Tool: Bézier Coefficient Matrix

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] ____ As always, these are my self-study materials. Let me know how I can make them more useful to you.

Ryan Hirst

 
Material Type
Tool
Tags
tools  parametric  splines  bezier  curves 
Target Group (Age)
19+
Language
English (United States)
 
 
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