Difference between revisions of "Spline Command"
From GeoGebra Manual
(Explain the weight parameter) |
m (Fix typo) |
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;Spline( <List of Points>, <Order ≥ 3> ) | ;Spline( <List of Points>, <Order ≥ 3> ) | ||
: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>. | :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>.}} | :{{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>.}} | ||
Revision as of 00:40, 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 usesqrt(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 asSpline(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.
