osculant: Locus of osculation between two families of ellipses In gmonette/spida: 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

 ```1 2 3 4``` ```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])

`cell`, `dell`, `ellplus`,`dellplus`,
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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') ```