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HTML 

              
                <canvas id="drawing" width="600" height="600">Canvas not supported.</canvas>
  
<div class="selector border">
  <div class="select-box border" id="scale" >Размер:
    <button class="button" id="scale-up">Up </button>
    <button class="button" id="scale-down">Down</button>
  </div>
  <div class="select-box border" id="moving">Движение:
    <button class="button" id="left-move">Left</button>
    <button class="button" id="right-move">Right</button>
    <button class="button" id="up-move">Up</button>
    <button class="button" id="down-move">Down</button>
  </div>
  <div class="select-box border" id="rotation">Вращение:
    <button class="button" id="left-rotate">Left</button>
    <button class="button" id="right-rotate">Right</button>
  </div>
  <div class="select-box border" id="auto-center">Масштабирование:
    <button class="button" id="auto-center">AUTO</button>
</div>
!

CSS 

              
                #drawing {
  border: 5px solid black;
  border-radius: 10%;
  background: white;  
  display: block;
  margin: 0 auto;
}

.border{
 font-size: 18px;
 border: 3px solid black;
 border-radius: 2%;
}

.selector{
    background: rgba(0, 255, 255, 0.6);
    padding: 10px 10px 10px 10px;
    margin-top: 1%;
    margin-left: 24%;
    width: 50%;
    height: 100%;
    display: flex;
    flex-wrap: wrap;
    justify-content: space-between;
}

.button{
    font: small-caps bold 12px/1 sans-serif;
    background-color: rgba(237, 85, 111, 1);
}

.select-box{
    padding: 5px 5px 5px 5px;
    font: small-caps bold 14px/1 sans-serif;
    gap: 5px;
    display: flex;
    flex-flow: column;

}
!

JS 

              
                const obj = document.getElementById('drawing');
const ctx = obj.getContext('2d');

const pointStep = 0.01;
const W = obj.width;
const H = obj.height;

class Point{
    constructor(x,y){
      this.x = x;
      this.y = y;
      this.X = x;
      this.Y = y;
    }
  }
  
class Style{
  constructor(fillColor='black', strokeColor='black', lineWidth=2){
    this.fillColor = fillColor;
    this.strokeColor = strokeColor;
    this.lineWidth = lineWidth;
  }
}

function button(ctx, pointsArr, koef){
  let scaleVal = Math.min(W,H)/320;
  let angleVal = 0;

  // Scale buttons
  document.getElementById('scale-up').addEventListener('click', function() {
    scale(1.2, pointsArr[1]);
    scaleVal*=1/1.2;
    draw(ctx, pointsArr);
  });
  document.getElementById('scale-down').addEventListener('click', function() {
    scale(0.8, pointsArr[1]);
    scaleVal*=1/0.8
    draw(ctx, pointsArr);
  });

  // Moving buttons
  document.getElementById('left-move').addEventListener('click', function() {
    setPosition(-20, 0, pointsArr[1]);
    draw(ctx, pointsArr);
  });
  document.getElementById('right-move').addEventListener('click', function() {
    setPosition(20, 0, pointsArr[1]);
    draw(ctx, pointsArr);
  });
  document.getElementById('up-move').addEventListener('click', function() {
    setPosition(0, -20, pointsArr[1]);
    draw(ctx, pointsArr);
  });
  document.getElementById('down-move').addEventListener('click', function() {
    setPosition(0, 20, pointsArr[1]);
    draw(ctx, pointsArr);
  });

  //Rotation buttons
  document.getElementById('right-rotate').addEventListener('click', function() {
    rotate(-15*koef, pointsArr[1]);
    angleVal-=15*koef;
    draw(ctx, pointsArr);
  });
  document.getElementById('left-rotate').addEventListener('click', function() {
    rotate(15*koef, pointsArr[1]);
    angleVal+=15*koef;
    draw(ctx, pointsArr);
  });

  // centering button
  document.getElementById('auto-center').addEventListener('click', function() {
    scale(scaleVal, pointsArr[1]);
    scaleVal = 1;
    rotate(-angleVal, pointsArr[1]);
    angleVal = 0;
    moveTo(W/2,H/2,pointsArr[1]);
    draw(ctx, pointsArr);
  });
}

function calcCenter(arr) {
  let sumX = 0;
  let sumY = 0;
  let count = 0;

  for (let i = 0; i < arr.length; i++) {
    for (let j = 0; j < arr[i].length; j++) {
      let point = arr[i][j];
      sumX += point.X;
      sumY += point.Y;
      count++;
    }
  }

  let cX = sumX / count;
  let cY = sumY / count;

  return new Point(cX, cY);
}

function makeLoop(X, Y, a, b, startAngle, endAngle){

  tmpArr = [];
  for (let i = startAngle*Math.PI/180; i <= endAngle*Math.PI/180;i+=pointStep){
    let x = a*Math.cos(i);
    let y = b*Math.sin(i);
    tmpArr.push(new Point(X+x,Y+y));
  }
  return tmpArr;
}

function moveTo(newX,newY,arr){
  let cPoint = calcCenter(arr);
  for(let i = 0; i < arr.length; i++){
    for(let j = 0; j < arr[i].length; j++){
      arr[i][j].X = arr[i][j].X - cPoint.X + newX;
      arr[i][j].Y = arr[i][j].Y - cPoint.Y + newY;
    }
  }
}

