Modeling curves from an equation


#1

Curious to know if SU will allow me somewhere to enter the equation

x^2 + 4x + 4 to create a parabolic curve that i then can turn into a solid.

My goal is to create a bowl shape that the curve of the inside of the bowl follows this eqation. Then my second goal is to create just the line of the curve itself.

thank you :slight_smile:

Matt


#2

SU has a scripting API using Ruby that allows you to use equations to generate geometry…

there are a few ‘extensions’ or ‘plugins’ that provide the means to simply add the equation into an input field…

john


#3

awesome. What are some good ones to use?

thanks


#4

You can use the U-V PolyGen plugin to create a parabola (among other curves).


#5

Hmm, i may have to try this. I hope i can choose certain parameters so that i can control where the focus of it is. This is a physics lab project and a calculus project that i am showing my students.

Ill try this one and in case, are there any others i should try?

thanks


#6

While the plugin is designed to plot 3D (x,y,z) in terms of the parametric inputs (u,v), you can use it to generate 2D curves. Three things to note: (1) the plugin is designed to work in inches (2) the curve is made of of a number of straight segments controlled by the number of steps (3) the functions to define x, y, and z must be entered in Ruby consistent syntax.

For example, these inputs:

image

produce this curve:

image

This can be rotated about its axis to produce a bowl shape:

image


#7

nice. i am going to download it and try it. I have several different equations i want to try out for this project haha.

Basically, when i am done, i will have printed my own satellite dish and be able to place a sending/receiving unit at the focus. Then i will be able to collect data or place a MIC there to demonstrate how the focus works.

Thanks for helping me with this:)

EDIT:

Wait a minute, did you design this plug in?

I also found your parabula with focus plugin.

Out of curiosity, which equation are you using for that?

is it y=(x^2)/4f

the reason i ask, I would want to put the focal length based off of the width/diameter of the parabolic. IE i use 101.6mm as my x value, and some given y value, i can find the focus and then input that into your plugin.

Or, is the plugin taking the given x value(width/2) and the given focal length, then solving for y

Thanks


#8

The plugin uses the height and width to first calculate the focal point:

p = w**2 / 16.0 / h

Then the y values are given by:

y = x**2 / 4.0 / p

Hope this helps.

BTW, the plugin is a text file that you can open in any text editor if you’re curious about how it works.


#9

that does help alot actually. I just checked it with my math using the following and then i used your utility and it was spot on. I LOVE IT THAT PLUGIN !!!

I used: y=((50.8)^2)/4(50.8) to get a y value of 12.7. I then put into your awesome plugin, width 101.6, focal 50.8 and then generated it and it gave me 12.7 for height:) so happy right now haha

I love math and engineering.