December 2013
Intermediate to advanced
508 pages
16h 50m
English
Content preview from Practical Algorithms for 3D Computer Graphics, 2nd Edition
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46 2. Basic theory and mathematical results
End of curve
Start of curve
Off curve
control points
Figure 2.26: Basic B´ezier curve with two control points on and two control points off
the curve.
Choosing µ such that 0 ≤ µ ≤ 1 returns a linearly interpolated point. When
µ =
1
2
then p = P
1
2
will lie midway between P
0
and P
1
.
In terms of the (x, y, z) co or d in ates of p three interpolating equations can be
written as
x = x
0
+ µ(x
1
− x
0
)
y = y
0
+ µ(y
1
− y
0
)
z = z
0
+ µ(z
1
− z
0
)
(x
0
, y
0
, z
0
) are the coordinates of P
0
and (x
1
, y
1
, z
1
) is P
1
.
2.14.2 Quadratic interpolation
Quadratic interpolation fits a quadratic to three points P
0
, P
1
and P
2
to be
taken together. The equation
p
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