Background Information and Techniques - Computer Animation: Algorithms and Techniques - page 465

formulation. The interior control points can be constructed by displacing the control points along the
tangent lines just formed. For example, for the segment between given points b i and b i 11 , the first con-
trol point for the segment, c

1
i

, can be positioned at b i þ (1/3) ( b i þ 1 b i 1 ). The second control point for

2
i

the segment, c ( b i þ 2 b i ) (see Figure B.51 ) .

Other methods exist. Farin [ 4 ] presents a more general method of constructing the Bezier curve and,
from that, constructing the B-spline control points. Both Farin [ 4 ] and Rogers and Adams [ 18 ] present a
method of constructing a composite Hermite curve through a set of points that automatically calculates
internal tangent vectors by assuming second-order continuity at the segment joints.

, can be positioned at b i þ 1 (1/3)

b i

b i 1

b i 2

b i 2 b i

b i 1 b i 1 b i 1

Four initial points with vectors drawn between pairs of
points adjacent to interior points (e.g., b i 1 and
b i 1 are adjacent to b i )

1
3

1
3

b i 1 ￿ ( b i 1 b i 1 ) b i 1 ￿ ( b i 1 b i )

b i 1 b i 2

Construction of interior control points

b i

b i 1

b i 2

b i 1

Bezier curve segment constructed

FIGURE B.51
Constructing a Bezier segment that interpolates points.