# AtoG: A Set Of Functions To Convert Among Various... In fitConic: Fit Data to Any Conic Section

 AtoG R Documentation

## A Set Of Functions To Convert Among Various Conic-Section-Defining Parameter Sets.

### Description

`AtoG` Convert from full quadratic "ABCDEF" to focus, axis, angle "hvab theta" parameters. `GtoA` Convert from "hvab theta" to "ABCDEF" parameters. `parab3toA` Simple conversion from a + bx + cx^2 to "ABCDEF" parameters. `FEDtoA` Convert focus, eccentricity, and directrix to "ABCDEF" parameters.

### Usage

``````AtoG(parA, tol = 1e-06)
GtoA(parG, conicType = c("e", "h"))
FEDtoA(focus = c(0, 0), directrix = c(1, 0, 1), eccentricity = 0.5)
``````

### Arguments

 `parA` The six coefficients in the quadratic Ax^2 + Bxy + Cy^2 +Dx + Ey +F = 0 `tol` A small value, used to check whether small coefficient values might be actually zero. See "Details." `parG` a five-element vector "h,v,a,b,theta" . See "Details" for the standard equation form for this. `conicType` Because the 'hvab' equation has a sign difference for ellipses vs. hyperbolas, it is necessary to indicate which kind of input is intended. See "Details." `focus` location of the conic sections focus. `directrix` the 3-element directrix. `eccentricity` the eccentricity of the conic section. `ADF` The A,D,F coeffients in the standard quadratic. Thus, the x^2 term, the x term, and the constant term. `theta` An angle by which the entire parabola is to be rotated.

### Details

The `tol` input for `AtoG` checks two conditions. First, is B practically zero, in which case B is set to exactly zero, implying no rotation of the conic section. Second, is B^2 - 4*A*C almost zero, implying that the conic is probably a parabola, and conversion to 'hvab' form is not useful.

The "hvab" form for describing an ellipse or a hyperbola looks like [Center(1:2), Axes(1:2)/2] angle A, to fill the equation

((x-h)cosA +(y-v)sinA)^2/a^2 + ((x-h)sinA-(y-v)cosA)^2/b^2 = 1 The length of the axes are 2*a, 2*b .

A discussion of the focus/directrix/eccentricity form of a conic section is rather lengthy and not presented here. One short introduction can be found at https://en.wikipedia.org/wiki/Conic_section#Eccentricity,_focus_and_directrix

### Value

for `AtoG`,

 `parG` c(h,v,a,b,theta) `exitCode` a value used in fitConic. 1,2, or 3 for ellipse, hyperbola, parabola `conicType` matching exitCode with a char "e", "h", or "p"

for `GtoA`

 `parA` the ABCDEF coefficients of the general quadratic `exitCode` a value used in fitConic. 1,2, or 3 for ellipse, hyperbola, parabola `conicType` matching exitCode with a char "e", "h", or "p"

for `FEDtoA`, the ABCDEF coefficients of the general quadratic for `parab3toA`,

 `parA` the ABCDEF coefficients of the general quadratic `exitCode` always numeric 3, a value used in fitConic `conicType` always char "p"

.

fitConic documentation built on Aug. 29, 2023, 1:12 a.m.