createConic {fitConic}

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)

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.

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).

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.

Author(s)

Carl Witthoft <[e-mail]>

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')