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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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