Difference between revisions of "Spline Command"

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:Creates a spline with given order through all points.
 
:Creates a spline with given order through all points.
 
;Spline( <List of Points>, <Order ≥ 3>, <Weight Function> )
 
;Spline( <List of Points>, <Order ≥ 3>, <Weight Function> )
:Creates a spline with given order through all points. The weight function says what should be the difference of t values for point P<sub>i</sub> and P<sub>i+1</sub> given their difference P<sub>i+1</sub>-P<sub>i</sub>=(x,y). To get the spline you expect from "function" algorithm you should use <code>abs(x)+0*y</code>, to get the GeoGebra's default spline you can use <code>sqrt(x^2+y^2)</code>.  
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:Creates a spline with given order through all points. The weight function says what should be the difference of ''t'' values for point ''P''<sub>i</sub> and ''P''<sub>i+1</sub> given their difference ''P''<sub>i+1</sub> - ''P''<sub>i</sub> = (''x'', ''y''). To get the spline you expect from "function" algorithm you should use <code>abs(x)+0*y</code>, to get the GeoGebra's default spline you can use <code>sqrt(x^2+y^2)</code>.  
:{{Note|The choice of default makes the result behave nicely when transformed, making sure that <code>Rotate(Spline(list), a)</code> gives the same as <code>Spline(rotate(list, a))</code>.}}
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:{{Note|The choice of default makes the result behave nicely when transformed, making sure that <code>Rotate(Spline(list), a)</code> gives the same as <code>Spline(Rotate(list, a))</code>.}}

Latest revision as of 08:54, 30 July 2020


Spline( <List of Points> )
Creates a cubic spline through all points.
Spline( <List of Points>, <Order ≥ 3> )
Creates a spline with given order through all points.
Spline( <List of Points>, <Order ≥ 3>, <Weight Function> )
Creates a spline with given order through all points. The weight function says what should be the difference of t values for point Pi and Pi+1 given their difference Pi+1 - Pi = (x, y). To get the spline you expect from "function" algorithm you should use abs(x)+0*y, to get the GeoGebra's default spline you can use sqrt(x^2+y^2).
Note: The choice of default makes the result behave nicely when transformed, making sure that Rotate(Spline(list), a) gives the same as Spline(Rotate(list, a)).

Comments

The result of the spline command is a curve. Spline algorithm is used for x and y coordinates separately: first we determine values of t that correspond to the points (based on Euclidian distances between the points), then we find cubic splines as functions t->x and t->y.

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