how to draw a curve that passes three points in canvas?

What I am going to do is to change the curve of a circle. If I click one point in a circle and drag it to other point, that arc of the circle should be extended or contracted accordingly. I was going to use beizer curve but there's no guarantee that the new beizer curve will pass the dragged point. Attached is the image showing a new curve when mouse dragged which I can not solve. can anyone help me on this matter? I will be looking forward to your reply

Solution

Fit circle to points

Maybe this will help.

The function at the top of the example fitCircleToPoints(x1, y1, x2, y2, x3, y3) will fit a circle to 3 points.

It returns an object

{
   x, y,   // center of circle
   radius, // radius of circle
   CCW,    // true if circle segment is counter clockwise
}

If the 3 points are all on the same line then there is no circle that can fit (radius Infinity is not valid) so the function returns undefined.

function fitCircleToPoints(x1, y1, x2, y2, x3, y3) {
    var x, y, u;
    const slopeA = (x2 - x1) / (y1 - y2); // slope of vector from point 1 to 2
    const slopeB = (x3 - x2) / (y2 - y3); // slope of vector from point 2 to 3
    if (slopeA === slopeB)  { return } // Slopes are same thus 3 points form striaght line. No circle can fit.
    if (y1 === y2) {   // special case with points 1 and 2 have same y 
        x = ((x1 + x2) / 2);
        y = slopeB * x + (((y2 + y3) / 2) - slopeB * ((x2 + x3) / 2));  
    } else if(y2 === y3) { // special case with points 2 and 3 have same y 
        x = ((x2 + x3) / 2);
        y = slopeA * x + (((y1 + y2) / 2) - slopeA * ((x1 + x2) / 2));  
    } else {
        x = ((((y2 + y3) / 2) - slopeB * ((x2 + x3) / 2)) - (u = ((y1 + y2) / 2) - slopeA * ((x1 + x2) / 2))) / (slopeA - slopeB);
        y = slopeA * x + u;
    }
    
    return {
        x, y, 
        radius: ((x1 - x) ** 2 + (y1 - y) ** 2) ** 0.5,
        CCW: ((x3 - x1) * (y2 - y1) - (y3 - y1) * (x2 - x1)) >= 0,
    };
}


requestAnimationFrame(update);

Math.TAU = Math.PI * 2;
const ctx = canvas.getContext("2d");
const mouse  = {x : 0, y : 0, button : false}   
function mouseEvents(e){
    const bounds = canvas.getBoundingClientRect();
    mouse.x = e.pageX - bounds.left - scrollX;
    mouse.y = e.pageY - bounds.top - scrollY;
    mouse.button = e.type === "mousedown" ? true : e.type === "mouseup" ? false : mouse.button;
}
["down","up","move"].forEach(name => document.addEventListener("mouse" + name, mouseEvents));
var w = canvas.width, h = canvas.height, cw = w / 2, ch = h / 2;
var nearest, ox, oy, dragging, dragIdx;
const points = [10,110,200,100,400,110];
function drawPoint(x, y, rad, col = "black") {
     ctx.strokeStyle = col;
     ctx.beginPath();
     ctx.arc(x, y, rad, 0, Math.TAU);
     ctx.stroke();
 }
function drawLines(idx, col = "black") {
     ctx.strokeStyle = col;
     ctx.beginPath();
     ctx.lineTo(points[idx++], points[idx++]);
     ctx.lineTo(points[idx++], points[idx++]);
     ctx.lineTo(points[idx++], points[idx++]);
     ctx.stroke();
} 
function drawPoints() {
  var i = 0, x, y;
  nearest = - 1;
  var minDist = 20;
  while (i < points.length) {
     drawPoint(x = points[i++], y = points[i++], 4);
     const dist = (x - mouse.x) ** 2 + (y - mouse.y) ** 2;
     if (dist < minDist) {
        minDist = dist;
        nearest = i - 2;
     }
  }
}

function update(){
    ctx.setTransform(1,0,0,1,0,0); // reset transform
    if (w !== innerWidth || h !== innerHeight) {
        cw = (w = canvas.width = innerWidth) / 2;
        ch = (h = canvas.height = innerHeight) / 2;
    } else {
        ctx.clearRect(0,0,w,h);
    }
    canvas.style.cursor = "default";
    drawPoints();
    if (nearest > -1) {
      if (mouse.button) {
        if (!dragging) {
            dragging = true;
            ox = points[nearest] - mouse.x;
            oy = points[nearest+1] - mouse.y;
            dragIdx = nearest;
        }
      } else {
          canvas.style.cursor = "move";
      }
      drawPoint(points[nearest], points[nearest + 1], 6, "red")
    }
    if (dragging) {
        if (!mouse.button) {
            dragging = false;
        } else {
            points[dragIdx] = mouse.x + ox;
            points[dragIdx + 1] = mouse.y + oy
            canvas.style.cursor = "none";
        }
    }
    
    drawLines(0, "#0002");
    const circle = fitCircleToPoints(points[0], points[1], points[2], points[3], points[4], points[5]);
    if (circle) {
        ctx.strokeStyle = "#000";
        const ang1 = Math.atan2(points[1] - circle.y, points[0]- circle.x);
        const ang2 = Math.atan2(points[5] - circle.y, points[4]- circle.x);
        ctx.beginPath();
        ctx.arc(circle.x, circle.y, circle.radius, ang1, ang2, circle.CCW);
        ctx.stroke();
    }
    requestAnimationFrame(update);
}

canvas { position : absolute; top : 0px; left : 0px; }

<canvas id="canvas"></canvas>
Use mouse to move points.