先看效果图：  左侧绿色线条和右侧蓝色线条是反射光线的法线，用来校正每条光线发射正确…… 下图是去掉法线的效果：  ``  改变颜色的目的，主要是为下一步做“频数”统计做准备； 即准备下一步的工作：即下一步需要统计每个点的光照频数。 主要思路和部分代码 （全部代码已经超出kancloud的允许长度） ``` //参数注释 ： 01hdc, 2:tt光线总长，3:入射弧度(非角度), 4(当前）光线入口x坐标x01；5当前光线入口Y坐标Y01; //调用例子：digui01andDrawlight(hdc, tt, 125, 190, 200); ////int digui01DrawLine01light(HDC hdc, long long tt, int rsjiaodu, int x01, int y01) int digui01Draw02Circle02light(HDC hdc, int whichCircle, long long tt, double rsHu01du01, int x01, int y01) //int digui01Draw02Circle02light(HDC hdc, int whichCircle, long long tt, double rsHu01du01, int rsjiaodu, int x01, int y01) {//int digui01andDrawlight112110 diguiAllTimes1++; printf_s("\r\nDiGuiTimes:%lld", diguiAllTimes1); // cout << "diguiAllTimes1:" << diguiAllTimes1 << endl; // printf_s("run112110Here!"); // cout << "run112110Here!" << endl; if (tt <= 1) { cout << "[tt=1?" << tt << "]" << endl; return 1; } // double rsHudu01 = ((double)rsjiaodu * 1000.0 / 180.0 / 1000.0 / 10000.0) * PI18 / 10000000000000;// 0; // double rsHudu01 = (double)rsjiaodu *PId / 180; //角度废弃 cout << "入射01弧度:" << rsHu01du01;// << endl; cout << "{入射01角度度:" << rsHu01du01*180/PId<<"}"<<endl; // rsHudu01 = (double)rsjiaodu*3.1415926 / 180.0; printf_s("_rsHu01du01:=%f", rsHu01du01); cout << endl; // cout << "rsHudu01:=" << rsHudu01 << endl; long lightDuanlen01 = 0;//当前光线 线段长度 // for (long long ii = 0; ii < tt; ++ii) {//for1110 ++lightDuanlen01; double danweiX01 = cos(rsHu01du01); double danweiY01 = sin(rsHu01du01); double yuanShiX001 = (double)lightDuanlen01*danweiX01; double yuanShiY001 = (double)lightDuanlen01*danweiY01; // int zhenShiX0001 = (double)yuanShiX001 + x01; int zhenShiY0001 = (double)yuanShiY001 + y01; //根据真实 实际坐标，描点成线--… SetPixel(hdc, zhenShiX0001, zhenShiY0001, RGB(0, 0, 200)); //亮蓝 //判断： // int C1s_rightTimes = 0; // int C2s_leftTimes = 0; //判断真实点的轴距 //判断 是否 撞过 C1 圆1： //真实轴距离 long long zhenshiZhouJvliToC1XY01 = zhenShiX0001 * zhenShiX0001 + (zhenShiY0001-200) * (zhenShiY0001-200); //zhenShiX0001>=200 一定跑出了 圆1,所以是废话(多重保险…… //2号圆的左侧弧: long long zhenshiZhouJvliToC2xy02 = (300 - zhenShiX0001) * (300 - zhenShiX0001) + (zhenShiY0001 - 200) * (zhenShiY0001 - 200); if ((/*3*/zhenshiZhouJvliToC1XY01 >= 200 * 200 /*3*/) && (/*3*/zhenshiZhouJvliToC2xy02 >= (200 * 200) /*3*/)) { return 0; } ////注意这里是撞 左侧大圆(1号圆)的右侧弧! if /*1*/ ( (/*2*/ 1==whichCircle/*2*/) && (/*2*/ (/*3*/zhenshiZhouJvliToC1XY01>= 200*200 /*3*/) || ( zhenShiX0001 >= 200 ) /*2*/) )/*1*/ //if (/*1*/ 1 == whichCircle && zhenShiX0001 >= 200 /*1*/) {//if11a10 ++C1s_rightTimes; cout << "C1s_rightTimes:" << C1s_rightTimes << endl; long long tt1new01 = tt - ii; //算法线: double faXian1Hudu01 = PId;// -0.1; //法线弧度初始设置为PI=π3.1415926... // faXian1Hudu01 = atan((double)zhenShiY0001-200) / (zhenShiX0001 ); // faXian1Hudu01 = PId + asin((double)(200.0-zhenShiY0001 ) / (200)); //OK1 faXian1Hudu01 = atan(((double) zhenShiY0001-200) / (zhenShiX0001) ); //测试这个圆心的比率就是 (法线的）角度 if (faXian1Hudu01 < (-1 * PId)) { faXian1Hudu01 += PId; } cout << "[撞圆1的法线角(弧度:" << faXian1Hudu01 << "]"; // //画辅助线-法线 int x01x1 = zhenShiX0001; int y01y1 = zhenShiY0001; int x02x2 = -200 * cos((double)faXian1Hudu01)+zhenShiX0001; int y02y2 = (200 * sin( -1*(double)faXian1Hudu01)+zhenShiY0001); MoveToEx(hdc, zhenShiX0001, zhenShiY0001, NULL); HPEN hPen; hPen = CreatePen(PS_SOLID, 1, RGB(0,255, 0)); // 创建一个亮绿色的法线 SelectObject(hdc, hPen); // LineTo(hdc, x02x2, y02y2); //画法线 double rusheHudu_faxianhudu = rsHu01du01 - faXian1Hudu01; rusheHudu_faxianhudu = faXian1Hudu01-rsHu01du01; cout << "[rusheHudu_faxianhudu:" << rusheHudu_faxianhudu << "]" << endl; double rsNewHudu01 = faXian1Hudu01;// +little_cita; //faXian1Hudu01; rsNewHudu01 = PId+ rusheHudu_faxianhudu + faXian1Hudu01; // if ((-1.0*PId / 2) < rsNewHudu01 && rsNewHudu01<0 ) rsNewHudu01 = PId - rsNewHudu01; // if ((PId ) < rsNewHudu01 && rsNewHudu01 < PId*2) rsNewHudu01 = rsNewHudu01-PId; //PId - faXian1Hudu01; //PId-faXian1Hudu01;//这是 正确方向的法线 向量； //BigA2 - rsHuDu_BuJiao + 3.0/2*PId; //(PId+faXian1Hudu01)-3.0/4*Pid; // littleCeta; //3.0/4*PId+2*faXian1Hudu01 - rsHu01du01; // double rsNewHudu01 = faXian1Hudu01 + PId; //faXian1Hudu01; // PId - faXian1Hudu01; //注意这里是撞 左侧大圆(1号圆)的右侧弧! // int rsNewJiao1du = ceil(rsNewHudu01 * 180 / PId); // if (rsNewJiao1du < 0) rsNewJiao1du += 360; // if (rsNewJiao1du > 360) rsNewJiao1du -= 360; lightDuanlen01 = 0;// 1; if (diguiAllTimes1 < 1900) {//if diguiAllTimes1 < 1900 //判断是否和第一个圆相撞，则切换到 第2号圆////切换 去第 1号圆的判断(和Draw digui01Draw02Circle02light(hdc, 2, (long long)tt1new01, rsNewHudu01, zhenShiX0001, zhenShiY0001); //digui01DrawLine01light(hdc, tt1new01, rsNewJiao1du, zhenShiX0001, zhenShiY0001); }//if diguiAllTimes1 < 1950//3000//1900 else { return 2; } if (C1s_rightTimes > 2) return 1; system("pause"); }//if11a10 //根据真实 实际坐标，描点成线--… SetPixel(hdc, zhenShiX0001, zhenShiY0001, RGB(0, 200, 0)); //亮绿 //判断 是否 撞过 C2 圆2： //真实轴距离 //2号圆的左侧弧: //long long zhenshiZhouJvliToC2xy02 = (300-zhenShiX0001) * (300-zhenShiX0001) + (zhenShiY0001-200) * (zhenShiY0001-200); if /*1*/ ( (/*2*/2 == whichCircle/*2*/) && (/*2*/ (/*3*/zhenshiZhouJvliToC2xy02 >= 200 * 200 /*3*/) || ( zhenShiX0001 <= 100 ) /*2*/) )/*1*/ {//if11a10 //if (/*1*/ 2 == whichCircle && zhenShiX0001 <= 100 /*1*/) {//if11a10 ++C2s_leftTimes; cout << "C2s_leftTimes:" << C2s_leftTimes << endl; long long tt1new01 = tt - ii; //算法线: double faXian1Hudu01 = 0; // (double)-PId; //初始法线弧度为0!