Command: BézierCf[<curve order>]
Output: Coefficient matrix C for the multiplication
[math]β(t) = P C τ(t) [/math]
P, the n+1 control points (row vector)
τ(t), powers of t: [math] 1, t, t^2, ... t^n [/math] (column vector)
β(t), 0≤t≤1, is the resulting [i]n[/i]th order Bézier curve.
In GGB, the curve can be created this way:
[list]
[*]Replace t with the variable x, so that
τ = Sequence[x^k, k, 0, n]
[*]Generate the x- and y- components of the curve
βx = Sum[Zip[a b, a, Join[{x(Pts)} C], b, τ]]
βy = Sum[Zip[a b, a, Join[{y(Pts)} C], b, τ]]
[*]β = Curve[βx(a), βy(a), a, 0, 1]
[/list]
Construction: [url]http://www.geogebratube.org/material/show/id/83830[/url]
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As always, these are my self-study materials. Let me know how I can make them more useful to you.
