Finding if a point is on a line

Question

Let\'s say I have a line drawn as so in HTML5 Canvas:

...
ctx.beginPath();
ctx.moveTo(x,y);
ctx.lineTo(x1,y1);
ctx.closePath();
...

I want

Answer 1

Here is the approach taken from Wikipedia article Distance from a point to a line (Line defined by two points)

        var Dx = x2 - x1;
        var Dy = y2 - y1;
        var d = Math.abs(Dy*x0 - Dx*y0 - x1*y2+x2*y1)/Math.sqrt(Math.pow(Dx, 2) + Math.pow(Dy, 2));

where (x0,y0) is your Point coordinates and your Line is ((x1,y1),(x2,y2)) However, this does not checks for boundaries of the line, so I had to add another check for it.

    function inBox(x0, y0, rect) {
        var x1 = Math.min(rect.startX, rect.startX + rect.w);
        var x2 = Math.max(rect.startX, rect.startX + rect.w);
        var y1 = Math.min(rect.startY, rect.startY + rect.h);
        var y2 = Math.max(rect.startY, rect.startY + rect.h);
        return (x1 <= x0 && x0 <= x2 && y1 <= y0 && y0 <= y2);
    }

Where your Line defined as rectangle. Hope this helps.

Answer 2

The first step is to find the normal projection of the point onto the line. This is actually quite simple: take the distance from point 1 to the target, and point 2 to the target, and call them D1 and D2 respectively. Then calculate D1+(D2-D1)/2. This is the distance to the projected point on the line from point 1.

You can now find that point, and get the distance from that point to the target. If the distance is zero, then the target is exactly on the line. If the distance is less than 5, then the target was less than 5px away, and so on.

EDIT: A picture is worth a thousand words. Here's a diagram:

_{(source: adamhaskell.net)}

(In hindsight, probably should have made those circles a different colour... Also, the purple line is supposed to be perpendicular to line AB. Blame my terrible aim with the blue line!)

Answer 3

You have two options for this. Your "simple" option is to use canvas to do it -- Read the pixel data wherever the mouse is and if it's the same color as your line then the user clicked on the line. This makes a lot of assumptions, however, like that everything on your canvas is rendered in a different solid color. This is possible, however, as a common trick is to render everything to an off-screen canvas in a different solid color. Then when the user clicks something you know exactly what it is by reading the color of that one pixel and mapping it back to the original object.

But that's not exactly what you asked for :)

You don't want to know if the user clicked on a line because they almost never will. A line is infinitely thin, so unless it's exactly horizontal or exactly vertical they will never click on it. What you want instead is to see how far the mouse is from the line. Kolink just answered that part, so I'll stop here :)