# Polar Curve Fitting

I am working on automated counting and one of my solutions is the use of the template matching algorithm (specifically using Chamfer Matching Algorithm). However, granted it is a template matching approach, I need to establish my template. The objects I am trying to count are individual coconut trees. Based on the definition of coconut tree crowns, they are star-shaped with feather-like leaves. I had the idea in my mind that I could derive that given a polar equation. However, since I am not a Math major, I looked for polar equations that could describe the above mentioned description and stumbled upon the link below An equation that generates a beautiful or unique shape for motivating students in mathematics and noticed the answer given by Luscian.

My question is, is this equation

$$r(t)=|cos(nt)|^{sin(2nt)}\text{ for }2n\text{ in between 1 and 8 and }t\in(0,2\pi)$$

an already defined one? I am not familiar with this, since my background on polar equations reached only up to cardiods and rhodonea curves.

Any help is greatly appreciated. Thanks!

• Welcome to Math.StackExchange! Interesting Question. Please check that the light notational edits (once accepted) match your intentions. math.stackexchange.com/help/notation Commented Jul 6, 2018 at 6:21
• In any manner, the polar form is amazing; for $n=5$, it looks like a starfish and for $n=8$ it remembered to me how Jean Lurçat represented the sun in some of his tapestries. Commented Jul 6, 2018 at 6:47