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Sloppy twisty worm

February 9th, 2009

In this worm, the pieces are all chained together and each piece is rotated 180 degrees on its base.

MEL code follows:

//--start--

// find the center of a face
proc vector centerOfFace(string $face) {
  // get locations of all vertices in an array
  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]>>;
}

// given three distances, get angle with law of cosines
proc float getAngle(float $distance) {
  // law of cosines: cos angle c = a^2+b^2-c^2/2ab
  $cSquared = `pow $distance 2`;
  // a and b in this case are both 1
  $cosAngleC = (2-$cSquared)/2;
  // fix rare sloppiness
  if ($cosAngleC < -1) {$cosAngleC = -1;}
  // solve for angle with arccosine, in degrees
  $degrees = `acosd $cosAngleC`;
  // round to two decimal places to account for roundoff
  $degrees = (floor(($degrees+.005)*100))/100;
  // get angle to closest corner
  return $degrees % 120;
}

//get distance between two vertices
proc float getDistance(string $vertA, string $vertB) {
  // get location of both vertices
  vector $aLoc = `xform -q -ws -t $vertA`;
  vector $bLoc = `xform -q -ws -t $vertB`;
  // get difference between two locations
  vector $cLoc = <<$aLoc.x-$bLoc.x, $aLoc.y-$bLoc.y, $aLoc.z-$bLoc.z>>;
  return mag($cLoc);
}

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 origin and freeze xforms
xform -t 0 0.707107 0;
makeIdentity -apply true -t 1;

// turn off constraint warnings
cycleCheck -e off;

$old = `ls -sl`;

for ($i=1; $i<500; ++$i) {
  // copy cone
  $new = `duplicate $old[0]`;
  if ($i != 1) {parent -w $new;} // move to world space

  // pick a random face on $old that isn't the base
  int $r = rand(3)+1;
  $selectedFace = ( $old[0] + ".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[0]+".vtx[3]"; // 3 is the tip

  // get angle between two vertices
  $dist = getDistance($newVertex, $oldVertex);
  $angle = getAngle($dist);

  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
    $dist = getDistance($newVertex, $oldVertex);
    $angle2 = getAngle($dist);
    // if still not aligned, go the other way twice
    if ($angle2 > 0) {
      $angle *= -2;
      xform -r -os -ro 0 $angle 0 $new[0];
    }
  }

  // animate visibility
  setKeyframe -attribute "visibility" -v 0 -t 0 $new; 
  setKeyframe -attribute "visibility" -v 1 -t ($i+1) $new;

  // create hierarchy
  parent -a $new[0] $old[0];
  $old = $new;
}
// animate rotations
select -all -hi;
setKeyframe -attribute "rotateX" -t 1 -ott flat; 
setKeyframe -attribute "rotateY" -t 1 -ott flat; 
setKeyframe -attribute "rotateZ" -t 1 -ott flat; 
currentTime 500;
xform -r -os -ro 0 180 0;
setKeyframe -attribute "rotateX" -t 500;
setKeyframe -attribute "rotateY" -t 500;
setKeyframe -attribute "rotateZ" -t 500;
// for some reason the -tt flags don't work on setKeyframe
keyTangent -attribute "rotateX" -t 500 -itt flat -ott flat;
keyTangent -attribute "rotateY" -t 500 -itt flat -ott flat;
keyTangent -attribute "rotateZ" -t 500 -itt flat -ott flat;

cycleCheck -e on;

}
doit();
print("done!");

//--end---
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