How to code an nth order Bezier curve

Question

Trying to code an nth order bezier in javascript on canvas for a project. I want to be able to have the user press a button, in this case 'b', to select each end point and the control points. So far I am able to get the mouse coordinates on keypress and make quadratic and bezier curves using the built in functions. How would I go about making code for nth order?

Answer 1

Here's a Javascript implementation of nth order Bezier curves:

// setup canvas
var canvas = document.getElementById('canvas');
var ctx = canvas.getContext('2d');

canvas.height = window.innerHeight;
canvas.width = window.innerWidth;

ctx.fillText("INSTRUCTIONS: Press the 'b' key to add points to your curve. Press the 'c' key to clear all points and start over.", 20, 20);

// initialize points list
var plist = [];

// track mouse movements
var mouseX;
var mouseY;

document.addEventListener("mousemove", function(e) {
  mouseX = e.clientX;
  mouseY = e.clientY;
});

// from: http://rosettacode.org/wiki/Evaluate_binomial_coefficients#JavaScript
function binom(n, k) {
  var coeff = 1;
  for (var i = n - k + 1; i <= n; i++) coeff *= i;
  for (var i = 1; i <= k; i++) coeff /= i;
  return coeff;
}

// based on: https://stackoverflow.com/questions/16227300
function bezier(t, plist) {
  var order = plist.length - 1;

  var y = 0;
  var x = 0;

  for (i = 0; i <= order; i++) {
    x = x + (binom(order, i) * Math.pow((1 - t), (order - i)) * Math.pow(t, i) * (plist[i].x));
    y = y + (binom(order, i) * Math.pow((1 - t), (order - i)) * Math.pow(t, i) * (plist[i].y));
  }

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

// draw the Bezier curve
function draw(plist) {
  ctx.clearRect(0, 0, canvas.width, canvas.height);
  var accuracy = 0.01; //this'll give the 100 bezier segments
  ctx.beginPath();
  ctx.moveTo(plist[0].x, plist[0].y);

  for (p in plist) {
    ctx.fillText(p, plist[p].x + 5, plist[p].y - 5);
    ctx.fillRect(plist[p].x - 5, plist[p].y - 5, 10, 10);
  }

  for (var i = 0; i < 1; i += accuracy) {
    var p = bezier(i, plist);
    ctx.lineTo(p.x, p.y);
  }

  ctx.stroke();
  ctx.closePath();
}

// listen for keypress
document.addEventListener("keydown", function(e) {
  switch (e.keyCode) {
    case 66:
      // b key
      plist.push({
        x: mouseX,
        y: mouseY
      });
      break;
    case 67:
      // c key
      plist = [];
      break;
  }
  draw(plist);
});

html,
body {
  height: 100%;
  margin: 0 auto;
}

<canvas id="canvas"></canvas>

This is based on this implementation of cubic Bezier curves. In your application, it sounds like you'll want to populate the points array with user-defined points.