javascript - Ellipse - 鼠标碰撞检测

Question

我正在尝试弄清楚如何判断鼠标是否位于 HTML5 Canvas 上的椭圆上。我需要比边界框检查更精确。

抱歉，这是一个模糊的问题。我完全被难住了。

任何帮助将不胜感激。

到目前为止我有这个:

// This is a pretend object. m.x and m.y will have the position of the mouse.
var m = {
    x:245,
    y:341,
    onEnter: function(){}
};

m.onEnter = function () {
    console.log('The mouse entered the ellipse!');
};

// The important parts of my ellipse object
var e = {
    width:100,
    height:50,
    x:132,
    y:143
};

// This is already working - I use a bounding-box first to increase performance.
if (m.x >= e.x - (e.width/2) && m.x <= e.x + (e.width/2) && m.y >= e.y - (e.height/2) && m.y <= e.y + (e.height/2)) {

    if (/* I havn't got the slightest idea what to put here. */) {
        m.onEnter();
    }

}

Answer 1

@pvg 的重复答案是可以的，但是重复的答案应该指出他们使用的变量是如何计算的:

// Given cx,cy,a,b defining an ellipse 
function isInEllipse(mouseX,mouseY){
    var dx=mouseX-cx;
    var dy=mouseY-cy;
    return ((dx*dx)/(a*a)+(dy*dy)/(b*b)<=1);
}

这是示例代码和演示:

var canvas=document.getElementById("canvas");
var ctx=canvas.getContext("2d");
var cw=canvas.width;
var ch=canvas.height;
function reOffset(){
  var BB=canvas.getBoundingClientRect();
  offsetX=BB.left;
  offsetY=BB.top;        
}
var offsetX,offsetY;
reOffset();
window.onscroll=function(e){ reOffset(); }
window.onresize=function(e){ reOffset(); }

var PI=Math.PI;
var PI2=PI*2;
var cx=cw/2;
var cy=ch/2;
var a=120;
var b=80;
var points=getPointsOnEllipse(cx,cy,a,b);

$("#canvas").mousemove(function(e){handleMouseMove(e);});

drawEllipse(points);


function dot(x,y,color){
  ctx.beginPath();
  ctx.arc(x,y,3,0,PI2);
  ctx.closePath();
  ctx.fillStyle=color;
  ctx.fill();
}

function isInEllipse(x,y){
  var dx=x-cx;
  var dy=y-cy;
  return ((dx*dx)/(a*a)+(dy*dy)/(b*b)<=1);
}

function drawEllipse(points){
  ctx.beginPath();
  ctx.moveTo(points[0].x,points[0].y);
  for(var j=0;j<points.length;j++){
    ctx.lineTo(points[j].x,points[j].y);
  }
  ctx.closePath();
  ctx.lineWidth=1;
  ctx.strokeStyle='forestgreen';
  ctx.stroke();
}

function getPointsOnEllipse(cx,cy,a,b){
  var startAngle=-PI/2;
  var lastX=cx-(a*Math.cos(startAngle));
  var lastY=cy+(b*Math.sin(startAngle));
  var points=[];
  for(var i=0;i<1000;i++){
    var angle=startAngle+PI2/1000*i;
    var x=cx-(a*Math.cos(angle));
    var y=cy+(b*Math.sin(angle));
    var dx=x-lastX;
    var dy=y-lastY;
    var length=parseInt(Math.sqrt(dx*dx+dy*dy));
    var eAngle=(Math.atan2(dy,dx)+PI2)%PI2;
    if(length>0){
      points.push({x:x,y:y,angle:eAngle});
      lastX=x;
      lastY=y;
    }
  }
  return(points);
}

function handleMouseMove(e){
  // tell the browser we're handling this event
  e.preventDefault();
  e.stopPropagation();

  mouseX=parseInt(e.clientX-offsetX);
  mouseY=parseInt(e.clientY-offsetY);

  var hit=isInEllipse(mouseX,mouseY);
  var color=(hit)?'red':'green';
  dot(mouseX,mouseY,color);

}

body{ background-color: ivory; }
#canvas{border:1px solid red; }

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<h4>Move mouse in & out of ellipse.<br>Red mouse dots are inside ellipse, Green outside.</h4>
<canvas id="canvas" width=300 height=300></canvas>