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from electromagnetism. The complexity of modelling can be reduced, because the
calculations are often prohibitive, with the help of some simplifying hypotheses.
In image synthesis, these models are also called virtual goniometers since it involves
simulating the measurement of a BRDF, whereas the physicists prefer the termof virtual
laboratory .
1D Models
A number of models were developed in the past for studying natural light sources like
stars or for heavy and complex applications like climate study. Because of their huge
sizes and the predominant role of gravity, the celestial or terrestrial atmospheres are
multi-storeyed environments made up of layers , where the physical properties vary
considerably more as per the gradient of gravity (“vertical'' plane) than as per the sup-
porting plane of the surface (“horizontal'' plane). A representation by layers (1D) is
thus sufficient for these environments. These layers are often considered to be horizon-
tally laid, plane and infinite, and the distribution of elements in these layers is assumed
to be homogenous. In remote sensing, sometimes we also talk about turbulent models.
3D models
In a more general case of a surface made up of heterogeneous elements, having highly
variable space scales, it is necessary to consider the phenomenon of reflection in its
complete variability, i.e. in 3D. For such complex surfaces, an analytical approach in
no longer possible and digital methods like the Monte Carlo method or the discrete
ordinates method are used. 1D models are, in fact, a sub-class of 3D models. In remote
sensing, sometimes we also talk about volume models. In case of rough surfaces, it is
common to talk of 2D models in the sense that the described surface is a 2D interface
on which the light is reflected.
This group of models cannot be used in virtual reality. The time for calculations
and the geometric complexity inherent to the explicit description of the surface are not
compatible with the constraints of real time rendering imposed by the interactive appli-
cations of virtual reality. However, these models can be used during the pre-calculation
phase to provide input data for adjusting implicit models on a given material.
Implicit modelling
An implicit model does not provide explicit representations of the surface for which the
BRDF is studied. It is a pragmatic approach that provides a correct BRDF but without
an actual understanding of physical processes taking place during the phenomenon of
light reflection. The common point between these models is that they require a set of
BRDF measurements as starting point in a physical context.
Phenomenological models
A phenomenological model provides an explicit expression of the BRDF (but with-
out an explicit description of the surface studied). It is a mathematical function that
depends on one or more parameters. These parameters can be fixed arbitrarily ( direct
approach), but are generally assessed on a set of measurements ( reverse approach 3 ).
3 We also talk of adjusting.
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