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4.4. COMPONENT DESIGN
therefore:


 k
v=
if x >= L
mx + c if l < x < L


0
if x <= l
From these, we can solve for m and c in terms of the three fundamental
numbers k, l, and L:
1. v = mx + c
2. 0 = lm + c therefore c = −lm (A) or m = −c/l (C)
3. k = Lm + c therefore c = k − Lm (B) or m = (k − c)/L (D)
4. From A and B −lm = k − Lm therefore m = k/(L − l)
5. From C and D −c/l = (k − c)/L therefore c = kl/(l − L)
These three numbers (k, l, and L) therefore, completely determine the traffic
behaviour. The design decision to use the simplest model possible allows the
project a wider scope in other aspects, however the model suffers in realistic
factors such as drivers’ reaction times, or limits to how fast a car can brake
or accelerate.
Animation of cars
A cars shape is a polygon. The centre of the polygon is positioned in the
centre of a lane. The rotation of the polygon is dependent upon the direction
of its current lane.
Figure 4.13: Intersection of two lines
In the Fig 4.13 the gradient of l1 is m1 and the gradient of l2 is m2 .