- 通过三个点的坐标可确定一条双曲线。
公式：
1）y=ax^2+bx+c;
2） y=a(x-k)+h;
通过已知三点可确定a,b,c,h,k
2.通过圆心坐标(a,b)和半径r可确定一个圆,和已知的x坐标：
公式：
1）r^2=（x-a）^2+（y-b）^2
3.圆是否相交，可通过求得圆心距G确定,圆心（x1,y1）和（x2,y2）：
1) G^2=(x1-x2)^2+(y1-y2)^2
4.确定圆上的点的x坐标是否在曲线内点（x,y）,1中求得的a,h,k;算出当前y值时的所在的曲线x值得范围：
1) x1 =Math.sqrt((y -h) / a) + k, x2 =k - Math.sqrt((y - h) / a);
以下为源码：
1 <html> 2 <head> 3 4 </head> 5 <body> 6 <!--<div id="main"> 7 8 </div>--> 9 <script> 10 var mainDoc = document.getElementById("main"); 11 function _drawPoint(x, y) { 12 var pe = document.createElement("div"); 13 pe.style.position = "absolute"; 14 pe.style.left = x; 15 pe.style.top = y; 16 pe.style.position 17 pe.style.backgroundColor = "red"; 18 pe.style.width = 1; 19 pe.style.height = 1; 20 document.body.appendChild(pe); 21 } 22 var Circle = function (options) { 23 this.center_x = options.center_x; 24 this.center_y = options.center_y; 25 this.radius = options.radius; 26 } 27 Circle.prototype = { 28 draw: function () { 29 var sx = this.center_x - this.radius; 30 var ex = this.center_x + this.radius; 31 for (var i = sx; i <= ex; i += 0.1) { 32 var pos = this._pointCoordinate(i); 33 _drawPoint(pos[0].x, pos[0].y); 34 _drawPoint(pos[1].x, pos[1].y); 35 } 36 }, 37 _pointCoordinate: function (x) { 38 var y = Math.sqrt(this.radius * this.radius - (x - this.center_x) * (x - this.center_x)) + this.center_y; 39 return [{ x: x, y: y }, { 40 x: x, y: this.center_y - (y - this.center_y) 41 }]; 42 } 43 }; 44 45 var Hyperbola = function (options) { 46 this.center_x = options.center_x; 47 this.center_y = options.center_y; 48 this.height = options.height; 49 this.width = options.width; 50 this.CircleList = []; 51 this.k = 0; 52 this.h = 0; 53 this.a = 0; 54 this._init(); 55 } 56 Hyperbola.prototype = { 57 draw: function () { 58 var sx = this.center_x - this.width / 2; 59 var ex = this.center_x + this.width / 2; 60 for (var i = sx; i <= this.center_x ; i += 0.1) { 61 var pos = this._pointCoordinate(i); 62 _drawPoint(pos[0].x, pos[0].y); 63 _drawPoint(pos[1].x, pos[1].y); 64 } 65 }, 66 _init: function () { 67 var x1 = this.center_x - this.width / 2, y1 = this.center_y - this.height; 68 var x2 = this.center_x, y2 = this.center_y; 69 var x3 = this.center_x + this.width / 2, y3 = this.center_y - this.height; 70 var b = ((y1 - y2) * (x2 * x2 - x3 * x3) - (y2 - y3) * (x1 * x1 - x2 * x2)) / ((x1 - x2) * (x2 * x2 - x3 * x3) - (x2 - x3) * (x1 * x1 - x2 * x2)); 71 var a = this.a = (y1 - y2 - b * x1 + b * x2) / (x1 * x1 - x2 * x2); 72 var c = y3 - a * x3 * x3 - b * x3; 73 var k = this.k = -b / (2 * a), h = this.h = (4 * a * c - b * b) / (4 * a); 74 }, 75 _pointCoordinate: function (x) { 76 var y = this.a * (x - this.k) * (x - this.k) + this.h; 77 return [{ x: x, y: y }, { 78 x: this.center_x + Math.abs(this.center_x - x), y: y 79 }]; 80 }, 81 _randomCircle: function () { 82 var count = 1000; 83 while (count > 0) { 84 var x = this.center_x - this.width / 2 + Math.random() * this.width; 85 var y = this.center_y - Math.random() * this.height; 86 var radius = 3; 87 if (this.CheckTheBoundary(x - radius, y) && this.CheckTheBoundary(x + radius, y) 88 && this.CheckTheBoundary(x, y - radius) && this.CheckTheBoundary(x, y + radius) 89 && this.CheckTheCircle(x, y, radius) 90 ) { 91 var c = new Circle({ center_x: x, center_y: y, radius: radius }); 92 c.draw(); 93 this.CircleList.push(c); 94 count--; 95 } 96 } 97 } 98 , 99 move: function () { 100 var speed = 5; 101 for (var i = 0; i < this.CircleList.length; i++) { 102 var c = this.CircleList[i]; 103 var x = this.center_x - this.width / 2 + Math.random() * this.width; 104 var y = this.center_y - Math.random() * this.height; 105 var radius = c.radius; 106 if (this.CheckTheBoundary(x - radius, y) && this.CheckTheBoundary(x + radius, y) 107 && this.CheckTheBoundary(x, y - radius) && this.CheckTheBoundary(x, y + radius) 108 && this.CheckTheCircle(x, y, radius) 109 ) { 110 c.center_y = y; 111 c.center_x = x; 112 console.log(c.center_y); 113 c.draw(); 114 } 115 } 116 }, 117 CheckTheBoundary: function (x, y) { 118 if (y < (this.center_y - this.height)) return false; 119 if (x < 0 || y < 0) return false; 120 if (y > this.center_y) return false; 121 var x1 = Math.sqrt((y - this.h) / this.a) + this.k, x2 = this.k - Math.sqrt((y - this.h) / this.a); 122 var maxx = Math.max(x1, x2); 123 var minx = Math.min(x1, x2); 124 //if (isNaN(maxx) || isNaN(minx)) return false; 125 if (x < minx || x > maxx) { 126 return false; 127 } 128 return true; 129 }, 130 CheckTheCircle: function (x, y, r) { 131 for (var i = 0; i < this.CircleList.length; i++) { 132 var g = Math.sqrt((x - this.CircleList[i].center_x) * (x - this.CircleList[i].center_x) 133 + (y - this.CircleList[i].center_y) * (y - this.CircleList[i].center_y)) 134 if (g < (r + this.CircleList[i].radius)) 135 return false; 136 } 137 return true; 138 } 139 }; 140 var h = new Hyperbola({ center_x: 700, center_y: 600, 800, height: 400 }); 141 h.draw(); 142 h._randomCircle(); 143 //setInterval(function () { 144 // h.move(); 145 //}, 1000); 146 </script> 147 </body> 148 </html>
效果：
