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