Circle Inversion

let p;

let q;

​

let a

let c;

let cnode;

​

function setup() {

    createCanvas(800, 800);

    background(100);

​

    c = new Circle(createVector(width*0.5,height*0.5),100);

    cnode = new Node("C");

    cnode.weight = 5;

    cnode.position = c.center;

    p = new Node("P");

​

    q = new Node("Q");

    a = new Node("A");

    a.weight = 7;

    update(700,400);

}

​

function draw() {

    background(255);

    noStroke();

  fill(0,0,255,30);

    triangle(a.position.x,a.position.y, c.center.x,c.center.y  ,  p.position.x,p.position.y)

    triangle(a.position.x,a.position.y, c.center.x,c.center.y  ,  q.position.x,q.position.y)

    stroke(0,125);

    noFill();

    line(c.center.x,c.center.y,p.position.x,p.position.y);

    line(c.center.x,c.center.y,q.position.x,q.position.y);

​

    stroke(0,255);

    noFill();

    c.draw();

  fill(0);

  cnode.draw();

    stroke(0);

    fill(0);

    p.draw();

​

    stroke(0);

    fill(255);

    q.draw();

​

    stroke(0);

    fill(0,0,255);

    a.draw();

​

}

​

function mousePressed() {

    update(mouseX,mouseY);

}

​

function mouseDragged() {

    update(mouseX,mouseY);

}

​

function update(x,y) {

    p.position = createVector(x,y);

    q.position = c.invert(p.position);

  let phi

  let d

  if(p.position.dist(c.center) > c.r) {

    phi  = p5.Vector.sub(p.position,c.center).heading();

    d = c.center.dist(q.position);

  }

  else {

    phi  = p5.Vector.sub(q.position,c.center).heading();

    d = c.center.dist(p.position);

  }

    let alpha = acos(d/c.r);

​

    let v = p5.Vector.fromAngle(phi + alpha);

    v.mult(c.r);

    a.position = p5.Vector.add(c.center,v);

}

​

function Node(name){

    this.position = createVector(0,0);

    this.name = name;

  this.weight = 10;

    this.draw = function() {

        ellipse(this.position.x,this.position.y,this.weight,this.weight);

        fill(50,50,255)

        textSize(16);

    text(this.name, this.position.x - 10,this.position.y - 10);

    }

}

​

function Circle(center,r) {

  this.r = r;

  this.center = center;

​

  this.containsPoint = function(p){

    return this.center.dist(p) < this.r;

  };

​

  this.invert = function(p){ 

      let op = this.center.dist(p);

​

      let oq = this.r*this.r/op;

​

      let dq = p5.Vector.sub(p,this.center).normalize().mult(oq);

      let newP = p5.Vector.add(this.center,dq)

      return newP;

  };

​

  this.draw = function() {

    ellipse(this.center.x,this.center.y, 2*this.r,2*this.r)

  }

}