const sc = 100;

const dtheta = 0.1;

let MYZ, MZY, MXZ, MZX;

​

function setup() {

  createCanvas(400, 400);

  P1 = createVector(1, 0, 0);

  P2 = createVector(0, 1, 0);

  P3 = p5.Vector.cross(P1, P2);

​

  MYZ = math.matrix([

    [1, 0, 0],

    [0 , cos(dtheta), -sin(dtheta)],

    [0 , sin(dtheta), cos(dtheta)]

  ]);

  MZY = math.matrix([

    [1, 0, 0],

    [0 , cos(dtheta), sin(dtheta)],

    [0 , -sin(dtheta), cos(dtheta)]

  ]);

  MXZ = math.matrix([

    [cos(dtheta), 0, -sin(dtheta)],

    [0, 1, 0],

    [sin(dtheta), 0, cos(dtheta)]

  ]);

  MZX = math.matrix([

    [cos(dtheta), 0, sin(dtheta)],

    [0, 1, 0],

    [-sin(dtheta), 0, cos(dtheta)]

  ]);

​

}

​

function draw() {

  background(220);

  translate(width / 2, height / 2);

  stroke(255, 0, 0);

  line(0, 0, P1.x * sc, P1.y * sc);

  stroke(0, 255, 0);

  line(0, 0, P2.x * sc, P2.y * sc);

  stroke(0, 0, 255);

  line(0, 0, P3.x * sc, P3.y * sc);

​

  if (keyIsDown(UP_ARROW)) rotVecs(MYZ);

  if (keyIsDown(DOWN_ARROW)) rotVecs(MZY);

  if (keyIsDown(RIGHT_ARROW)) rotVecs(MXZ);

  if (keyIsDown(LEFT_ARROW)) rotVecs(MZX);

  findOrthVec();

}

​

function rotVecs(M) {

  let result = math.multiply(M, [P1.x, P1.y, P1.z]);

  P1 = createVector(result.subset(math.index(0)), result.subset(math.index(1)), result.subset(math.index(2)));

  result = math.multiply(M, [P2.x, P2.y, P2.z]);

  P2 = createVector(result.subset(math.index(0)), result.subset(math.index(1)), result.subset(math.index(2)));

  P3 = p5.Vector.cross(P1, P2);

}

​

function findOrthVec() {

  const max_its = 100;

  let p1 = math.matrix([[P1.x],[P1.y],[P1.z]]);

  let p2 = math.matrix([[P2.x],[P2.y],[P2.z]]);

  let p3 = math.matrix([[random()],[random()],[random()]]);

  let v = math.matrix([[0],[0],[-1]]);

  for (let ni = 0; ni<max_its; ni++){

    G = math.transpose(math.concat(p1,p2,p3,1));

    S = math.matrix([[1,0,0],[0,1,0],[0,0,0.5]]);

    p3 = math.subtract(p3,math.multiply(math.multiply(math.inv(G),S),math.add(math.multiply(G,p3),v)));

  }

}