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Parametric curves 2
#14
Those harmonographs are more complicated than I first thought. I may return to them some later time.

I added a damping feature to the Lissajous plugin. The new plugin version is 1.8 in

http://kmarkku.arkku.net/Parametric_curv...aster.html

When you open the Lissajous GUI you see there three new input fields:
  • Damping: Mode
  • Damping: Amount (0..10)
  • Damping: Cycles
The Modes are three: "No damping", "Linear damping", "Exponential damping". If you choose "No damping" you get the old behaviour and then the two other new inputs are ignored.

Examples: Letting m=2, n=3, k=0 and trying Amount=10 and Cycles=20, we get the following (with some patience). First "No damping", then "Linear damping", then "Exponential damping":

   

The same with n=1, m=3:

   

With n=1, m=1 we get a circle and two spirals, archimedean and logarithmic:

   

"Amount" controls the total amount of damping, which means how close to the center the curve reaches. If Amount=10 (the maximum), the curve reaches the center (except that when the damping is exponential the center is never quite reached). If Amount=5, say, an empty space will be left in the center.

"Cycles" is the number of the (damped) cycles drawn. Only integers are allowed, so only whole cycles can be drawn. Note that a large number of cycles makes the plugin slow, but to have anything interesting it should be perhaps from 20 to 100.

One more: Here n=2, m=3, k=0.5. First "No damping", then "Linear damping" with Amount=10 and Cycles=40, then "Exponential damping" with Amount=5 and Cycles=100.

   

Better to keep n and m small, otherwise the figure becomes a mess. Also, Cycles must be large enough so that the pattern shows.

By the way, this project was more useful than I expexted. Thanks denzjos for the interesting question! Adding the damping to the Lissajous plugin was quick and easy. No problems there. But when I began to test it, the resulting paths appeared to have occasional faults. It turned out that my algorithms (approximation and so on) had bugs. To find and fix those bugs has taken almost a week. The bugs became apparent only when the algorithms were tried on such hard cases as this Lissajous+damping. But now the algorithms are that much better. I also had to fix and update the general-purpose plugin Parametric Curves. It is now version 2.2, in the same place.

Please report any apparently wrong workings of the plugins.
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Messages In This Thread
Parametric curves 2 - by Ottia Tuota - 07-30-2021, 09:04 AM
RE: Parametric curves 2 - by Ottia Tuota - 07-30-2021, 05:06 PM
RE: Parametric curves 2 - by Ottia Tuota - 07-31-2021, 10:25 AM
RE: Parametric curves 2 - by Ottia Tuota - 08-23-2021, 04:30 PM
RE: Parametric curves 2 - by Ottia Tuota - 08-24-2021, 08:54 AM
RE: Parametric curves 2 - by Ottia Tuota - 08-24-2021, 04:06 PM
RE: Parametric curves 2 - by denzjos - 08-24-2021, 06:29 PM
RE: Parametric curves 2 - by Ottia Tuota - 08-25-2021, 12:25 PM
RE: Parametric curves 2 - by PixLab - 08-25-2021, 04:08 PM
RE: Parametric curves 2 - by denzjos - 08-25-2021, 06:41 PM
RE: Parametric curves 2 - by denzjos - 08-26-2021, 03:51 PM
RE: Parametric curves 2 - by denzjos - 08-26-2021, 06:06 PM
RE: Parametric curves 2 - by Ottia Tuota - 08-26-2021, 07:39 PM
RE: Parametric curves 2 - by Ottia Tuota - 09-02-2021, 02:33 PM
RE: Parametric curves 2 - by Ottia Tuota - 09-22-2021, 08:33 AM
RE: Parametric curves 2 - by Ottia Tuota - 09-22-2021, 01:30 PM
RE: Parametric curves 2 - by Ottia Tuota - 10-10-2021, 02:15 PM
RE: Parametric curves 2 - by PixLab - 10-21-2021, 06:41 AM
RE: Parametric curves 2 - by Ottia Tuota - 10-21-2021, 03:40 PM
RE: Parametric curves 2 - by PixLab - 10-22-2021, 04:39 AM

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