Ball Bi-Lerp

(bi-linear interpolation)

 

by

Duane Palyka

March 23, 2003

 

 

Starting with four spheres with modified cv's:

 

 

 

 

And applying the following MEL script:

SphereMatrix( "ball" );

 

global proc SphereMatrix( string $name ) {

       SphereLerp( $name, 1, 41, 8 );
SphereLerp( $name, 8, 48, 8 );
for ($i = 1, $j = 8; $i <= 48; $i += 8, $j += 8 ) {
SphereLerp( $name, $i, $j, 1 );
}
}

global proc SphereLerp( string $name, int $nbeg, int $nend, int $nstep ) {
SphereFill( $name, $nbeg, $nend, $nstep );
LerpSphere( $name, $nbeg, $nend, $nstep );
}

global proc SphereFill( string $name, int $nbeg, int $nend, int $nstep ) {
string $attr, $n;
int $u, $v;
int $i, $k;
int $num;
float $pos[3], $pos1[3], $pos2[3];
$num = ($nend - $nbeg) / $nstep;
$n = $name + $nbeg;
$attr= $n + ".spansU";
$u = `getAttr $attr`;
$attr= $n + ".spansV";
$v = `getAttr $attr`;
$attr = $n + ".translate";
$pos1 = `getAttr $attr`;
print( $n + ": spansU=" + $u + ", spansV=" + $v);
print( ", pos= (" + $pos1[0] + "," + $pos1[1] + "," + $pos1[2] + ")\n" );
$n = $name + $nend;
$attr = $n + ".translate";
$pos2 = `getAttr $attr`;
for ($i=$nbeg + $nstep; $i<$nend; $i += $nstep) {
$n = $name + $i;
for($k=0; $k < 3; $k++)
$pos[$k] = ylerp( (float) $i, $nbeg, $nend,
$pos1[$k], $pos2[$k] );
sphere -ax 0 1 0 -s $u -nsp $v -name $n;
move -a $pos[0] $pos[1] $pos[2];
}
}

global proc LerpSphere( string $name, int $nbeg, int $nend, int $nstep )
{
string $attr, $n;
int $u, $v;
int $i, $j, $k, $m;
int $num;
string $attr, $attr1, $attr2;
string $at;
float $pt[3], $pt1[3], $pt2[3];
$num = ($nend - $nbeg) / $nstep;
$n = $name + $nbeg;
$attr= $n + ".spansU";
$u = `getAttr $attr`;
$attr= $n + ".spansV";
$v = `getAttr $attr`;
$attr = $n + ".translate";
$pos1 = `getAttr $attr`;
print( $n + ": spansU=" + $u + ", spansV=" + $v + "\n");
$n1 = $n;
$n2 = $name + $nend;
for ($i=$nbeg + $nstep; $i<$nend; $i += $nstep) {
$n = $name + $i;
for($j=0; $j <= $u; $j++){
for($m=0; $m <= $v; $m++){
$n = $name + $i;
$at = ".cv[" + $j + "][" + $m + "]";
$attr1 = $n1 + $at;
$pt1 = `getAttr $attr1`;
$attr2 = $n2 + $at;
$pt2 = `getAttr $attr2`;
for($k=0; $k < 3; $k++)
$pt[$k] = ylerp( (float) $i, $nbeg, $nend,
$pt1[$k], $pt2[$k] );
$attr = $n + $at;
setAttr $attr $pt[0] $pt[1] $pt[2];
}
}

}
}

global proc float ylerp( float $x, float $x0, float $x1, float $y0, float $y1 )
{
float $slope, $y;
$slope = ($y1 - $y0) / ($x1 - $x0);
$y = $slope * ($x - $x0) + $y0;
return $y;
}

Using the above MEL script, we get the following result: