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Thread: Gyroid

  1. #1
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    Gyroid

    Hi,

    There are various formulas of Gyroid,
    here is a simple one, as a compound node,
    for shape displacement (Null ->Shape ->Empty Volume)

    Click image for larger version. 

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    SDF Gyroid_nodes.zip

    Intersecting with a sphere,

    Click image for larger version. 

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    Also as a shader through a gradient, boring on a box, more interesting
    on a curved mesh.

    Click image for larger version. 

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    Denis.

  2. #2
    Those are cool! the empty volume is very cool, shame it's slow to render.

  3. #3
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    Quote Originally Posted by Tobian View Post
    ...shame it's slow to render.
    These ones,...are very very slow to render,
    Click image for larger version. 

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    Repetition with this compound node, the (faked) output ID and Center of each shape
    are used to colorize, rotate and move (slightly) each pseudo instance,
    using the DP Kit Move and Rotate Tools.

    SDF Repetition_nodes.zip

    Denis.

  4. #4
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    Of course you can use formulas for transformation,
    but here a torus shape is easy to animate with the Twist node from DP Kit,
    though the shape a precision of 0.05.

    (animated gif)

    Click image for larger version. 

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    Denis.

  5. #5
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    ...Blending shapes is cool,
    you can use the native smoothMin node, probably the Exponential version,
    while the Polynomial is faster,
    SDF Blend_nodes.zip

    Still using the DP Kit Move and Rotate nodes,
    (animated gif)
    Click image for larger version. 

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    Denis.

  6. #6
    Registered User ianr's Avatar
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    In the end Dennis It looks good !

  7. #7
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    I modified the Gyroid compound node,

    SDF Gyroid_2_nodes.zip

    removed the invert node, then it is possible to add thickness,

    Click image for larger version. 

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    Click image for larger version. 

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    possible also to convert the shape to a level set mesh,

    Click image for larger version. 

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    Denis.

  8. #8
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    Pitting the Gyroid, just adding a Math scalar Max node with Dot procedural,
    before pluging in Displacement,

    Click image for larger version. 

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    Next a Double Gyroid,

    Click image for larger version. 

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    Attachment 144651

    Here a bit distorted with premilinary Gradient Scaling over distance,
    Scaling goes over the sphere intersection,
    (including artefacts caused by limited accuracy).

    Click image for larger version. 

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    Animated,

    Click image for larger version. 

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    (updated: missing connection in SDF Double Gyroid nodes)

    Denis.
    Attached Files Attached Files
    Last edited by dpont; 04-03-2019 at 05:59 AM.

  9. #9
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    Triplic Periodic Functions

    A shorter title for
    Triply Periodic Bicontinuous Cubic Microdomain Morphologies
    the math web page is here:
    http://www.msri.org/publications/sgp...ext/final.html

    Or even shortly known as minimal surfaces,
    you can use basic functions, named F100, F110 etc,
    (meaning you are using cosinus or sinus, simple coordinates or by a factor of 2 or 3),
    with one or an addition of these functions with a scaling factor,
    sometimes a constant offset...

    Click image for larger version. 

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    for the following équations, including the Gyroid,
    (each reference is illustrated on the web page above)


    Figure 1a. A level set approximation for the P surface:
    F(100).

    Figure 1b. A level set approximation to the I-WP surface:
    F(110) + 0.25.

    Figure 1c. Two-parameter experiment.
    s*F(100) + (1 - s)*F(110) - t.

    Figure 1d. An approximation of the O, CT-O surface.
    0.6*F(110) - 0.4*F(111) - 1.

    Figure 1e. An approximation to the Neovius’ surface C(P).
    0.6*F(100) - 0.4*F(111) + 0.3.

    Figure 1f. P+C(P) surface approximation.
    0.35*F(111) + 0.2*F(100) + 0.2*F(222) + 0.1*F(200) + 0.05*F(300) +0.1*F(110).

    Figure 1g. K surface approximation. This surface was also discovered by Karcher
    0.3*F(100) + 0.3*F(110) - 0.4*F(200) + 0.2.

    Figure 1h. F-RD surface approximation.
    0.8*F(111) + 0.1*F(222) - 0.1*F(220).

    Figure 2a. G (gyroid) level surface:
    F(110).

    Figure 2b. G' surface level set:
    G' has several new features as compared to the gyroid, e.g. extra holes and tunnels.
    by von Schnering and Nesper).
    F(211) + 0.32.

    Figure 2c. Two-parameter experiment
    s*F211 + (1-s)*F220 - t.

    Figure 2d. Double gyroid surface approximation.
    0.8*F(211) - 0.2*F(220).

    Figure 2e. An approximation to the L surface. The equation is:
    0.5*F(211) - F(220) + 0.15.

    Figure 3a. D surface level set approximation, shifted here by p /4 for a more familiar representation:
    F(111).

    Figure 3b. D' surface level set:
    0.5*F(111) - 0.5*F(220) - 0.2.

    Figure 3c. Double diamond surface
    0.5*F(110) + 0.5*F(111).

    Figure 4. The P2-DG surface.
    It arises as a combination of terms of the double gyroid and P-surface level sets.
    0.7*F(211) - 0.1*F(220) - 0.2*F(200).




    Triplic Periodic Functions Nodes.zip


    Hope there's not typo errors in my transcription...
    As you can see in the above screenshot, the radius of the Shape is set to 4,
    and you get only the shape starting, you may also scale
    the Object Position before the connection.


    Denis.
    Last edited by dpont; 04-03-2019 at 08:06 AM.

  10. #10
    Golly, Denis,
    You make math look fun. In my eyes, that's darned hard to do!
    Thanks!
    Robert
    Robert Wilson, MA Deaf Ed.
    Indiana Deaf School
    This e-mail may contain information protected under the Family Educational Rights and Privacy Act.

  11. #11
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    Eggy

    Lot of such shape as 3D printed object on the web,

    Click image for larger version. 

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    Egg_Gyroid_srf.zip
    Radius of the Empty Shape must be increased.

    Denis.

  12. #12
    da what? daforum's Avatar
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    Hi denis. Will any of the node setups you have attached here work in earlier versions of LW?
    Montage Reel, Portfolio, PIN_01, Prime......«« go on, click on a link!

  13. #13
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    Quote Originally Posted by daforum View Post
    Hi denis. Will any of the node setups you have attached here work in earlier versions of LW?
    Shape and Signed Distance was introduced in LW 2019,
    except my shading example in the first post, this is required for using those setups.

    Denis.

  14. #14
    Not so newbie member lardbros's Avatar
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    These are absolutely BRILLIANT Denis!

    Thank you so much for sharing your efforts, it's so cool to see some of these really difficult mathematical shapes being done in LW.

    I have a feeling it may be possible to mesh these using VDB?
    LairdSquared | 3D Design & Animation

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  15. #15
    Super Member omichon's Avatar
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    Yes, brilliant ! Thanks for sharing this, Denis

    Quote Originally Posted by lardbros View Post
    I have a feeling it may be possible to mesh these using VDB?
    See post #7
    www.oliviermichon.fr | 3D Animation, Motion Graphics and Broadcast Design.

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