draw egg curves from an equation

hello

im trying to figure out how to draw an egg curve using the equation (x²+y²)²=ax³+(a-b)xy² taken from this website http://www16.ocn.ne.jp/~akiko-y/Egg/index_egg_E.html#1

expression with inputs a and b gave me no results as well as f2 ( function with two variables)

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Permalink Reply by hatem on June 19, 2012 at 1:46am

when i input the equation in a f(n) component i get an error saying (Syntax error: Unknown variable encountered: x)

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Permalink Reply by Danny Boyes on June 19, 2012 at 3:04am

The Expression you are using has both sides of the equation already. What you require is an expression where F={EXPRESSION} where F is the only output.

For your egg curve you need to find the y={Expression} to plug into an Fx3 component with x, a and b as inputs. x is a range of 0 to 4. when a = 4

See image below and attached definition.

Attachments:

eggcurve.gh, 3 KB

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Permalink Reply by Danny Boyes on June 19, 2012 at 3:13am

Here's my modification to add a curve through all the points

Attachments:

eggcurve.gh, 6 KB

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Permalink Reply by Johan Rooijackers on June 19, 2012 at 2:50am

Have a look at this post http://www.grasshopper3d.com/profiles/blogs/supperellipse which is based on this formula's

You will have to feed the inputs of the formula component otherwise it collects null values, and when only a and b are variables as inputs then you x and y are unknown. to solve this add two more inputs with the names x and y (fn comp).