
566 Chapter 11 Curves
Figure 11.8 Parameters τ = 0, γ =0, β =−1.
11.8 Parametric Subdivision
For drawing purposes, it is sometimes necessary to produce a piecewise linear ap-
proximation to a curve with n + 1 curve points that will be the line segment end-
points. If t
i
are the selected curve parameters for 0 ≤ i ≤ n, then the set of points
X
i
= X(t
i
) for 0 ≤ i ≤n isreferredtoasasubdivision of the curve. Three methods
are discussed.
11.8.1 Subdivision by Uniform Sampling
The simplest way to subdivide is to uniformly sample [t
min
, t
max
]as t
i
= t
min
+
(t
max
− t
min
)i/n for 0 ≤ i ≤ n. Although easy to compute, the resulting polyline is
not always a good approximation ...