osculant: Locus of osculation between two families of ellipses

Description Usage Arguments Value Author(s) See Also Examples

View source: R/fun.R

Description

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

Usage

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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 ([email protected])

See Also

cell, dell, ellplus,dellplus,

Examples

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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/spida documentation built on May 17, 2019, 7:25 a.m.