Creative Coding with G'MIC

Software G'MIC
25

2D Slices of 3D Gaussians

This morning, I needed to code a small function that draws oriented Gaussians in a discrete 3D volume, and so I tested out this function intensively with gaussians of various sizes, orientations, colors, opacities, etc., to see how they would look.

The fun thing about generating continuous data in a discrete 3D volume is that you can then store each slice of the volume as a frame in a output video file, and it sometimes makes for some cool stuff to watch.

That’s what happened here!

Here’s a video of each slice of a 3D volume generated by starting from an empty volume and drawing Gaussian shapes in it, randomly varying their size, orientation, color and opacity. I used a little trick to make the video loop perfectly, so that I could turn it into an animated gif.

anim_ellipses3d-ezgif.com-optimize

I won’t detail the code here, I just copy/paste it below, so you can reproduce it if you wish!

anim_ellipses :
  180,180,160,3
  2000,1,1,1,":
    draw_gauss3d(ind,xc,yc,zc,u,v,w,siz,anisotropy,R,G,B,A) = (
      unref(dg3d_mask,dg3d_one,dg3d_rgb,dg3d_isiz2);
      dg3d_vU = unitnorm([ u,v,w ]);
      dg3d_vUvUt = mul(dg3d_vU,dg3d_vU,3);
      dg3d_T = invert(dg3d_vUvUt + max(0.025,1 - sqrt(anisotropy))*(eye(3) - dg3d_vUvUt));
      dg3d_expr = string('T = [',v2s(dg3d_T),']; X = ([ x,y,z ] - siz/2)/siz; exp(-12*dot(X,T*X))');
      dg3d_mask = expr(dg3d_expr,siz,siz,siz);
      dg3d_rgb = [ vector(##siz^3,R),vector(##siz^3,G),vector(##siz^3,B) ];
      const dg3d_isiz2 = int(siz/2);
      draw(#ind,dg3d_rgb,xc - dg3d_isiz2,yc - dg3d_isiz2,zc - dg3d_isiz2,0,siz,siz,siz,3,A/255,dg3d_mask);

      # Trick: These two lines allow to generate a perfectly looping animation.
      draw(#ind,dg3d_rgb,xc - dg3d_isiz2,yc - dg3d_isiz2,zc - dg3d_isiz2 + d#0/2,0,siz,siz,siz,3,A/255,dg3d_mask);
      draw(#ind,dg3d_rgb,xc - dg3d_isiz2,yc - dg3d_isiz2,zc - dg3d_isiz2 - d#0/2,0,siz,siz,siz,3,A/255,dg3d_mask);
    );

    X = [ u([w#0,h#0] - 1),u(d#0/4,3*d#0/4) ];
    U = unitnorm([g,g,g]);
    siz = v(5);
    anisotropy = u(0.6,1);
    R = u(20,255);
    G = u(20,255);
    B = u(20,255);
    A = u(20,255)/(1 + siz)^0.75;

    siz==0?draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],11,anisotropy,R,G,B,A):
    siz==1?draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],21,anisotropy,R,G,B,A):
    siz==2?draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],31,anisotropy,R,G,B,A):
    siz==3?draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],41,anisotropy,R,G,B,A):
    siz==4?draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],51,anisotropy,R,G,B,A):
           draw_gauss3d(#0,X[0],X[1],X[2],U[0],U[1],U[2],61,anisotropy,R,G,B,A)"
  rm.
  rs 250%,250%,6 c 0,255 normalize_local , n 0,255
  slices {[d/4,3*d/4-1]}

Nice, isn’t it ? :wink:

1 Like