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jed

Logarithmic Spirals

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I saw a video on YouTube by a guy who makes kinetic art mobiles. He had an interesting one made out of toothed spirals, so I had a go at recreating it in C4D.

 

I tried using a helix spline, but couldn't seem to get the objects to interact correctly, so I made a proper log spiral using tracer. The movement is generated using dynamics - there's one collider that's rotated in XPresso driving 2 rigid bodies.

 

demo.c4d

 

https://en.wikipedia.org/wiki/Logarithmic_spiral

 

make log spiral.c4d

Edited by jed
added a file

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Whoa-- amazing!    It was only when camera dollied back that I perceived what you had achieved.    Amazing and very tricky to do.     Is that a phi  (golden ratio) spiral?

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This is really awesome, nice job Jed. Keep them coming, its always interesting to see what you have to show and share. I would like to see those shared on the Market, just so they are not forgoten and burried inside forums. 


| MAXON Quality Assurance Specialist | 3D Asset Creator | C4D Cafe Manager |

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  • @rasputin I just used the general log spiral equation

     

    515096430_logspiralformula.png.79b888f12d6c401895c3eaa607caa510.png

     

    where angle is in radians, e is the natural log base (aka Euler's number 2.71828) and tweaked the constants a + k until it looked right. I tried using a helix and radial bias but the gears were jumping. I guess it's the properties of logs that makes it work. Also, when I added the struts, with a helix I had to use a spline on the step effector to make things fit, but with the log curve the struts fitted without a spline.

     

    I usually animate gears with XPresso, but with the varying radii that would be beyond my math skills. Dynamics to the rescue !

     

    The video above is version 2 - I didn't like how dynamics had introduced a small collision gap, so after baking for TR I increased the teeth size. The dynamics is Compound Collision Shape, but with all the geometry it was too slow in the viewport. I added some switched off rigid body tags to parts that don't contribute to the dynamics calculation.

     

    Here's the video I got the design from. The guy has some good stuff eg non-circular gears

     

     

    I'm still trying to figure out square gears...

     

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    Fantastic work Jed,

    If you havn't already, check out a book called "The power of Limits" It's quite old, but talks about geometry of nature. 

    I've found it very interesting, although the math stuff is way over my head, but I think you should be able to translate alot of the content into your tests judging by the work posted here.

     

    There's also a Houdini artist named Serjan Burlak that does a lot of this kind of work, I found out about the book from a podcast he was a guest on.

     

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    @jed

     

    Use formula spline to your advantage where you can enter formulas in parametric form. It is designed for that 🙂

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  • @Hrvoje can formula spline use polar coordinates ie radius + angle ? Spirals are easiest described (and understood) using polar vs cartesian.

     

    TBH I've never really understood what 't' is in formula spline.

     

    in math -

    y = f(x) ie y is a function of x

     

    in C4D

    x = f(t) ie x is a function of t

    y = f(t) ie y is a function of t

     

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    As far as I can see, formula uses parametric equations. t is a form of time (not scene time), basically a range from 0 to 2 * Pi. Try this in formula spline 🙂

     

     

    Spiral.png

     

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  • I think we're going to have to agree to differ on this.

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    @jed

    Err, not sure I follow? Differ on what? 🙂

     

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