osculant: Locus of osculation between two families of ellipses

In gmonette/spida15: Collection of miscellaneous functions for mixed models etc. prepared for SPIDA 2009+ (development version)

Description

Generates points on the curve of osculation between the centers of two families of ellipses

Usage

osculant(center1, shape1, center2, shape2, n = 100, range = c(0, 1), maxu = 100)

## Default S3 method
osculant(center1, shape1, center2, shape2, n = 100, range = c(0, 1), maxu = 100)

Arguments

center1	of first family of ellipses.
shape1	(i.e. 'variance matrix') of first family of ellipses.
center2	of second family.
shape2	of second family.
n	n + 1 is the number of points to generate along the locus. n = 1 generates the two centers, n=0 generates to point on the first ellipse that lines on the locus of osculation provided the centre of the second family lines outside the first ellipse.
range	of values of u to use to generate points. (See the algorithm in the code)

Value

The set of points on the locus is retuned as an n+1 by p matrix where p is the number of rows or columns of the shape matrices.

Author(s)

Georges Monette ([e-mail])

See Also

cell, dell, ellplus,dellplus,

Examples

v1 <- 36*diag(2)
v2 <- .5 * (diag(2) - .4)
v2[2,2] <- 2
plot( 0:10,0:10,type = 'n')
lines( ell( c(2,2), v1))
lines( ell( c(4,4), v2), col = 'red')
osculant(  c(2,2), v1, c(4,4), v2, n = 3)
osculant(  c(2,2), v1, c(4,4), v2, n = 1)
lines( osculant( c(2,2), v1, c(4,4), v2), col = 'red')

lines( ell( c(8,8), v2), col = 'blue')
lines( osculant( c(2,2), v1, c(8,8), v2), col = 'blue')
points( osculant( c(2,2), v1, c(8,8), v2, n=1),pch = 16, col = 'blue')
points( osculant( c(2,2), v1, c(8,8), v2, n=0),pch = 16, col = 'blue')
points( osculant( c(8,8), v2, c(2,2), v1,  n=0),pch = 16, col = 'blue')

gmonette/spida15 documentation built on May 17, 2019, 7:26 a.m.