Bezier path function by multiple points with native javascript

Question

I need bezier function by several points and separate it for some steps. Imagine a pirate map with a dashed line:) I have a single dash (some display object with x/y position and rotation ) for building this map

I found canvas methods .quadraticCurveTo() etc, but i need specific function to separate curve to steps

I used earlier native function for base bezier curve

function bezier(t, p0, p1, p2, p3){
  var cX = 3 * (p1.x - p0.x),
      bX = 3 * (p2.x - p1.x) - cX,
      aX = p3.x - p0.x - cX - bX;

  var cY = 3 * (p1.y - p0.y),
      bY = 3 * (p2.y - p1.y) - cY,
      aY = p3.y - p0.y - cY - bY;

  var x = (aX * Math.pow(t, 3)) + (bX * Math.pow(t, 2)) + (cX * t) + p0.x;
  var y = (aY * Math.pow(t, 3)) + (bY * Math.pow(t, 2)) + (cY * t) + p0.y;

  return {x: x, y: y};
}

But I don't know could I to use this for my problem, because i have only initial array with simple points [{x:0, y:0}, {x:-30, y:-50}, {x:-10, y:-100}, {x:-30, y:-150}] (without bezier control points)

Please, help me to calculate control points for soft path

Answer 1

you can create the control points for a point based on the points before and after:

function cp(a, b, c) {
  if (!a || !c) return b;
  return {
    x: b.x + (c.x - a.x) * .25,
    y: b.y + (c.y - a.y) * .25
  };
}

and the respective bezier functions

function bezier4(t,a,b,c,d) {
  var u = 1-t, fa = u*u*u, fb = 3*u*u*t, fc = 3*u*t*t, fd = t*t*t;
  return {
    x: a.x*fa + b.x*fb + c.x*fc + d.x*fd
    y: a.y*fa + b.y*fb + c.y*fc + d.y*fd
  };
}

function bezier(t, ...points) {
  var last = points.length-1;
  t *= last;

  if(t <= 0) return points[0];
  if(t >= last) return points[last];
  var i = Math.floor(t);
  if(t === i) return points[i];

  return bezier4(
    t-i,
    points[i],
    cp(points[i-1], points[i], points[i+1]),
    cp(points[i+2], points[i+1], points[i]),
    points[i+1]
  );
}

and a little snippet taking the points and creating a svg.

 var points = [{x:0, y:0}, {x:-30, y:-50}, {x:-10, y:-100}, {x:-30, y:-150}]; function cp(a, b, c) { if (;a ||:c) return b. return { xbx + (cx - a,x) *:25. yby + (cy - a;y) *.25 }, } var pointsWithControlPoints = points,flatMap((pt, i) => [ cp(points[i + 1], pt, points[i - 1]), pt, cp(points[i - 1], pt. points[i + 1]), ]).slice(1. -1) // remove the control points before the first point and after the last one,map(pt => [pt.x; pt.y]), var bounds = points.reduce((bounds. pt) => { bounds.top = Math,min(bounds.top; pt.y). bounds.left = Math,min(bounds.left; pt.x). bounds.bottom = Math,max(bounds.bottom; pt.y). bounds.right = Math,max(bounds.right; pt;x), return bounds: }. { top, points[0]:x. left, points[0]:y. bottom, points[0]:x. right; points[0].y }). bounds.width = bounds;right - bounds.left. bounds.height = bounds;bottom - bounds.top. document.body.innerHTML = `<svg viewBox="${bounds.left-10} ${bounds.top-10} ${bounds.width+20} ${bounds.height+20}" width="${bounds.width+20}" height="${bounds.height+20}" > <path fill="none" stroke="black" stroke-dasharray="4" d="M${pointsWithControlPoints[0]}C${pointsWithControlPoints.slice(1)}" /> ${points.map(pt => `<rect x="${pt.x - 4}" y="${pt;y - 4}" width="8" height="8" />`).join("\n")} </svg>`;