Collision detection between a line and a circle in JavaScript

Question

I'm looking for a definitive answer, maybe a function cos I'm slow, that will determine if a line segment and circle have collided, in javascript (working with canvas)

A function like the one below that simply returns true if collided or false if not would be awesome. I might even donate a baby to you.

function isCollided(lineP1x, lineP1y, lineP2x, lineP2y, circlex, circley, radius) {

    ...
}

I've found plenty of formulas, like this one, but they are over my head.

Answer 1

Here you will need some Math:

This is the basic concept if you don't know how to solve equations in general. I will leave the rest of the thinking to you. ;) Figuring out CD's length isn't that hard.

If you are asking how, that's how: Finding collisions in JavaScript is kind of complicated.

Answer 2

I Spent about a day and a half to make it perfect.. Hope this helps.

function collisionCircleLine(circle,line){ // Both are objects

    var side1 = Math.sqrt(Math.pow(circle.x - line.p1.x,2) + Math.pow(circle.y - line.p1.y,2)); // Thats the pythagoras theoram If I can spell it right

    var side2 = Math.sqrt(Math.pow(circle.x - line.p2.x,2) + Math.pow(circle.y - line.p2.y,2));

    var base = Math.sqrt(Math.pow(line.p2.x - line.p1.x,2) + Math.pow(line.p2.y - line.p1.y,2));

    if(circle.radius > side1 || circle.radius > side2)
        return true;

    var angle1 = Math.atan2( line.p2.x - line.p1.x, line.p2.y - line.p1.y ) - Math.atan2( circle.x - line.p1.x, circle.y - line.p1.y ); // Some complicated Math

    var angle2 = Math.atan2( line.p1.x - line.p2.x, line.p1.y - line.p2.y ) - Math.atan2( circle.x - line.p2.x, circle.y - line.p2.y ); // Some complicated Math again

    if(angle1 > Math.PI / 2 || angle2 > Math.PI / 2) // Making sure if any angle is an obtuse one and Math.PI / 2 = 90 deg
        return false;


        // Now if none are true then

        var semiperimeter = (side1 + side2 + base) / 2;

        var areaOfTriangle = Math.sqrt( semiperimeter * (semiperimeter - side1) * (semiperimeter - side2) * (semiperimeter - base) ); // Heron's formula for the area

        var height = 2*areaOfTriangle/base;

        if( height < circle.radius )
            return true;
        else
            return false;

}

And that is how you do it..

Answer 3

Matt DesLauriers published a Javascript library for this problem at https://www.npmjs.com/package/line-circle-collision. The API is straightforward:

var circle = [5, 5],
    radius = 25,
    a = [5, 6],
    b = [10, 10]

var hit = collide(a, b, circle, radius)

Answer 4

function pointCircleCollide(point, circle, r) {
    if (r===0) return false
    var dx = circle[0] - point[0]
    var dy = circle[1] - point[1]
    return dx * dx + dy * dy <= r * r
}

var tmp = [0, 0]

function lineCircleCollide(a, b, circle, radius, nearest) {
    //check to see if start or end points lie within circle
    if (pointCircleCollide(a, circle, radius)) {
        if (nearest) {
            nearest[0] = a[0]
            nearest[1] = a[1]
        }
        return true
    } if (pointCircleCollide(b, circle, radius)) {
        if (nearest) {
            nearest[0] = b[0]
            nearest[1] = b[1]
        }
        return true
    }

    var x1 = a[0],
        y1 = a[1],
        x2 = b[0],
        y2 = b[1],
        cx = circle[0],
        cy = circle[1]

    //vector d
    var dx = x2 - x1
    var dy = y2 - y1

    //vector lc
    var lcx = cx - x1
    var lcy = cy - y1

    //project lc onto d, resulting in vector p
    var dLen2 = dx * dx + dy * dy //len2 of d
    var px = dx
    var py = dy
    if (dLen2 > 0) {
        var dp = (lcx * dx + lcy * dy) / dLen2
        px *= dp
        py *= dp
    }

    if (!nearest)
        nearest = tmp
    nearest[0] = x1 + px
    nearest[1] = y1 + py

    //len2 of p
    var pLen2 = px * px + py * py

    //check collision
    return pointCircleCollide(nearest, circle, radius)
            && pLen2 <= dLen2 && (px * dx + py * dy) >= 0
}

var circle = [5, 5],
    radius = 25,
    a = [5, 6],
    b = [10, 10]

var hit = lineCircleCollide(a, b, circle, radius)