fitConic (version 1.2.1)

createConic: Create A Conic Section Dataset Based on Parameter Set

Description

Given a vector of x-values and a parameter set defining a conic section, produce an array of x- and y- values, optionally with noise added, for the specified conic section.

Usage

createConic(x, param, conicType, ranFun = NULL, noise = 1, seedit = NULL, tol = 1e-06)

Value

An N x 2 array of the x,y pairs. Warning: since there are often two possible y-values for a given x-value (these being quadratic equations), the array does contain duplicate x-values. This may "annoy" some other packages' functions which don't allow that sort of repeated value. If this presents a problem, I'd recommend applying a very small amount of noise to the x-values in this output.

Arguments

x

Vector of (real) values

param

Either a 6-value set representing the standard quadratic form Ax^2 + Bxy + Cy^2 +Dx + Ey +F = 0 or a 5-value set representing the "hvab,theta" form ((x-h)cosA +(y-v)sinA)^2/a^2 + ((x-h)sinA-(y-v)cosA)^2/b^2 = 1 . In the latter case the value conicType is required.

conicType

Either the character "e" for ellipse or "h" for hyperbola. Only required if the "hvab,theta" form is used in param .

ranFun

If random noise is to be added to the calculated y-values, provide a vectorized function which takes a single input (x). See Details.

noise

Optional argument to multiply the output of ranFun .

seedit

Optional argument to set a starting seed for ranFun to use.

tol

A (small) value used to decide whether various parameter terms are so small that they should be zero. This is used to facilitate distinguishing, e.g., parabolas from hyperbolas.

Author

Carl Witthoft <[e-mail]>

Details

When supplied ranFun is used as follows. y <- y + ranFun(y)*noise . Make sure any function supplied fits that form (no other input argument required; only a vector returned).

Examples

# create noisy ellipse
parGr <- c(-2.3,4.2,5,3,pi/4)
xe <-seq(-8,9,by=.05)
elipGrn <- createConic(xe, parGr, 'e',ranFun=rnorm, noise=0.25)
elipGr <- createConic(xe,  parGr, 'e')
plot(elipGrn, pch='.',cex = 4, asp = TRUE)  #, xlim = c(-5,8), ylim = c(0,7))
lines(elipGr,col='green')