找到点和圆画布之间的切线 [英] Find tangent between point and circle Canvas

问题描述

确定一些我对我的三角学有点生锈。

Ok some i'm a bit rusty on my trigonometry.

基本上我想在画布上做一个聚光灯。我试图保持一个9度的角度，这就是为什么这有点棘手。这是我的小提琴到目前为止。

Essentially I'm trying to make a sort of spotlight in canvas. I'm trying to maintain a 9 degree angle which is why this is a little tricky. Here's my fiddle so far.

http://jsfiddle.net / uq8fe /

it's a bit long please refer to the fiddle /\

很接近，但我需要圆上的切点，所以我可以在这两点和鼠标之间画一个三角形，所以我看起来像一个很好的光滑梁。

Pretty close, but i need the tangent points on the circle so i can draw a triangle between those two points and the mouse, so i looks like a nice smooth beam.

http：// en。 wikipedia.org/wiki/File:Inscribed_angle_theorem4.svg

以上是我需要实现的图表和公式。我需要点T和S.我希望这有意义。

Above is essentially the diagram and formula i need to implement. I need point T and S. I hope this makes sense.

推荐答案

这是计算切线的代码：
演示

This is the code to calculate tangents: Demo

    //Calculate Tangents
    var pointDistance = {
        x: beamCenter.x - mousePos.x,
        y: beamCenter.y - mousePos.y,
        length: function () {
            return Math.sqrt(this.x * this.x + this.y * this.y)
        }
    }

    var radius = getDist(p1.x, p1.y, p2.x, p2.y) / 2;
    //Alpha
    var a = Math.asin(radius / pointDistance.length());
    //Beta
    var b = Math.atan2(pointDistance.y, pointDistance.x);
    //Tangent angle
    var t = b - a;
    //Tangent points
    var T1 = {
        x: beamCenter.x + radius * Math.sin(t),
        y: beamCenter.y + radius * -Math.cos(t)
    };

    t = b + a;
    var T2 = {
        x: beamCenter.x + radius * -Math.sin(t),
        y: beamCenter.y + radius * Math.cos(t)
    }

这篇关于找到点和圆画布之间的切线的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！