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input of 120,000 is 85.7076 FPS. However, the measured frame rate is
approximately 104. Hence the error is approximately 18.3 FPS.
2. The moving average of the gradient with a window of 200 frames is
7.0482 × 10
-4
. The estimated frame rate at a steady-state vertex count input
of 120,000 is 84.578. However, the measured frame rate is approximately
104. Hence the error is approximately 19.4 FPS.
3. The moving average of the gradient with a window of 500 frames is
6.6301 × 10
-4
. The estimated frame rate at a steady-state vertex count input
of 120,000 is 79.56. However, the measured frame rate is approximately
104. Hence the error is approximately 24.44 FPS.
The above results obtained from the second frame time estimation technique show
errors approximately four to six times larger than the output from the system model
using our proposed approach. In brief, our modelling framework out-performs both
the first and second estimation techniques.
3.8
SUPERPOSITION IN 3D RENDERING SYSTEM MODEL
The system models derived in the previous sections are based on a specific configu-
ration of the rendering state machine. In this section, we want to further investigate
and extend the proposition of a system model for the rendering process that may be
broken down further into multiple system models. In the context of real-time render-
ing, this may be explained as the dissection of a rendering process into its constituent
components. Why is this important? The formulation of a rendering process system
model if proven to adhere to the principle of superposition is pivotal for gaining the
following benefits:
•
The output of a combination of rendering processes can be determined
without additional modelling.
•
A suitable controller can be designed for each constituent rendering process
model. This provides greater flexibility and accuracy in controlling the out-
put of the combined rendering process.
At this juncture, we want to establish the validity that each constituent process sys-
tem model contributes to the combined rendering system model. A hypothesis in
componentised modelling of 3D rendering based on the principle of superposition
is proposed.
3.8.1
P
RinciPle
of
s
uPeRPosition
In system theory, the net response at a given place and time caused by two or more
stimuli for linear systems is the sum of the responses that would have been caused
by each stimulus individually. Thus, if input
A
produces response
X
and input
B
produces response
Y
, input (
A
+
B
) produces response (
X
+
Y
). Mathematically, for
all linear systems,
y
=
F
(
x
) where
x
is some sort of stimulus (input) and
y
is some
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