How do you create mathematical models?

Discussion in 'Design and Modeling' started by 394883_deleted, Jan 13, 2015.

  1. So I have seen many mathematical models under the mathematical art heading and they are superb. I was considering implementing something of the sort in a current project. I know this is such a vague question but any help at all in how to get started with something like this would be greatly appreciated, thanks.
     
  2. I can speak for the 3D software I've used, Blender, Wings3d, Art Of Illusion, netfabb (basic). They all have options
    for creating Torus (Torii?) of various specifications as well as Polyhedrons - stellated and otherwise.

    (For the record, my OS is Linux Mint 17.1 on a Dell E5520 laptop w/8mb memory)

    In Inkscape - 2D, it's possible to create Polygons and Stars and either save them as bitmaps for the
    2D - 3D shapeways app OR save them as Object (or Stroke)- Converted to Path and import them into
    Blender for further modification. You might also find some interesting options under the "Extensions"
    tab (try - Render) or experiment with Clones (Edit, Clones)

    Blender also has math functions for the more mathematically inclined for creating more elaborate
    designs.

    Last, Mathematica has the ability to create objects and save them in STL format, but, I don't know
    of any free or low cost option they may have for this.

    If you search the web there's no shortage of info on this.

    Thingiverse generally has some models which can be downloaded in STL format which is a common
    format used by most 3D software.

    blenderartists.org is an excellent resource for getting started with Blender.

    There are no doubt comparable resources for commercial software (3DSMax, Maya, SolidWorks) as well.

    Here's a site that has several Torus Knots which can be downloaded in OBJ format:

    http://www.colab.sfu.ca/KnotPlot/KnotServer/

    Look at the:

    "many-stick tube knot (as in above picture)" link

    and right click, save the:

    "Get this model as a Alias|Wavefront OBJ file."

    It can then be imported into most 3D software.

    Hope that helps.

    P.S. Merry Christmas (or the holiday of your choice):

    https://kovacsv.github.io/JSModeler/documentation/examples/s olids.html

    Updated:

    http://kovacsv.github.io/JSModeler/documentation/demo/demons tration.html#platonic

    For the more mathematically inclined, do-it-yourself-ers, there's this:

    Golden Rectangle in Blender:
    https://www.youtube.com/watch?v=x3TtWRd7zHo (Icosahedron / Truncated Icosahedron)

    If you really want to get into the math of it, there's K3DSurf / MathMod (which exports to OBJ and some of the formulas can be directly transposed into
    Blender's XYZ funcion):

    http://k3dsurf.sourceforge.net/
    NOTE: The Win32 version works fine in Linux using WINE

    MathMod

    https://www.facebook.com/pages/MathMod/529510253833102
    Download: http://sourceforge.net/projects/mathmod/ - Windows / Linux64 (Click on Files then the version of your choice)
    NOTE: The Win32 version works fine in Linux using WINE
    Download: http://www.macupdate.com/app/mac/50963/mathmod - Mac

    Just found another excellent program for math art design: TopMod (Exports to OBJ / STL (and others))

    Downloads Link:
    https://code.google.com/p/topmod/downloads/list
    NOTE: The Win32 version works fine in Linux using WINE

    Youtube Channel:- Popular TopMod Videos
    https://www.youtube.com/watch?v=Tj4_-vg31LE&list=PLMN_7M hzh0R_jhU0z_Ri_JYbZHDcUQNp9

    Another great little program (Attention Celtic Knot Lovers): (Exports to: POV, OBJ, STL)

    http://www.stevenabbott.co.uk/Knots/knots.html
    NOTE: The Win32 version works fine in Linux using WINE

    Yet another online tool I've stumbled on (exports to OBJ, VRML2, PNG(2D))

    Polyhedrisme
    http://levskaya.github.io/polyhedronisme/

     
    Last edited: Apr 9, 2015
  3. Deleted
     
    Last edited: Mar 13, 2015
  4. Seriously this is all great stuff Unkerjay, thank you so much. My design has taken a different route so I will probably not be using mathematical modelling after all, however I will definitely look more into your links as I really like the idea of the thing, some very interesting stuff. cheers!
     
  5. Glad to hear it.

    Happy Modeling!
     
