TY - GEN
T1 - A Study Of Discretization Errors In Volume Rendering Integral Approximations
AU - Etiene, Tiago
AU - Kirby, Robert M.
AU - Silva, Cláudio T.
N1 - Funding Information:
This work was in part supported by ARO W911NF-12-1-0375 (Program Manager Dr. Mike Coyle), National Science Foundation (CNS-1229185, CNS-1153503, IIS-0905385, IIS-1142013, and AGS 0835821), the Department of Energy, and ExxonMobil.
Publisher Copyright:
© The Eurographics Association 2013.
PY - 2013
Y1 - 2013
N2 - We present a study of the influence of different approximation schemes on the convergence rate of volume rendering integral (VRI) numerical approximations. We experimentally evaluate the impact of numerical integration techniques on the rate of convergence to the correct solution of the VRI on a single ray. We report that the discretization of both the inner and outer integrals have influence on the overall convergence rate. Then, we present results related to the (traditional) pre-integrated and second-order pre-integrated algorithms. In practice, we observed that pre-integrated lookup tables provide second and third order convergence rates for the VRI approximation, respectively. Our results also suggest that the convergence rate drops one order of magnitude for the second-order algorithm when lookup tables are numerically computed using low sample rates. Also, the convergence of both algorithms drops to linear when the attenuation within ray segment is neglected.
AB - We present a study of the influence of different approximation schemes on the convergence rate of volume rendering integral (VRI) numerical approximations. We experimentally evaluate the impact of numerical integration techniques on the rate of convergence to the correct solution of the VRI on a single ray. We report that the discretization of both the inner and outer integrals have influence on the overall convergence rate. Then, we present results related to the (traditional) pre-integrated and second-order pre-integrated algorithms. In practice, we observed that pre-integrated lookup tables provide second and third order convergence rates for the VRI approximation, respectively. Our results also suggest that the convergence rate drops one order of magnitude for the second-order algorithm when lookup tables are numerically computed using low sample rates. Also, the convergence of both algorithms drops to linear when the attenuation within ray segment is neglected.
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U2 - 10.2312/PE.EuroRVVV.EuroRVVV13.001-005
DO - 10.2312/PE.EuroRVVV.EuroRVVV13.001-005
M3 - Conference contribution
AN - SCOPUS:84959427765
T3 - EuroRV3 2013 - EuroVis Workshop on Reproducibility, Verification, and Validation in Visualization
SP - 1
EP - 5
BT - EuroRV3 2013 - EuroVis Workshop on Reproducibility, Verification, and Validation in Visualization
PB - The Eurographics Association
T2 - 2nd EuroVis Workshop on Reproducibility, Verification, and Validation in Visualization, EuroRV3 at EuroVis 2013
Y2 - 17 June 2013 through 18 June 2013
ER -