, ai = 1 - exp(-ksiDx) • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smokeview adjusts each aiin real time for non-axis aligned view distances using • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain) • Smoke may be drawn faster by skipping planes (need to adjust a’s for planes that remain)

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