경로매개변수 명령
GeoGebra Manual
- PathParameter( <Point On Path> )
- Returns the parameter (i.e. a number ranging from 0 to 1) of the point that belongs to a path.
- 예:Let
f(x) = x² + x - 1andA = (1, 1)is a point attached to this function.PathParameter(A)yields a = 0.47.
In the following table f(x)=\frac{x}{1+|x|} is a function used to map all real numbers into interval (-1,1) and \phi(X,A,B)=\frac{\overrightarrow{AX}\cdot\overrightarrow{AB}}{|AB|^2} is a linear map from line AB to reals which sends A to 0 and B to 1.
| Line AB | \frac{f(\phi(X,A,B))+1}2 |
| Ray AB | f(\phi(X,A,B)) |
| Segment AB | \phi(X,A,B) |
| Circle with center C and radius r | Point X=C+(r\cdot cos(\alpha),r\cdot sin(\alpha)), where \alpha\in(-\pi,\pi) has path parameter \frac{\alpha+\pi}{2\pi} |
| Ellipse with center C and semiaxes \vec{a}, \vec{b} | Point X=C+\vec{a}\cdot cos(\alpha)+\vec{b}\cdot sin(\alpha), where \alpha\in(-\pi,\pi) has path parameter \frac{\alpha+\pi}{2\pi} |
| Hyperbola | Point X = C \pm \vec{a} ·cosh(t) + \vec{b} ·sinh(t) has path parameter \frac{f(t)+1}{4} or \frac{f(t)+3}{4} |
| Parabola with vertex V and direction of axis \vec{v}. | Point V+\frac{1}{2}p\cdot t^2\cdot \vec{v}+p\cdot t \cdot \vec{v}^{\perp} has path parameter \frac{f(t)+1}2. |
| Polyline A1...An | If X lies on AkAk+1, path parameter of X is \frac{k-1+\phi(X,A,B)}{n-1} |
| Polygon A1...An | If X lies on AkAk+1 (using An+1=A1), path parameter of X is \frac{k-1+\phi(X,A,B)}{n} |
| List of paths L={p1,...,pn} | If X lies on pk and path parameter of X w.r.t. pk is t, path parameter of X w.r.t.L is \frac{k-1+t}{n} |
| List of points L={A1,...,An} | Path parameter of Ak is \frac{k-1}{n}. Point[L,t] returns A_{\lfloor tn\rfloor+1}. |
| Locus | |
| Implicit polynomial | No formula available. |
