Proposition: [i]Create a tool which gives the Bézier curve of order n through n+1 given points. [/i]
[b]Tool (.ggt):[/b] [url]http://www.geogebratube.org/material/show/id/83845[/url]
[math]\;\;\;\;[/math]BezierCurve1[<number n>, <Polyline (n+1 points)>]
The tricky bit was [i]to let the user choose any number of points.[/i]
Solution: Pass a Polyline (which may be of any length) as the Tool input.
Using the polyline's path parameter, make a duplicate list of points.
Build the curve on this dummy list.
For better performance, I use BezierCf[n] for the coefficients, and then complete the curve manually (see previous worksheet).
BezierCurve1[] is easier to use, and still quite fast.
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These are my self-study materials. Let me know how I can make them more useful to you.
Bézier Curves: 2. High Order Curves
[list]
[*] Standard Curve:
[math] \;\;\;[/math]Coefficient Matrix[color=#1551b5](+TOOL)[/color]: [url]http://www.geogebratube.org/material/show/id/83830[/url]
[math] \;\;\;[/math] [b]→Bézier Curve of Order n[color=#1551b5] (+TOOL)[/color][b]
[/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]
