Can someone help me create a spiral (helix) similar to the one shown in the image? How might this be done except from drawing the curves perfectly by hand?
I achieved the desired result, but very painstakingly by drawing everything from hand. See the pictures below. To specify my question: Is there a simpler way to draw a shape similar to this?
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I have made a tool that (jooGraphFunction) allows you to graph mathematical functions as curves. As part of the documentation, there is a example of how to do this as well as instructions on how to run scripts.
I will summarize the script briefly here for sake of completeness and posterity should my bitbucket account go under or change too much. The parametric function for a circle is
You will want to squish that equation a bit to make it look as if seen from side. Or you can use orthographic projection in which case the equation becomes:
0.86605 * cos(t) - 0.86605 * sin(t) -0.5 * cos(t) - 0.5 * sin(t)
Then add variables for size and just slide it upwards as much as you like for a final equation of:
0.86605 * radius *cos(t) - 0.86605 * radius * sin(t) -0.5 * radius* cos(t) - 0.5 * radius* sin(t) + pitch*t
inject this in the script dialog. Other projections are possible. Then adjust the max range to get the desired length of spiral.
Image 1: Spirals with different pitch.
The benefit of graphing is that you can do arbitrarily complex shapes and once you have the formula its easy to repeat it over and over again. Off course you can develop more complex formulas.
Image 2: A few simple extension to the previous helix for inspiration.
1) Begin by cutting an oval in half,
2) Duplicate this curve and move it down as far as you’d like,
(some guides might help keep everything even)
3) Draw an oval which meets in the middle with the center two ends of the previous curves and cut it in half as well,
4) Copy and paste the curves from steps 2 and 3 to achieve the desired length.
This is the best I found, although it is in Korean. I don’t speak a lick of it, but I still got the gist and figured it out.