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Sloppy worm knot

February 10th, 2009

Here’s a knot of 20 worms of 500 segments each, branching from the same seed segment. The code below has smaller, child-proof default values.

MEL code follows:


// find the center of a face
proc vector centerOfFace(string $face) {
  // get locations of all the face's vertices
  float $pos[] = `xform -q -ws -t ($face)`;
  // get length of the array: # vertices * 3
  int $posSize = size($pos);
  // put the average of all vectors into 1st vector 
  for ($i = 0; $i < 3; $i++){
    for ($j = $i + 3; $j < $posSize; $j += 3){
      $pos[$i] += $pos[$j];
    $pos[$i] /= ($posSize / 3);
  return <<$pos[0], $pos[1], $pos[2]>>;

//get angle between two vertices with respect to a third point
proc float getAngle(string $vertA, string $vertB, vector $orig) {
  // get location of both vertices
  vector $aLoc = `xform -q -ws -t $vertA`;
  vector $bLoc = `xform -q -ws -t $vertB`;
  // normalize locations to the face center
  vector $aOrig = <<$aLoc.x - $orig.x, $aLoc.y - $orig.y, $aLoc.z - $orig.z>>; 
  vector $bOrig = <<$bLoc.x - $orig.x, $bLoc.y - $orig.y, $bLoc.z - $orig.z>>; 
  // use law of cosines via dot product
  float $dot = dotProduct( $aOrig, $bOrig, 1 );
  float $angle = rad_to_deg(acos($dot));
  //round answer down to two decimal places
  return (floor(($angle+.005)*100))/100;

proc string[] copyCone(string $old) {
  // copy cone
  $new = `duplicate $old`;
  // pick a random face on $old that isn't the base
  int $r = rand(3)+1;
  $selectedFace = ($old + ".f[" + $r + "]");
  // move $new to selected face
  vector $fc = centerOfFace($selectedFace);
  xform -a -t ($fc.x) ($fc.y) ($fc.z) $new[0];
  // aim $new at face with a temporary normal constraint
  string $tmpConst[] = `normalConstraint -aim 0 1 0 $selectedFace $new`;
  delete $tmpConst[0];
  // pick a vertex on each pyramid
  $newVertex = $new[0]+".vtx[0]"; // 0 is on the base
  $oldVertex = $old+".vtx[3]"; // 3 is the tip
  // get angle between two vertices
  $angle = getAngle($newVertex, $oldVertex, $fc);
  if ($angle > 0) { // if not already aligned
    // rotate $new to align the corners
    xform -r -os -ro 0 $angle 0 $new[0];
    // check the result
    $angle2 = getAngle($newVertex, $oldVertex, $fc);
    // if still not aligned, go the other way twice
    if ($angle2 > 0) {
      $angle3 = $angle * -2;
      xform -r -os -ro 0 $angle3 0 $new[0];
  return $new;

proc doit() {
  // make a regular tetrahedron and select it
  select `polyCone -r 1 -h 1.414214 -sx 3`;
  // move its pivot point to the bottom face
  xform -rp 0 -0.707107 0;
  // move to orig and freeze xforms
  xform -t 0 0.707107 0;
  makeIdentity -apply true -t 1;

  //delete the bottom face to lighten the load
  string $old[] = `ls -sl`;
  $selectedFace = ( $old[0] + ".f[0]" );
  delete $selectedFace;

  string $list[];
  int $numBranches = 10;
  int $branchLength = 50;

  int $i,$j;
  //initialize branches
  for ($i=0; $i<$numBranches; ++$i) {
    $new = copyCone($old[0]);
    $list[$i] = $new[0];
    //print("$list["+$i+"]: "+$list[$i]+"\n");
    //animate visibility
    setKeyframe -attribute "visibility" -v 0 -t 0 $new; 
    setKeyframe -attribute "visibility" -v 1 -t 1 $new;

  for ($i=0; $i<$branchLength; ++$i) {
    for ($j=0; $j<$numBranches ; ++$j) {
      $new = copyCone($list[$j]);
      $list[$j] = $new[0];
    //animate visibility
    setKeyframe -attribute "visibility" -v 0 -t 0 $new; 
    setKeyframe -attribute "visibility" -v 1 -t ($i+2) $new;

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