Computer Aided Engineering Design

156 COMPUTER AIDED ENGINEERING DESIGN

clamped B-splines have already been shown in Figure 5.16. Figure 5.20 shows a schematic of 7 cubic
(p= 4) basis functions to explain what happens when the knot multiplicity is raised. Recall from the

Figure 5.19 (a) Linear segments with B-spline curves, (b) B-spline curve passing through an intermediate
point, (c) curve passing through an intermediate data point and is also tangent to the line
containing it, (d) curve clamped at the first data point using multiplicity p–1 of data points,
(e) curve clamped at both ends using multiplicity p–1 of end points and (f) a closed spline
using multiplicity of data points

02468

x(t)

(b)

3

2

1

0

–1

–2

–3

y(t)

0246 8

x(t)

(d)

6

4

2

0

–2

–4

y(t)

y(t)

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x(t)

(f)

6

4

2

0

–2

–4

–6

02468

x(t)

(a)

3

2

1

0

–1

–2

–3

y(t)

024 68

x(t)

(c)

5 4 3 2 1 0

–1

–2

–3

y(t)

024 68

x(t)

(e)

6

4

2

0

–2

–4

y(t)