# arcLengthEllipse: Arc length of an ellipse In RConics: Computations on Conics

## Description

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.

## Usage

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

## Arguments

 p1 a (2 \times 1) vector of the Cartesian coordinates of point 1. p2 a (2 \times 1) vector of the Cartesian coordinates of point 2 (optional). saxes a (2 \times 1) vector of length of the semi-axes of the ellipse. n the number of iterations used in the numerical approximation of the incomplete elliptic integral of the second kind.

## Details

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.

## Value

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

## References

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.

pEllipticInt

## Examples

  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) 

### Example output

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


RConics documentation built on May 30, 2017, 5:22 a.m.