Bézier Curve, arbitrary order

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. ______ 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]


Ryan Hirst

Resource Type
bezier  curves  exploration  parametric-curves  splines 
Target Group (Age)
English (United States)
GeoGebra version
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