28.2.2 Ellipse

Function

f = \left(\frac{x-x_c}{a}\right)^2 + \left(\frac{y-y_c}{b}\right)^2 - 1

Brief Description

Implicit ellipse equation whose major and minor axes coincide with XY axes.

Sample Curve

Ellipse.png

Parameters

Number: 4

Names: xc, yc, a, b

Meanings: xc = x center, yc = y center, a = major radius, b = minor radius

Lower Bounds: a > 0.0, b > 0.0

Upper Bounds: none

Derived Parameters

Area=\pi ab \;


e=\sqrt{ 1 - \left(a>b ? \frac{b}{a} : \frac{a}{b}\right)^2 }

ApproxC=\pi(a+b)\frac{1 + 3\left(\frac{a>b ? (a-b) : (b-a)}{a+b}\right)^2}{10 + \sqrt{4 - 3\left(\frac{a>b ? (a-b) : (b-a)}{a+b}\right)^2}}

Script Access

nlf_Ellipse(x,y,xc,yc,a,b)

Function File

FITFUNC\ELLIPSE.FDF

Category

Implicit