View source: R/arcLengthEllipse.R
arcLengthEllipse | R Documentation |
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.
arcLengthEllipse(p1, p2 = NULL, saxes, n = 5)
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. |
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.
pEllipticInt
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)
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