DESIGN OF CURVES 93r 33 ( ) = [ 33 32 1] 332–21 1
–3 3 –2 –1
0010
100032
6–1
10
1–1uuuu , 0 1u⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥≤≤or r 33 (uuuuuu) = [–4^33 + 6 32 + + 3, 5 – 8 3 33 32 + 2]
PointC(3, 2) appears as a junction point between segments r 2 (u) and r 3 (u) and both segments
would get modified after C is relocated to (1.5, 4). The new segments would be
r 2 new( 2 ) = [ 23 22 22 1]2–21 1
–3 3 –2 –1
0010
100012
1.5 4
11/3
10uuuu , 0 1u⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥≤≤or r 2 new(uu uu 2 ) = [^32 – 1.5 22 + 2 + 1, –3.4 2 u u u 23 + 4.85 23 + 0.58 + 2] 2
and r 3 new( 3 ) = [ 33 23 1] 33
2–21 1
–3 3 –2 –1
0010
10001.5 4
6–1
10
1–1uuuu , 0 1u⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥⎡⎣⎢
⎢
⎢
⎢⎤⎦⎥
⎥
⎥
⎥≤≤or r 3 new(uuuu uu 3 ) = [–7^33 + 10.5 32 + + 1.5, 9 3 33 – 14 32 + 4]
The original and modified composite C^1 continuous Ferguson curves are shown in Figure 4.5(a).
Note that the composite curve gets modified only partially.
Figure 4.5 (a) Original (solid) and modified (dashed) C^1 continuous Ferguson
curves in Example 4.3 showing local control in shape change5 4 3 2 1 0–1y012345 6
xB
CAD