[b]Tool (.ggt):[/b] [url]http://www.geogebratube.org/material/show/id/83831[/url] [math] \;\;\;\;[/math]Command: BezierCf[n] [math] \;\;\;\;[/math]Output: (n+1)×(n+1) matrix [math] C [/math]
Given a list of Points [math]\;\;\; {\rm Pts} = [A_0, A_1, .... A_n], [/math] and a variable of motion, [i]t[/i] [math] \;\;\;\tau(t) = [1, t, t^2 , ..., t^n]^T,[/math] In GGB,[i]t[/i] can be used as a scalar parameter, with the Locus[] command. For a Curve[], trade t for x: [math] \;\;\;[/math]τ = Sequence[x^k, k, 0, n] The x- and y- components of the curve are then [math] \;\;\;[/math]βx = Sum[Zip[a b, a, Join[{x(Pts)} C], b, τ]] [math] \;\;\;[/math]βy = Sum[Zip[a b, a, Join[{y(Pts)} C], b, τ]] From which the Bézier curve is [math] \;\;\;[/math]β = Curve[βx(a), βy(a), a, 0, 1] [i]What?[/i] GGBScript is not math. In math, the product [math]\;\;\;\;[/math]β = Pts C τ(t), 0≤t≤1 is immediate and unambiguous. It's cute that math people wonder why students have a hard time with math at the computer. ? When did we make it possible for them to do math at the computer? ________ Bézier Curves: 2. High Order Curves [list] [*] Standard Curve: [math] \;\;\;[/math][b]→ Coefficient Matrix[color=#1551b5](+TOOL)[/color][/b] [math] \;\;\;[/math] Bézier Curve of Order n[color=#1551b5] (+TOOL)[/color]: [url]http://www.geogebratube.org/material/show/id/83844[/url] [/list] [list] [*]Curve from Path: [url]http://www.geogebratube.org/material/show/id/84017[/url] [math] \;\;\;[/math]Coefficient Matrix [color=#1551b5](+TOOL)[/color]: [url]http://www.geogebratube.org/material/show/id/84218[/url] [math] \;\;\;[/math]Bézier Path of Order n [color=#1551b5](+TOOL)[/color]: [url]http://www.geogebratube.org/material/show/id/84231[/url] [/list]