function setPosition(dX,dY,arr){
  for(let i = 0; i < arr.length; i++){
    for(let j = 0; j < arr[i].length; j++){
      arr[i][j].X = arr[i][j].X + dX;
      arr[i][j].Y = arr[i][j].Y + dY;
    }
  }
}

function scale(N, arr){
  let dX = calcCenter(arr).X*N - calcCenter(arr).X;
  let dY = calcCenter(arr).Y*N - calcCenter(arr).Y;

  for(let i = 0; i < arr.length; i++){
    for(let j = 0; j < arr[i].length; j++){
      arr[i][j].X = arr[i][j].X*N - dX;
      arr[i][j].Y = arr[i][j].Y*N - dY;
    }
  }
}

function rotate(degree, arr){
  const radians = degree*Math.PI/180;

  const cos = Math.cos(radians);
  const sin = Math.sin(radians);

  let cPoint = calcCenter(arr);

  for(let i = 0; i < arr.length; i++){
    for(let j = 0; j < arr[i].length; j++){
      const newX = (arr[i][j].X - cPoint.X) * cos - (arr[i][j].Y - cPoint.Y) * sin;
      const newY = (arr[i][j].X - cPoint.X) * sin + (arr[i][j].Y - cPoint.Y) * cos;

      arr[i][j].X = newX + cPoint.X;
      arr[i][j].Y = newY + cPoint.Y;
    }
  }
}

function draw(ctx, arr){
  ctx.fillStyle = 'rgb(0, 255, 255)';
  ctx.fillRect(0,0,W,H);

  let styleArr = arr[0];
  let pointsArr = arr[1];

  for(let i = 0; i < pointsArr.length; i++){
    ctx.beginPath();
    ctx.moveTo(pointsArr[i][0].X, pointsArr[i][0].Y);
    for(let j = 1; j < pointsArr[i].length; j++){
      ctx.lineTo(pointsArr[i][j].X, pointsArr[i][j].Y);
    }
    ctx.closePath();

    ctx.lineWidth = styleArr[i].lineWidth;
    ctx.fillStyle = styleArr[i].fillColor;
    ctx.strokeStyle = styleArr[i].strokeColor;

    ctx.fill();
    ctx.stroke();
  }
}

let pointsArr = [[],[]];

const eyeGrad = ctx.createLinearGradient(W/2, H/2-30, W/2, H);

eyeGrad.addColorStop(0, 'rgba(0, 194, 208, 1)');
eyeGrad.addColorStop(0.5, 'rgba(0, 236, 255, 1)');
eyeGrad.addColorStop(1,'rgba(186, 250, 255, 1)');

pointsArr[0].push(new Style(eyeGrad, 'black', 6)); // left eye main
pointsArr[1].push(makeLoop(W/2-50,H/2,20,28,120,423.5));

pointsArr[0].push(new Style(eyeGrad, 'black', 6)); // right eye main
pointsArr[1].push(makeLoop(W/2+50,H/2,20,28,120,423.5));

pointsArr[0].push(new Style('white', 'white', 4)); // left eye ball white
pointsArr[1].push(makeLoop(W/2-50,H/2+10,11,11,0,360));

pointsArr[0].push(new Style(eyeGrad, eyeGrad, 4)); // left eye ball little
pointsArr[1].push(makeLoop(W/2-50,H/2+5,9,9,0,360));  

pointsArr[0].push(new Style('white', 'white', 4)); // right eye ball white
pointsArr[1].push(makeLoop(W/2+50,H/2+10,11,11,0,360));

pointsArr[0].push(new Style(eyeGrad, 'rgba(255, 85, 143, 0)', 0)); // right eye ball little
pointsArr[1].push(makeLoop(W/2+50,H/2+5,9,9,0,360)); 

pointsArr[0].push(new Style('rgba(255, 85, 143, 1)', 'black', 4));
pointsArr[1].push([new Point(W/2-8,H/2+30), new Point(W/2+8,H/2+30), new Point(W/2+3,H/2+40), new Point(W/2-3,H/2+40)]); // mouth

pointsArr[0].push(new Style('rgba(255, 85, 143, 0.8)', 'rgba(255, 85, 143, 0.4)', 5)); // right pink ball
pointsArr[1].push(makeLoop(W/2+70,H/2+30,6,6,0,360)); 

pointsArr[0].push(new Style('rgba(255, 85, 143, 0.8)', 'rgba(255, 85, 143, 0.4)', 5)); // left pink ball
pointsArr[1].push(makeLoop(W/2-70,H/2+30,6,6,0,360)); 

pointsArr[0].push(new Style('white', 'white', 2));
pointsArr[1].push([new Point(W/2-48,H/2+3), new Point(W/2-48,H/2)]); // left eye smile one

pointsArr[0].push(new Style('white', 'white', 2));
pointsArr[1].push([new Point(W/2-52,H/2+3), new Point(W/2-52,H/2)]); // left eye smile two

pointsArr[0].push(new Style('white', 'white', 2));
pointsArr[1].push([new Point(W/2+48,H/2+3), new Point(W/2+48,H/2)]); // right eye smile one

pointsArr[0].push(new Style('white', 'white', 2));
pointsArr[1].push([new Point(W/2+52,H/2+3), new Point(W/2+52,H/2)]); // right eye smile two

pointsArr[0].push(new Style('black', 'black', 6)); // nose
pointsArr[1].push(makeLoop(W/2,H/2+20,1,1,0,360)); 

scale(2, pointsArr[1]);
draw(ctx, pointsArr);

button(ctx,pointsArr,1.5);
!
999px

Console