  6. Two more things to add here for the benefit of those who might be interested:

    Openscad:

    www.openscad.org (Windows / Linux / Mac)

    Kit (Chris) Wallace has done some AMAZING work with Polyhedron here:

    http://kitwallace.co.uk/3d/solid-index.xq

    Models can be exported to openscad as:

    *shell
    *wire
    **stellate
    antistellate
    antistellate-cutout
    spherical
    **modulated-shell
    **modulated-wire
    engrave
    spacefill
    dual

    * - will work
    ** - recommended

    (attached examples - zip - octahedron / openscad - stl formats)

    Turns out the Stellated Octahedron is otherwise knows as the:

    "Stella Octangula"

    http://mathworld.wolfram.com/StellaOctangula.html

    (who knew? - not me)

    There's also the CDF format (Wolfram - Mathematica)

    Requires the CDF Player (Mac, Windows, Linux):

    http://www.wolfram.com/cdf-player/

    and opens CDF (Computational Document Format) files:

    http://demonstrations.wolfram.com/new.html

    Enjoy.

     

    Attached Files:

  7. Luxxeon3D
    Luxxeon3D Well-Known Member
    I have several tutorials on my channel that utilize some standard polygonal modeling techniques to achieve mathematical models such as a "solid" mobius strip, star ball, and some other arbitrary models based in mathematical form. No knowledge of programming or algebraic equations necessary.

    https://www.youtube.com/user/luxxeon3d/videos

    Most of the tutorials are for 3dsmax 2010 or higher, but the techniques can easily translate to any polygon modeling software. I also have several videos for Blender 2.7 and higher on the channel too. Most of the models are manifold, and capable of 3d printing.

     
  8. Thank you, luxxeon.

    Really have my eye and mind on your star ball.

    Going to give that a crack.

    Anyone else figures it out, especially using Blender,
    please share, not just the results, but the process as
    well.


     
  9. Tangentially, there's also some great stuff by

    David Brinner
    https://www.youtube.com/results?search_query=David+Brinner

    out there using WIngs3D:

    https://www.youtube.com/results?search_query=David+Brinnen+W ings3D

    as well as by

    Peter Stammbach
    https://www.youtube.com/channel/UCQ2NYo3MqqKi96TqQyl5_jQ

    using Luxology:
    https://www.youtube.com/results?search_query=Peter+Stammbach +luxology

    Proof of concept, I gave his Hilbert Sphere a crack using Blender and
    came up with this:

    http://www.thingiverse.com/thing:786956

    and some other examples as well.

    This guy does some really GREAT stuff with Blender.
    He does it in Greek. I don't speak Greek, but, I use Blender
    quite a bit.

    If you DO speak Greek, you might really appreciate his tutorials:

    Asopticom
    https://www.youtube.com/channel/UCbDOt8COFotFyEwYDGYc_Aw

    If you DO figure them out and wish to share the details in English
    PLEASE do.

    Relative to this discussion and luxxeon's idea, he's got this tutorial
    which while a star ball, isn't quite the same as luxxeon's, but it IS
    done using Blender, which might help in translating luxxeon's star
    ball, for example, from 3DSMax to Blender:

    Blender 3D tutorial - Σφαίρα από Αστέρια - StarSphere
    https://www.youtube.com/watch?v=uCS46_eTSUU
     
    Last edited: Apr 23, 2015
  10. Luxxeon3D
    Luxxeon3D Well-Known Member
    I was going to do a Blender tutorial on how to translate my 3dsmax technique to Blender for you, but the examples you posted make it a moot point. Very good examples.

    I actually have two tutorials for different variations of star balls, but both are for 3dsmax. One technique utilizes a free addon plugin to achieve the shape, but the other is done using standard polygonal techniques, which should translate to any polygon package in theory. Let me know if you find anything else you'd like to see done in Blender. I intend on making more Blender-specific tutorials in the near future, but for now, I'm concentrating on doing them for 3dsmax.

     
  11. I'm going to see how far I get using your method.

    The others are close, but, not quite yours.
     
  12. Here's what I've got so far. Proof positive that when you don't know
    what you're doing, it's pretty easy to mangle the results.

    Mostly good progress, with a little help at blenderartists getting over
    the tricky spots.

    Here's the blender file and two STL results.

    So, luxxeon, where did I go wrong and how badly?

    Reference:

    3d Tutorial | Floral Star Ball Technique | 3dsmax
    https://www.youtube.com/watch?v=NRgBBcCbi14

    Little Help (BlenderArtists):

    http://blenderartists.org/forum/showthread.php?369241-Rotate -Edge-Loops-Think-Spaghetti-on-a-fork&p=2858653#post2858 653

    The one tutorial above:

    http://blenderartists.org/forum/showthread.php?320626-Modell ing-a-twisted-Loop-shape-Best-Shortest-method

    talks about "dupliverts". First, it's a mashup for Duplication - Verts (under the Object Menu).

