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Thread: Is there a Mathematician in the house? (Geodesic domes)

  1. #1
    Rift Disciple Atmospherik's Avatar
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    Default Is there a Mathematician in the house? (Geodesic domes)

    So last night I had this great idea, why not build a Geodesic dome in my new dimension. I know a little about them, but rather then do some research I just came up with a crazy plan and just started building, it's just a bunch of triangles right? lol

    So this was my first mistake, my plan was based on the assumption that all the triangles are the same size. So just for the entertainment of everyone i'll briefly walk you through last nights misadventure.

    So I figure all I need to do is build one good vertex and save it with toolbox, I used full size wood pillars

    Is there a Mathematician in the house? (Geodesic domes)-2014-09-02_171457.jpg

    Then started putting them together, rotating them by hand. I figured I'd make one arch, then save that and rotate it into a full dome.

    Is there a Mathematician in the house? (Geodesic domes)-2014-09-02_171651.jpg

    It was all going so well...

    Is there a Mathematician in the house? (Geodesic domes)-2014-09-02_174133.jpg

    Until I ran into this mess....

    so the lessen here is to stay in school kids, and pay attention in math class hehe

    So i figured i'd see if anyone else has tried one of these in their dimension, and has an easier or better way to throw one together. I'm just using toolbox, i haven't tried the other addon, but i can't see any way to avoid the hand rotating, since toolbox can't rotate multiple objects.

    After doing some reading today i do have a new plan. i think i just need to make a second vertex, out of slightly smaller wood pillars, forming a pentagon, and the combination of the two should form a dome.... we'll see
    Atmospherik - 60 Rogue on Faeblight

    <La Nostra Famiglia>
    Check out my Dimensions FallingWat3r - a tribute to Frank Lloyd Wright,
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  2. #2
    RIFT Fan Site Operator Feendish's Avatar
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    One you can check out (made with hexes, not triangles), is called The Greenhouse Dome, by Cordalia@Laethys.

    I have a picture of it here, but seeing it in person is way, way better.

    Heca does some amazing structural work, and excels with complex geometrical shapes. Enjoy!

    I believe she also posted a tutorial on Rift Dream Dimensions, but I may be mistaken on that one.
    Last edited by Feendish; 09-02-2014 at 06:00 PM.
    Dimensions on Greybriar and Zaviel


    Baradara@Greybriar

  3. #3
    RIFT Fan Site Operator
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    Cheers Baradara, Heca did indeed do a post on Domes here:

    Dream Techniques

    And also Dimension Tools has Default set Domes here:

    Dimension Tools Advanced

    There is other helpful info there is needed. Have fun!

  4. #4
    Telaran
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    My maths isn't great and my toolbox ability is poor but I'm pretty sure that those posts aren't complete perfect rectangles (no idea on the geometric correct term but hope you know what I mean) so if you are lining them up by eye and trying to rotate them I'm guessing it would cause you grief.

  5. #5
    Rift Disciple echoesofeternity's Avatar
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    Make "guide dots" first. You can use a bunch of sourcestone spheres as the dots, to get a perfect sphere (or half-sphere), and divide it into symmetrical sections. It's much easier to calculate the positions for those, you just need to get them to form a spherical grid.

    Then see where certain major intersections of your dome should be, geometrically, and put more guide dots of different colors there. So when you're putting the triangles up, you'll immediately know if you're on the right track or not and you can adjust accordingly.
    Last edited by echoesofeternity; 09-03-2014 at 07:04 AM.

  6. #6
    Rift Disciple Atmospherik's Avatar
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    Ahh very cool I'm going to make an alt and go check out the greenhouse dome right now, I knew someone else must have had this same idea already hehe

    And the guide dot idea is great too echoesofeternity thanks.

    After some serious searching of the internets yesterday I found the key piece of info that I was missing. For the type of dome I'm trying to build I needed three different lengths, which means I need to resize the wood pillars slightly.

    In this highly technical guide to making a geodesic dome out of skewers and gumdrops I found the ratios between the three lengths.

    http://sci-toys.com/scitoys/scitoys/...dome/dome.html

    100%, 97.85%, and 84.53%

    so a full size wood pillar is a 2, i just had to resize the others to 1.957 for medium
    and 1.6906 for short.

    Then i made a pentagon out of the shortest pieces, and a octagon out of the longest, and saved them both with toolbox, and started putting them together using the same method that Hecateria describes. Basically i built a 1/5 dome, and saved that, and spun it out into a full dome.

    and it worked!!!!

    but you'll all have to wait until i build a dimension around it before you can see it
    Atmospherik - 60 Rogue on Faeblight

    <La Nostra Famiglia>
    Check out my Dimensions FallingWat3r - a tribute to Frank Lloyd Wright,
    and The Tower House on Faeblight

  7. #7
    Ascendant Xenoheart's Avatar
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    The mistake made here was starting out with a random agular measurement for creating your triangles.

    The problem is regular enclosed 3D (or 2D) polygons with N sides have angles of A that are discrete in value but more continuous like in nature as N increases.

    What this means is the only way to figure out what angles you need to start with, you have to determine the number of sides you want. As those sides become more and more, the angle possibilities get closer and closer together such that they mimic continuous values. The smaller number of sides have larger jumps between their angular solution but no matter what they are all essentually discrete values with nothing in between.

    Here is a good description of this with what people are familiar with in 2D. Scroll down for the example and the actual formula. A simular formula and examples exist for regular enclosed 3D polygons.

    http://www.mathsisfun.com/geometry/polygons.html

    TLDR: Random angles wont guarantee a regular enclosed polygon either in 2D or 3D. Regular enclosed polygons of all types have exactly determined discrete angles. Nothing else will work no matter that size of said polygon. Thus you need to determine number of sides you want first, then use the corresponding angle to build it if you want to generate a perfectly closed polygon with N sides.

    Finally my math degree helped with something lol. *Gets back to work cutting out pictures on a computer.*
    Last edited by Xenoheart; 09-03-2014 at 10:14 AM.
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  8. #8
    Rift Disciple Atmospherik's Avatar
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    While some of that was way over my head, hehe... I did understand most of it. and I think I'm beginning to understand what went wrong the first time.

    Unfortunately due to the flexible and delicious nature of gumdrops, the first guide I read didn't get into angles all that much. but on my second attempt I guess using three different length pillars, gave me the angles I needed.

    This has been an interesting learning experience
    Atmospherik - 60 Rogue on Faeblight

    <La Nostra Famiglia>
    Check out my Dimensions FallingWat3r - a tribute to Frank Lloyd Wright,
    and The Tower House on Faeblight

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