18 research outputs found
RAY DENSITY ANALYSIS FOR VIRTUAL SPECTROPHOTOMETERS
Virtual spectrophotometric measurements have important applications in
physically-based rendering. These measurements can be used to evaluate
reflectance and transmittance models through comparisons with actual
spectrophotometric measurements. Moreover, they can also be used to
generate spectrophotometric data, which are dependent either on the
wavelength or on the illuminating geometry of the incident radiation,
from previously validated models. In this paper the ray casting based
formulation for virtual spectrophotometers is discussed, and a mathematical
bound, based on probability theory, is proposed to determine the number of
rays needed to obtain asymptotically convergent readings. Specifically, the
exponential Chebyshev inequality is introduced to determine the ray density
required to obtain reflectance and transmittance measurements with a high
reliability/cost ratio. Practical experiments are provided to illustrate
the validity and usefulness of the proposed approach.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]
APPLYING THE EXPONENTIAL CHEBYSHEV INEQUALITY TO THE NONDETERMINISTIC COMPUTATION OF FORM FACTORS
The computation of the fraction of radiation power that leaves a surface and
arrives at another, which is specified by the form factor linking both
surfaces, is central to radiative transfer simulations. Although there are
several approaches that can be used to compute form factors, the application
of nondeterministic methods is becoming increasingly important due to the
simplicity of their procedures and their wide range of applications. These
methods compute form factors implicitly through the application of standard
Monte Carlo techniques and ray casting algorithms. Their accuracy and
computational costs are, however, highly dependent on the ray density used in
the computations. In this paper a mathematical bound, based on probability
theory, is proposed to determine the number of rays needed to obtain
asymptotically convergent estimates for form factors in a computationally
efficient stochastic process. Specifically, the exponential Chebyshev
inequality is introduced to the radiative transfer field in order to determine
the ray density required to compute form factors with a high reliability/cost
ratio. Numerical experiments are provided which illustrate the validity and
usefulness of the proposed bound.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]