    Second any explanation I've been able to find, makes it clear as mud how it works, especailly relative to
    the tutorial. At this point, someone can correct me, demonstrating just how blindingly simple it is. Feel
    free to.

    That's why I didn't choose THAT tutorial.

    Seems like that particular tutorial, unlike yours, luxxeon, would be easier in TopMod
    where it's easier to follow:

    https://www.youtube.com/watch?v=8SUjZITJIOw

     

    Attached Files:

  13. Luxxeon3D
    Luxxeon3D Well-Known Member
    I downloaded your Blend file, and messed around with it some. In the end, I decided to redo it entirely from scratch. Attached is my blend file, leaving off at the part where you bevel the star shaped edges. If you use the percent type bevel, the results I feel are better than offset, width, or depth, and provide a clean result. You can try picking it up from here. Please notice that I didn't save your scene notes in this file, so you may wish to rename it after downloading, so you don't overwrite your original notes.

    In the meantime, I will try to do a quick tutorial for you in Blender tonight, which you could use to follow along if necessary. Otherwise, give it a go from the point where I left off in this file, and see how you do.
     

    Attached Files:

  14. The more I messed with your file, luxxeon, without knowing
    what I'm doing, the worse it got.

    So, I may wait to see what you come up with. I defer to you.

    I did try playing around with Asopticom's star sphere.

    Came up with the stl below, from the Blender file.

    His was designed as a sphere, rather than a ball,
    That accounts for the lack of solidity to his finished
    product (or mine for that matter).

    I just deleted the fill in parts leaving just the star
    shape - solidify / smooth, rinse, repeat, you know
    the drill.

    For you and others, for what it's worth.

    I'll try to update it in the near future as I did with
    my attempts at yours - annotating the file for whoever
    might want to have a crack at it.

    The blender file isn't completely done. it's about
    halfway to two-thirds done.

    For reference, here's Asopticom's youtube tutorial:

    https://www.youtube.com/watch?v=uCS46_eTSUU

    My file picks up about the 2:45 mark of his tute.

    (for the record, the beginning steps are to create, essentially,
    a rhombicosidodecahedron, which is readily available under
    the Math Functions, Solids, Custom menu. You can save yourself
    some effort in the translation, and in the creation by just starting there.
    The squares are rectangles when he's done, but, the same structure.)

     

    Attached Files:

    Last edited: Apr 24, 2015
  15. Luxxeon3D
    Luxxeon3D Well-Known Member
    I'm recording a tutorial video now. Unfortunately, the sound may not come out in this one. My mic is acting up here, but I will create annotations in the video if the audio fails me. I should have this available for you within the next couple hours. I'll post here when it's available for you to check out.

    There's a few steps in Blender that aren't in my Max tutorial, because of the difference in the tools. Just a few extra steps. But then again, there's some routines in the process for Blender that are shorter than in Max. You'll see the difference in workflow. I can see how, if you're following my Max tutorial, you can get messed up badly in Blender. There's definitely some unforeseen differences that really do require a separate tutorial to clarify.
     
  16. Luxxeon3D
    Luxxeon3D Well-Known Member
    Here's a preliminary version of the video I uploaded to Vimeo for you. Unfortunately, I didn't have time to annotate or voice-over narrate this yet, but hopefully you can still follow along, and understand what I'm doing here. If not, I'll be uploading a annotated or narrated version to my Youtube channel as soon as I can. If you have any questions about what's going on here in this video, please let me know and I'll do my best to explain. I think it's pretty straight forward, but please pay special note to the parameter changes I make on some of the tools involved.

    https://vimeo.com/125967608

    I think the process in Blender turns out a very nice looking model. I recommend 3 iterations of subdivision if you intend to print, for a very smooth and clean result. Again, if you have any problems following this without audio, I'm working on a narrated version, but will answer any questions to the best of my ability. Hope this helps.
     
  17. Nice video.

    Going to be a challenge without the keystrokes.

    Blender has a screencast for key capture.

    I think it used to be buiilt in. Now you've got
    to add it separately.

    This covers it (German) pretty straightforward.
    Basically, pulling the addon from an earlier version
    of Blender 2.71 or 2.72.

    https://www.youtube.com/watch?v=owQ1DR4G1MU

    I'll give it a shot later today. Hopefully this evening
    I'll have something.

    Thanx
     
  18. Luxxeon3D
    Luxxeon3D Well-Known Member
    Nice. I used to use the keystroke addon for, but found it somewhat unreliable. Often it would show keys twice which weren't being used twice, etc. I might be able to do my narrated version of this later today, so it may actually be online before you even get started. I'll let you know.