How to create logarithmic spiral in generative shape design workbench?

[Pen_theApprentice]

Good morning engineers!
I'm tring to create a logarithmic spiral driven by equations.
the general equation for that is:
r=ae^(b*θ)
and I converted this equation in terms of y, z, so i can determine the coordinates in cartisian system:
y=a*e^(b*θ)*cos(θ)
z=a*e^(b*θ)*sin(θ)
a, b and θ are pre created parameters in that part.
The problem is, as in law editor, only two variables can be involved as i know,
how can I work this out?
thank you!

 

[LWolf]

you create each equation as a fog-law (located behind the design-table icon). a and b are just ordinary real parameters, BUT y and t(heta) are your formal parameters
i.e y=a*exp(b*t)*cos(t*180/PI)
so you end up with three fog laws, which you then use to define your "curve from equations" in GSD

 

[Pen_theApprentice]

you create each equation as a fog-law (located behind the design-table icon). a and b are just ordinary real parameters, BUT y and t(heta) are your formal parameters
i.e y=a*exp(b*t)*cos(t*180/PI)
so you end up with three fog laws, which you then use to define your "curve from equations" in GSD

Hi LWolf, Thank you for your reply!
I have tried this way but I'm still finding difficulties.
1. I have read and watched different articles tutorials posts and youtube videoes, they add y (or x) and t(theta) with different types
y as length is commonly agreed, but for t(theta), some of them made it in Real type and manually add *1rad in the equation to give it unit, some in Angle type, what do you reckon?

2. I see in your example: y=a*exp(b*t)*cos(t*180/PI)
you added 180/PI for the t in cos bracket, but didn't do the same for t as power of exponent. May I ask the purpose?

3. How could I specify the range of t the curve covers? i.e. if I want only the 180<=t<=720deg to be graphed, how should i appliy this restriction?


Thank you

Regards
Pen

 

[LWolf]

yeah, sorry I was a bit sloppy...
x,y,z and t are real.
trig functions need deg or rad as a unit, that is why I explicitly multiply my real parameter t with the unit (*1deg).
Angle.1 parameter is already defined as [deg]
t runs always from 0 to 1 so the below will draw a helix (circle if z=0) with start angle defined by Angle.1 parameter and number of turns (540/360)
x=1*cos(t*(720-180)*1deg+Angle.1 )
y=1*sin(t*(720-180)*1deg+Angle.1 )
z=t