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1cstypes
2
3bezier
4
5Type bezier specifies a sequence of Bezier curves of similar degree, each
6beginning where the prior terminated. If there are multiple curves in the
7sequence, then the initial control point of a latter curve is not explicitly
8specified since it is equal to the last control point of the prior curve.
9
10Consider the following example.
11
12 curv2 -6 -5 -4 -3 -2 -1 -6
13
14When the degree is 3, the above specifies two Bézier curves: C₁=(-6,-5,-4,-3) and
15C₂=(-3,-2,-1,-6).
16
17The Bézier curve functions are taken to be branches of a peicewise function C
18obtianed by dividing the parameter space into regions and mapping each region
19to a different curve. For example,
20
21 parm u 0.00 1.00 2.00
22
23specifies two intervals, [0,1] and [1,2]. If the parameter is between 0 and 1,
24it will be mapped via the first curve C₁ and if it is between 1 and 2, it will
25be mapped via the second curve C₂. In order to maintain continuity, an affine
26transformation will be applied first to obtain a value between 0 and 1 so that
27C(1.5) = C₂(0.5).
28