Finding points on curves in HTML 5 2d Canvas context.

Question

Given lines drawn by 2d canvas context functions bezierCurveTo, quadraticCurveTo or arcTo, how can I find points along those lines?

My intent is to draw an object at the midpoint of a curve. Using the SVG DOM, I can do this with methods getPointAtLength & getTotalLength, but I can't see an equivalent in HTML canvas.

Answer 1

You find them the hard way :(

There isn't an equivalent in HTML canvas. You have to find the midpoints yourself with plain old math.

I did an example of how to find midpoint of bezier curves for you. See it live at jsFiddle here. A copy of the javascript is pasted below.

Real curve is red, midpoint is the tiny green rectangle. Everything else is just a visual aid.

var ctx = $("#test")[0].getContext("2d")
function mid(a,b) {
 return (a+b) / 2;
}


var cp1x = 100;
var cp1y = 150;
var cp2x = 175;
var cp2y = 175;
var x = 200;
var y = 0;

ctx.lineWidth = 4;
ctx.strokeStyle = "red";
ctx.fillStyle = "rgba(0,0,0,0.6)";

ctx.beginPath();
ctx.moveTo(0, 0);
ctx.bezierCurveTo(cp1x, cp1y, cp2x, cp2y, x, y);
ctx.stroke();

//line goes from start to control point 1
ctx.strokeStyle = "rgba(0,0,200,0.4)";
ctx.beginPath();
ctx.moveTo(0, 0);
ctx.lineTo(cp1x , cp1y);
ctx.stroke();

//line goes from end to control point 2
ctx.beginPath();
ctx.moveTo(x, y);
ctx.lineTo(cp2x , cp2y);
ctx.stroke();

//line goes from control point to control point
ctx.strokeStyle = "rgba(200,0,200,0.4)";
ctx.beginPath();
ctx.moveTo(cp1x, cp1y);
ctx.lineTo(cp2x , cp2y);
ctx.stroke();

// now find the midpoint of each of those 3 lines
var ax = mid(cp1x,0);
var bx = mid(cp2x,x)
var cx = mid(cp1x,cp2x)

var ay = mid(cp1y,0)    
var by = mid(cp2y,y)    
var cy = mid(cp1y,cp2y)


// draw midpoints for visual aid 
// not gonna look exact 'cause square
// will be drawn from top-right instead of center
ctx.fillRect(ax, ay, 4, 4);
ctx.fillRect(bx, by, 4, 4);
ctx.fillRect(cx, cy, 4, 4);


//now draw lines between those three points. These are green
ctx.strokeStyle = "rgba(0,200,0,0.4)";
ctx.beginPath();
ctx.moveTo(ax, ay);
ctx.lineTo(cx , cy);
ctx.stroke();

ctx.beginPath();
ctx.moveTo(bx, by);
ctx.lineTo(cx , cy);
ctx.stroke();

//now the midpoint of the green lines:
// so g1 and g2 are the green line midpoints
var g1x = mid(ax,cx);
var g2x = mid(bx,cx);

var g1y = mid(ay,cy); 
var g2y = mid(by,cy);  

//draw them to make sure:
ctx.fillRect(g1x , g1y, 4, 4);
ctx.fillRect(g2x , g2y, 4, 4);

//now one final line, in gray
ctx.strokeStyle = "rgba(20,20,20,0.4)";
ctx.beginPath();
ctx.moveTo(g1x , g1y);
ctx.lineTo(g2x , g2y);
ctx.stroke();

//whew! We made it!
var FinallyTheMidpointx = mid(g1x,g2x); 
var FinallyTheMidpointy = mid(g1y,g2y); 

//draw something at the midpoint to celebrate
ctx.fillStyle = "rgba(0,255,0,1)";
ctx.fillRect(FinallyTheMidpointx, FinallyTheMidpointy, 4, 4);

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