How do I give this Equation so that I get the geometry out of it?

(x² + 9/4 y² + z² - 1)³ - x²z³ - 9/80 y²z³ = 0

Replies to This Discussion

Permalink Reply by Danny Boyes on May 20, 2013 at 9:58am

you need to paramaterize it.

Where did you get it from? There is probably a paramaterised version. For Instance Wolfram Mathworld gives the Equations of a circle like this. But in GH you will want either of the equations in the Red Ellipses.

Permalink Reply by Ahmed Hossam on May 20, 2013 at 10:07am

Dannyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy :)

I got it from here: http://www.mathematische-basteleien.de/herz12.gif

No how do I parametrise something like that?

Permalink Reply by Danny Boyes on May 20, 2013 at 10:16am

I haven't found the 3D version but here is a 2D version Parameterised.

Attachments:

EquationOfTheHeart.gh, 14 KB

Permalink Reply by recife on May 20, 2013 at 10:27am

nice stuff !!

try the excellent K3Dsurf...

Permalink Reply by Vicente Soler on May 20, 2013 at 11:49am

If you don't want to leave GH you can use isosurface component from the millipede plugin.

Permalink Reply by Ahmed Hossam on May 20, 2013 at 6:48pm

hmmm ...

What is the component, that comes after the domain box component?

how do you give this formula in the evaluate component?

how should this component know x,y and z?!

Permalink Reply by Vicente Soler on May 20, 2013 at 7:01pm

1. Range

2. I connected a panel component with the formula written on it to the F input

3. If you connect a point to an input of an evaluate component (say the input is named P) you can retrieve the x, y and z values by using P.x, P.y and P.z as variables in the formula.

Permalink Reply by Ahmed Hossam on May 21, 2013 at 1:38am

aha

and what does the "star" in the domain "number of steps" mean?

Permalink Reply by Danny Boyes on May 21, 2013 at 2:23am

It's an Expression (right Click the input to get the context Menu and select Expression)

At a guess it is "N-1" other wise you will have 1 more than you need in the output.

For example when you divide a curve into 60 segments you will get 61 points.

Permalink Reply by Ahmed Hossam on May 21, 2013 at 2:24am

N-1?

What are Expressions?

How many Expressions are out there?

Permalink Reply by Danny Boyes on May 21, 2013 at 2:54am

Where N is the input (in this case 60)

Therefore N-1 = 60-1 = 59

This could have been done out side of the Range component by using [Subtraction] but it looks neater to have it as an expression.

Expression (mathematics), a finite combination of symbols that are well-formed according to applicable rules
Expression (programming), an instruction to execute something that will return a value

Technically the formula you have in the beginning is an expression

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