Modelling Non-Linear Rendering Processes - Real-Time Rendering: Computer Graphics with Control Engineering - page 51

4 Modelling Non-Linear

Rendering Processes

4.1 INTRODUCTION
The real-time rendering process is inherently non-linear [38]. This can be understood
from the fact that computer systems on which software runs are constructed using
electronic components that exhibit non-linear material properties. Consequently,
using a single linear model to describe the behaviour of a non-linear system would
be inadequate. In this chapter, we describe an approach by which this non-linear
characteristic can be captured sufficiently with appropriate system models using
advanced techniques in soft computing.

4.2 BACKGROUND

4.2.1 s ystem m odelling with n euRal n etwoRks
In system identification, it is often necessary to begin with the assumption that
the underlying model is linear and then apply the appropriate model structures
described above. However, an actual system may not always exhibit linear char-
acteristics throughout an operating range. For example, research conducted by
Hook and Bigos [38] showed that the time required to process a single vertex varies
even when parameters such as rendering states and display resolution are fixed.
Therefore, it is useful to conduct a comprehensive analysis to better understand the
dynamics of a system.
In this research, we introduce the application of artificial neural networks (ANNs)
to model the non-linearity in the real-time rendering process. Soft computing tech-
niques based on the artificial neuron proposed by McCulloch and Pitts [39] spread
widely into many other fields of study in recent decades. The distinctive nature of the
artificial neurons in various network configurations provided the capability to model
both linear and non-linear systems with good accuracy.
The first artificial neuron proposed by McCulloch and Pitts mimicked the func-
tioning of biological neurons through a multiple-input-single-output model. The
artificial neuron is essentially a processing unit that sums the weighted values of its
inputs to produce an intermediate output that is then fed as an input to an activation
function that produces the final output. An ANN is formed with layers of inter-
connected neurons and is frequently used to simulate the functions of many systems.
Figure 4.1(a) illustrates the structure of the artificial neuron. ANNs must be
trained to capture the characteristics of the systems they model. Training algorithms

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