Fit logarithmic spiral to x,y data

Fits logarithmic sprial r=a*exp(b*theta) to x,y data points.

Description

Logaritmic spirals often occur in nature such as the cross section of a chambered nautilus, atmospheric vortices around regions of low pressure and spiral arms of galaxies. Polar form for a log spiral with center at the origin is r=a*exp(b*theta). A general log sprial with center at xc,yc is then x=xc+r*cos(theta) and y=yc+r*sin(theta). This code fits coefficients a,b and center location xc,yc to data points along the log spiral curve. It uses the nonlinear Nedler-Mead simplex routine "fminsearch" to find the best center location and a simple linearized least-squares solution for coefficients a,b. The code provides an RMS measure for goodness-of-fit.

• MATLAB release: MATLAB 7.5 (R2007b)