How can I draw a parabola?

[thirit]

Hello, I am new to SketchUp and to the SketchUP Community Forums aswell.

I wanted to model a surface defined by z=-x^2/10-y^2/10+10 which is a paraboloid facing down. I thought I could just draw a cut-through parabola, defined by y=-x^2/10+10 and then use the "follow me" tool with a circle to make a revolution.
But my problem is that I don´t know how can I graph it on a plane without having to plot several points and then joining them.

Thanks a lot.

[remus]

I reckon the best thing to do would be to use one of the graphing rubys available.

Theres a few here , including:
eq_grapher
graphit
k tools

[Wo3Dan]

Taff,

I have not looked into the mathematical correctness. No doubt that the parabolas are correct.
But what if you adjust (scale) the image (explode first) to fit the grouped parabola on the left. The parabolas are now equal but their focal points are not. There can only be one.
(Or could it just be a scaling issue where one needs to construct the focal point again?)

Wo3Dan

[TaffGoch]

thirit,

I'm more accustomed to drawing a parabola based on desired external dimensions, say for a parabolic dish (or trough) solar collector. I plot points and connect with lines, as you suggested, but don't use any mathematics at all. You may find that the math plugins referenced by remus are exactly what you need.

If you need to size your parabola to particular dimensions, and want to avoid mathematics entirely, this model should provide a method you can use:
Parabola Construction Tutorial

Note that you can scale a parabola (shallower or deeper) and it remains a parabola.You will have to locate the new focal point, but the dish shape will still reflect incident radiation to a single point. If you need to 'fine tune' the size of the dish with the SketchUp scale tool, you don't have to worry about 'breaking' the functionality of the parabolic shape.

Taff

[TaffGoch]

@wo3dan said:

...where one needs to construct the focal point again?

Yes, indeed. I've highlighted the pertinent phrase in my previous post, to draw more attention to that fact. It's very easy, however, to re-establish the focal point with a 2:1 triangle intersection.

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[thirit]

Great responses, I managed to plot my parabola quite good (actually I graphed one with external software and used it as a texture just to compare and it was amazingly similar).
Thanks a lot guys.

[TaffGoch]

thirit,

Glad to hear of your success. I hope our responses helped you plot that curve in SketchUp.

...and welcome to the community, by the way.

Taff

[Gaieus]

It's always good to see some maths-brained people around

(I have already forgotten that little which I'd learnt in secondar/high school )

[Jean Lemire]

Hi folks.

I tried another possibility and it seems to work well.

I used a spreadsheet software to obtain the X,Y data for the points on the parabola.

I set all Z values to 0.

I saved the file as a comma spaced value (csv).

I used the SU plugin to generate a cloud of points from the csv file.

I got the points on a parabolic curve.

I tried using the triangulate points feature but all points where not triangulated. After that I erased unwanted lines to delete the surfaces resulting from the triangulation and added missing lines to join the points forgotten by the triangulation process.

The result is a decent looking parabola.

Just ideas.

[TaffGoch]

Hi, Jean

That's exactly how I used to do it! (...although I typically used a DXF import, rather than CSV/cloud.) The spreadsheet method is undoubtedly more precise.

When I first found the parabola 'construction' method in an old drafting textbook, I thought it was so cool. I figured others might not be familiar with the technique and find it intriquing, as well. When you know your desired external dimensions, it constructs so nicely. (And it can be used in the workshop, during actual solar-collector fabrication.)

I suppose that appreciating the beauty of such a 'trick' makes me a bit of a 'math geek.' (I know that Gai wrote 'maths-brained,' but we all know what that really means.)

[Gaieus]

Ha, did I write something that I don't know about incidentally?

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BW - as I heard from Tommy, you will soon be able to fully utilize your spreadheet and maths expertise!