计算圆与通过中心的直线的交点

我如何获得直线和圆的交点..我有很多关于这个主题的信息，但我的要求不匹配..

我得到了一条线，其一个端点位于圆的原点..而另一端位于圆之外的某处..现在我需要这条线和圆的交点..

我尝试使用下面的公式从圆外找到最近的边缘点，但无法破解它 -

closestCirclePoint = function(px, py, x, y, ray){
    var tg = (x += ray, y += ray, 0);
    return function(x, y, x0, y0){return Math.sqrt((x -= x0) * x + (y -= y0) * y);}(px, py, x, y) > ray ?
        {x: Math.cos(tg = Math.atan2(py - y, px - x)) * ray + x, y: Math.sin(tg) * ray + y}
        //{x: (px - x) / (length / ray) + x, y: (py - y) / (length / ray) + y}
        : {x: px, y: py};
};

有什么办法可以解决这个问题..?? 提前致谢！

Lindenhovius 答案的 JavaScript 版本如下所示：

/**
 * Finds the intersection between a circles border 
 * and a line from the origin to the otherLineEndPoint.
 * @param  {Vector} origin            - center of the circle and start of the line
 * @param  {number} radius            - radius of the circle
 * @param  {Vector} otherLineEndPoint - end of the line
 * @return {Vector}                   - point of the intersection
 */
function findIntersect (origin, radius, otherLineEndPoint) {
    var v = otherLineEndPoint.subtract(origin);
    var lineLength = v.length();    
    if (lineLength === 0) throw new Error("Length has to be positive");
    v = v.normalize();
    return origin.add(v.multiplyScalar(radius)); 
}

但是你需要自己实现向量“类”*：

function Vector (x, y) {
    this.x = x || 0;
    this.y = y || 0;
}

Vector.prototype.add = function (vector) {
    return new Vector(this.x + vector.x, this.y + vector.y);
};

Vector.prototype.subtract = function (vector) {
    return new Vector(this.x - vector.x, this.y - vector.y);
};

Vector.prototype.multiply = function (vector) {
    return new Vector(this.x * vector.x, this.y * vector.y);
};

Vector.prototype.multiplyScalar = function (scalar) {
    return new Vector(this.x * scalar, this.y * scalar);
};

Vector.prototype.divide = function (vector) {
    return new Vector(this.x / vector.x, this.y / vector.y);
};

Vector.prototype.divideScalar = function (scalar) {
    return new Vector(this.x / scalar, this.y / scalar);
};

Vector.prototype.length = function () {
    return Math.sqrt(Math.pow(this.x, 2) + Math.pow(this.y, 2));
};

Vector.prototype.normalize = function () {
    return this.divideScalar(this.length());
};

*JavaScript 中没有真正的类——只是构造函数 https://developer.mozilla.org/de/docs/Web/JavaScript/Reference/Global_Objects/Object/constructor and 原型 https://developer.mozilla.org/de/docs/Web/JavaScript/Reference/Global_Objects/Object/prototype，随着 ES6 的出现，事情发生了变化，但那是另一个话题了。