Hi,

I'm having some difficulty generating a spiral with that will go through all the points described in the representation of Euclidean 2D space at the end of this post. I've marked each point that needs to be gone through by a hex number from 1 - C. Each + is separated by 4 (i.e. these are 1/4th divisions) and is to scale.

If anyone has an idea how I could accomplish this, I would be very grateful.

Thanks,


Maxx

Welcome Maxx!

And welcome may be about all I can say. If I understand Eudlidean space (Wikipedia) you need to represent the spiral in simulated 3D. While Inkscape is capable of simulating 3D, by the use of several drawing techniques (i.e. like on paper), you may be better off using a dedicated 3D program, such as Blender.

Is the spiral the same diameter all the way along its length, or is the diameter larger on one end and smaller on the other. For example, is it like a cylinder (spring) or is it shaped like a cone? (which I ask mostly out of curiosity )

There's a 3D Polyhedron extension, which might work, except that a spiral is not a polyhedron. Extensions menu > Render > 3D Polyh > Model File tab has a dropdown menu (Object: ) with different types of polyhedrons. The last item in the list is "Load from file". Of course this is all outside my understanding, and I'm guessing it can't be used to make a spiral. I don't even know what kind of file is needed there. (although the manual probably offers some clues) But I mention only on a long shot of a chance it could work (because it creates 3D objects).

A couple of other extensions -- Function Plotter, and Parametric Curves. I'm thinking if the spiral is more of a cylinder/spring than a cone, the curves required would be parabolic, and share the same equation all the way along its length. So perhaps the Function Plotter can make the parabolic curves. I've never used that extension, because it's mostly over my head. So I don't know if it could draw the whole "spring" or not. It can probably only draw 2D parabolas, but with some patience, perhaps they could be node edited to connect them properly. Ah-ha! Thanks to Wikipedia again, I see that a spring is called a helix. I see that parametric curves might include parabolas or helixes, among many others. So perhaps you could make use of these extensions?

Otherwise, I'd suggest looking at 3D drawing programs, such as Blender (which I mention because like Inkscape, it's open source and free). Or maybe someone else has some ideas?

maxxon wrote: I've marked each point that needs to be gone through by a hex number from 1 - C.

Is this your very own notation system? I'm sure it works in some specific circumstances but it is not very communicative at all. Just saying.
When you say

maxxon wrote: Each + is separated by 4 (i.e. these are 1/4th divisions) and is to scale.

You do mean the '+' signs are evenly spaced grid points, right? Because that's not the way it comes out when you use the 'code' tag to post it. I think you are talking about a spiral of 2.75 turns, inner radius of 4 units, outer radius of 15 units, with a pitch of 1? is that about right?



The best way to do this is to use the pen tool with the 'spiro' spline option. Click-drag on each point that you want your curve to pass through and at the end hit enter and 'Inky' will smooth out the curve perfectly.



Here's the file if it helps...

Thanks brynn, I meant 2-space, not 3. I.e. a Cartesian coordinate system.

Great druban. Yeah, I know that it is off scale due to the fact that the characters are not a 1:1 aspect ratio, and I wasn't going to bother with preparing a grid in an image. Too lazy. I come from the ASCII art generation.

The information is helpful, if not a bit late. I actually gave up on this forum because it took so long to get my post even viewable (> 12 hours I think). I wrote a programme to generate the curve in C#/.NET and it works. I would have had to do this eventually, but I just wanted to generate a proof of concept without writing any code.

The info is still useful though, thanks!


Maxx