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library(conicfit)
# demo for ellipse fitting
# created by Prof. Chernov 2014
XY <- matrix(c(1,7,2,6,5,8,7,7,9,5,3,7,6,2,8,4),8,2,byrow=TRUE)
# XY is the coordinates of the data points.
# This is a benchmark example from the journal paper
# W. Gander, G. H. Golub, and R. Strebel,
# "Least squares fitting of circles and ellipses"
# BIT, volume 34, (1994), pages 558-578
ParGini <- matrix(c(0,0,2,1,0),ncol=1)
# Parameters of the initial ellipse are chosen arbitrarily:
# center (0,0), axes 2 and 1, angle of tilt 0
LambdaIni <- 0.1
# initial value for the control parameter "lambda" set to 0.1
tmp <- fit.ellipseLMG(XY,ParGini,LambdaIni)
print(tmp)
# ParG =
# 2.6996
# 3.8160
# 6.5187
# 3.0319
# 0.3596
# RSS = 1.3733
# iters = 15
# TF = 0
# geometric ellipse fit returns parameters of the best fitting ellipse
# correct answers:
# center at (2.6996,3.180), axes (6.5187,3.0319), angle of tilt 0.3596
ParAini <- GtoA(ParGini)
# A B C D E F
# 0.25 0 1 0 0 -1
# algebraic parameters of the initial ellipse
tmp <- fit.conicLMA(XY,c(ParAini),LambdaIni)
ParA <- tmp$ParA
RSS <- tmp$RSS
iters <- tmp$iters
print(tmp)
# ParA =
# 0.0551
# -0.0908
# 0.1588
# 0.0489
# -0.9669
# 0.1620
# RSS = 1.3733
# iters = 18
# code = 1
# geometric conic fit using algebraic parameters
# returns algebraic parameters of the best fitting conic
tmp <- AtoG(ParA)
print(tmp)
# ParG =
# 2.6996
# 3.8160
# 6.5187
# 3.0319
# 0.3596
# code = 1
# convert the algebraic to geometric parameters
RSS
iters
# 1.373306
# 18
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