法线弧度为 // faXian1Hudu01 = atan((double)zhenShiY0001-200.0) / (300.0-zhenShiX0001 ); faXian1Hudu01 = asin( ((double)zhenShiY0001 - 200.0) / 200 ); cout << "圆2号左侧faXian1Hudu01:" << faXian1Hudu01 << endl; // //画辅助线-法线 int x01x1 = zhenShiX0001; int y01y1 = zhenShiY0001; int x02x2 = 200 * cos((double)faXian1Hudu01) + zhenShiX0001; int y02y2 = (200 * sin(-1 * (double)faXian1Hudu01) + zhenShiY0001); MoveToEx(hdc, zhenShiX0001, zhenShiY0001, NULL); HPEN hPen; hPen = CreatePen(PS_SOLID, 1, RGB(0, 0,128)); // 创建一个蓝色的法线 SelectObject(hdc, hPen); // LineTo(hdc, x02x2, y02y2); //画法线 double rusheHudu_faxianhudu = rsHu01du01 - faXian1Hudu01; rusheHudu_faxianhudu = faXian1Hudu01 - rsHu01du01; cout << "[rusheHudu_faxianhudu:" << rusheHudu_faxianhudu << "]" << endl; // // double rsNewHudu01 = -(double)faXian1Hudu01;// -rsHu01du01 + PId; // double rsNewHudu01 = -(double)faXian1Hudu01;// +(PId - rsHu01du01); // -rsHu01du01 + PId; cout << "撞圆2时的入射角弧度:" << rsHu01du01<<endl; double rsNewHudu01 = -(double)faXian1Hudu01;// +getRs1Hudu_andFaxianJiajiao(faXian1Hudu01, rsHu01du01); // double rsNewHudu01 = PId-(rsHu01du01 -2 * faXian1Hudu01); rsNewHudu01 = -( faXian1Hudu01 - (PId - rsHu01du01 - faXian1Hudu01)); //OK了 //;// +getHudu1bound180rad01(rsHu01du01) - faXian1Hudu01;//;;// -getHudu1bound180rad01(rsHu01du01);// +(PId - rsHu01du01); // -rsHu01du01 + PId; int rsNewJiao1du = 0;//faXian1Hudu01;//废弃 //ceil( (double)150 * PId / 180); ////rsNewHudu01 * 180 / PId; // if (rsNewJiao1du < 0) rsNewJiao1du += 360; // if (rsNewJiao1du > 360) rsNewJiao1du -= 360; lightDuanlen01 = 0;// 1; if (diguiAllTimes1 < 1900) {//if diguiAllTimes1 < 1900 lightDuanlen01 = 1; //切去第 1号圆的判断(和Draw cout << "[22:rsNewHudu01" << rsNewHudu01 << "]" << endl; //rsNewJiao1du废弃 digui01Draw02Circle02light(hdc, 1, tt1new01, rsNewHudu01, zhenShiX0001, zhenShiY0001); //digui01DrawLine01light(hdc, 1, tt1new01, rsNewHudu01, rsNewJiao1du, zhenShiX0001, zhenShiY0001); }//if diguiAllTimes1 < 1950 if (C2s_leftTimes > 2) return 1; system("pause"); }//if11a10 //根据真实 实际坐标，描点成线--… SetPixel(hdc, zhenShiX0001, zhenShiY0001, getColor1RGB1(diguiAllTimes1 % 7)); //RGB(200, 0, 0)); //亮红 }//for1110 // return 1; }//int digui01Draw02Circle02light // ``` 期间还试用了一些其它语言完成，当然效率比c++还是差一些； 下次右时间还可以优化，提高效率。改进方向包括： 1、异步产生数据，最后同意绘图显示； 2、用空间换时间 3、不再迭代…… 迭代和递归的优点当然是程序代码清晰易懂、易调试、易修改。 不用迭代，用存储空间（数组或链表等）存储、绘制数据……效率会更高、更好些…… whatever... C++在我的 macbookpro2011(I7cpu，8G内存)上面跑已经速度足够(快)了。