Description Usage Arguments Details Value References See Also Examples

This function computes the arc length of an ellipse centered in *(0,0)* with the semi-axes aligned with the *x*- and *y*-axes. The arc length is defined by the points *1* and *2*. These two points do not need to lie exactly on the ellipse: the *x*-coordinate of the points and the quadrant where they lie define the positions on the ellipse used to compute the arc length.

1 | ```
arcLengthEllipse(p1, p2 = NULL, saxes, n = 5)
``` |

`p1` |
a |

`p2` |
a |

`saxes` |
a |

`n` |
the number of iterations used in the numerical approximation of the incomplete elliptic integral of the second kind. |

If the coordinates `p2`

of the point *2* are omitted the function `arcLengthEllipse`

computes the arc length between the point *1* and the point defined by *(0,b)*, *b* beeing the minor semi-axis.

The length of the shortest arc of the ellipse defined by the points 1 and 2.

Van de Vel, H. (1969). *On the series expansion method for Computing incomplete elliptic integrals of the first and second kinds*, Math. Comp. 23, 61-69.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
p1 <- c(3,1)
p2 <- c(0,2)
# Ellipse with semi-axes: a = 5, b= 2
saxes <- c(5,2)
# 1 iteration
arcLengthEllipse(p1,p2,saxes,n=1)
# 5 iterations
arcLengthEllipse(p1,p2,saxes,n=5)
# 10 iterations
arcLengthEllipse(p1,p2,saxes,n=10)
``` |

```
[1] 3.045829
[1] 3.036814
[1] 3.036808
```

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