Sphere-Sphere Intersection

var sphereA;

var sphereB;

​

function setup() {

  createCanvas( 600, 400 );

  sphereA = {};

  sphereA.pos = [ 120, 200 ];

  sphereA.radius = 100;

  sphereB = {};

  sphereB.pos = [ 400, 200 ];

  sphereB.radius = 100;

}

​

function draw() {

  sphereB.pos[0] = mouseX;

  sphereB.pos[1] = mouseY;

  sphereB.radius = 150 + sin( frameCount * 0.03 ) * 20;

​

  // computation of direction from sphereA center to sphereB center

  var dirAB = [

    sphereB.pos[0] - sphereA.pos[0],

    sphereB.pos[1] - sphereA.pos[1]

  ];

  // computation of the vecto length

  var l = sqrt( pow(dirAB[0],2) + pow(dirAB[1],2) );

  // and normalizing the vector

  dirAB[0] /= l;

  dirAB[1] /= l;

  if ( l < sphereA.radius && l < sphereB.radius ) {

    dirAB[0] *= -1;

    dirAB[1] *= -1;

  }

  // computation of the angle of the direction

  var angle = atan2( dirAB[1], dirAB[0] ) + PI * 0.5;

  // rendering the normal of the direction

  var normal = [ cos(angle), sin(angle) ];

  // computation of the radius of the spheres intersection

  // http://mathworld.wolfram.com/Sphere-SphereIntersection.html

  var a = 

    ( 1.0 / ( 2.0 * l ) ) * 

    sqrt( 

      ( 4 * pow(l,2) * pow(sphereA.radius,2) ) -

      pow( pow(l,2) - pow(sphereB.radius,2) + pow(sphereA.radius,2), 2 )

    );

  // computation of the distance to find the center of the intersection circle

  // hypo² = basis² + opposite²

  var basis_length = sqrt( pow(sphereA.radius,2) - pow(a,2) );

  // absolute position of the intersection center

  var middot = [

    sphereA.pos[0] + dirAB[0] * basis_length,

    sphereA.pos[1] + dirAB[1] * basis_length

  ];

  // display of values

  background(0);

  strokeWeight( 1 );

  noFill();

  stroke( 255 );

  ellipse( sphereA.pos[0], sphereA.pos[1], sphereA.radius * 2, sphereA.radius * 2 );

  ellipse( sphereB.pos[0], sphereB.pos[1], sphereB.radius * 2, sphereB.radius * 2 );

  noStroke();

  fill( 255,0,0 );

  ellipse( middot[0], middot[1], 5, 5 );

  fill( 0,255,255 );

  ellipse( middot[0] + normal[0] * a, middot[1] + normal[1] * a, 10, 10 );

  strokeWeight( 2 );

  stroke( 0,255,0 );

  line( 

    sphereA.pos[0], sphereA.pos[1],

    middot[0], middot[1]

  );

  stroke( 0,255,255 );

  line( 

    middot[0], middot[1],

    middot[0] + normal[0] * a, middot[1] + normal[1] * a

  );

  noStroke();

  fill(255);

  text( "intersection radius: " + a, 10, 25 );

}