AS3贝塞尔曲线类

贝塞尔曲线被广泛用于塔防类的游戏,当然一些特殊的缓动效果有些 也用 到这个 , 目前 这个没必要我们担心 , TweenMax 为我们提供了这些功能.

package com.ainy.benz
{
    import flash.geom.Point;
                                   
    public class Bezier{
                                       
        //  =====================================  属性
                                       
        //  对外变量
        private  var p0:Point;                  // 起点
        private  var p1:Point;                  // 控制点
        private  var p2:Point;                  // 终点
        private  var step:uint;                 // 分割份数
                                       
        //  辅助变量
        private  var ax:int;
        private  var ay:int;
        private  var bx:int;
        private  var by:int;
                                       
        private  var A:Number;
        private  var B:Number;
        private  var C:Number;
                                       
        private  var total_length:Number;           // 长度
                                       
        private static var $instance : Bezier;
        public static function instance() : Bezier{
            if(null == $instance){
                $instance = new Bezier();
            }
            return $instance;
        }
        public function Bezier(){
            if($instance != null ){
                throw new Error("Bezier 类被设计成单例了!!!");
            }else{
                $instance = this;
            }
        }
                                       
        //  =====================================  方法
                                       
        //  速度函数
        private  function s (t:Number):Number
        {
            return Math.sqrt(A * t * t + B * t + C);
        }
                                       
        //  长度函数
        private  function L (t:Number):Number
        {
            var temp1:Number = Math.sqrt(C + t * (B + A * t));
            var temp2:Number = (2 * A * t * temp1 + B *(temp1 - Math.sqrt(C)));
            var temp3:Number = Math.log(B + 2 * Math.sqrt(A) * Math.sqrt(C));
            var temp4:Number = Math.log(B + 2 * A * t + 2 * Math.sqrt(A) * temp1);
            var temp5:Number = 2 * Math.sqrt(A) * temp2;
            var temp6:Number = (B * B - 4 * A * C) * (temp3 - temp4);
                                           
            return (temp5 + temp6) / (8 * Math.pow(A, 1.5));
        }
                                       
        //  长度函数反函数，使用牛顿切线法求解
        private  function InvertL (t:Number, l:Number):Number{
            var t1:Number = t;
            var t2:Number;
            do{
                t2 = t1 - (L(t1) - l)/s(t1);
                if (Math.abs(t1-t2) < 0.000001) break;
                t1 = t2;
            }while(true);
            return t2;
        }
                                       
                                       
        //  返回所需总步数
            
        public  function init ($p0:Point, $p1:Point, $p2:Point, $speed:Number):uint
        {
            p0   = $p0;
            p1   = $p1;
            p2   = $p2;
            //step = 30;
                                           
            ax = p0.x - 2 * p1.x + p2.x;
            ay = p0.y - 2 * p1.y + p2.y;
            bx = 2 * p1.x - 2 * p0.x;
            by = 2 * p1.y - 2 * p0.y;
                                           
            A = 4*(ax * ax + ay * ay);
            B = 4*(ax * bx + ay * by);
            C = bx * bx + by * by;
                                           
            //  计算长度
            total_length = L(1);
                                           
            //  计算步数
            step = Math.floor(total_length / $speed);
            if (total_length % $speed > $speed / 2)  step ++;
                                           
            return step;
        }
                                       
        // 根据指定nIndex位置获取锚点：返回坐标和角度
        public  function getAnchorPoint (nIndex:Number):Array
        {
            if (nIndex >= 0 && nIndex <= step)
            {
                var t:Number = nIndex/step;
                //  如果按照线行增长，此时对应的曲线长度
                var l:Number = t*total_length;
                //  根据L函数的反函数，求得l对应的t值
                t = InvertL(t, l);
                                               
                //  根据贝塞尔曲线函数，求得取得此时的x,y坐标
                var xx:Number = (1 - t) * (1 - t) * p0.x + 2 * (1 - t) * t * p1.x + t * t * p2.x;
                var yy:Number = (1 - t) * (1 - t) * p0.y + 2 * (1 - t) * t * p1.y + t * t * p2.y;
                                               
                //  获取切线
                var Q0:Point = new Point((1 - t) * p0.x + t * p1.x, (1 - t) * p0.y + t * p1.y);
                var Q1:Point = new Point((1 - t) * p1.x + t * p2.x, (1 - t) * p1.y + t * p2.y);
                                               
                //  计算角度
                var dx:Number = Q1.x - Q0.x;
                var dy:Number = Q1.y - Q0.y;
                var radians:Number = Math.atan2(dy, dx);
                var degrees:Number = radians * 180 / Math.PI;
                                               
                return new Array(xx, yy, degrees);
            }
            else
            {
                return [];
            }
        }
    }
}

应用:

steps = Bezier.instance().init(startPoint,controlPoint,endPoint,8);
            var tmpArr:Array = Bezier.instance().getAnchorPoint(crtStep);
            arrow.x =  tmpArr[0];
            arrow.y =  tmpArr[1];
            arrow.rotation =  tmpArr[2];
            this.crtStep++;
            if(crtStep>steps){
                crtStep=0;
                if(Math.random()>0.5){
                    tower.shooterLeft.GotoAndPlay(2);
                }else{
                    tower.shooterRight.gotoAndPlay(2);
                }
            }

Http://blog.sqstudio.com/as3/algorithm/768.html#codesyntax_2