实现了一个基于LS（L系统）的二维分形演示程序。

实现这个演示程序的第一步当然是理解LS文法。咋看之下似乎有点难度，其实一点也不难。

举个例子就明白了：

LS文法先定义了绘图规则：

F：以当前方向前进一步，并画线；

f：以当前方向前进一步，不画线；

＋：逆时针旋转角；

－：顺时针旋转角；

[：将海龟当前信息压栈；

]：将“[”时刻的海龟信息出栈。

Koch曲线的LS文法如下：

w：F（初始字母）

a ：60(旋转角度)

P：F → F ＋ F － － F ＋ F（F的替代文法）

根据这一文法生成Koch曲线的步骤（假设迭代两次）：

第一步： 得到迭代两次的文法。

第一次迭代结果：

F ＋ F － － F ＋ F

第二次迭代结果：(第一次迭代得到的结果的每一个F用规则P替换)

F ＋ F － － F ＋ F ＋ F ＋ F － － F ＋ F － － F ＋ F － － F ＋ F ＋ F ＋ F － － F ＋ F

第二步：按照迭代得到的文法绘图。

界面使用GLUI实现，写得比较简单。可以自己根据规则DIY文法，得到各种图形。全部演示程序代码如下：

#include <GL/glui.h>
#include<iostream>
#include<cmath>
#include<string>
#include<stack>
#define PI 3.1415926
#define lsSize 14using namespace std;
/** These are the live variables passed into GLUI ***/
int   wireframe = 0;int   main_window;int curr_string = 0;
int obj_type = 0;
GLfloat startX = 0.0f;
GLfloat startY = 0.0f;
GLUI_Panel  *obj_panel;
GLUI_Panel  *data_panel;
GLUI_Panel  *basic_data_panel;
GLUI_Panel  *tree_panel;
GLUI_RadioGroup  *radio;GLUI_EditText *textF;
GLUI_EditText *textX;
GLUI_EditText *textY;
GLUI_EditText *textS;string diyS;
string diyF;
string diyX;
string diyY;
GLfloat diyAngle;GLfloat  angle = 30.0; //步进角度
GLfloat len = 0.05f; //线段长度
GLint  depth = 4; //递归深度struct L_Sys{string name;string startStr;string replaceF;string replaceX;string replaceY;GLfloat angle;L_Sys(string nname,string nstartStr,string nreplaceF,string nreplaceX,string nreplaceY,GLfloat nangle){name = nname;startStr = nstartStr;replaceF = nreplaceF;replaceX = nreplaceX;replaceY = nreplaceY;angle = nangle;}
};  struct L_Sys ls[] = {L_Sys("Koch curve","F","F-F++F-F","","",60.0),L_Sys("Quadratic Koch IsLand","F+F+F+F","F+F-F-FF+F+F-F","","",90.0f),L_Sys("Dragon Curve","X","F","X+YF+","-FX-Y",90.0f),L_Sys("Gosper hexagonal curve","XF","F","X+YF++YF-FX--FXFX-YF+","-FX+YFYF++YF+FX--FX-Y",60.0),L_Sys("Sierpinski gasket","FXF--FF--FF","FF","--FXF++FXF++FXF--","",60.0f),L_Sys("SIerpinski arrowhead","YF","F","YF+XF+Y","XF-YF-X",60.0f),L_Sys("Hilbert curve","X","F","-YF+XFX+FY-","+XF-YFY-FX+",90.0f),L_Sys("F[+F]F[-F]F","F","F[+F]F[-F]F","","",30.0f),L_Sys("F[+F]F[-F][F]","F","F[+F]F[-F][F]","","",20.0f),L_Sys("FF-[-F+F+F]+[+F-F-F]","F","FF-[-F+F+F]+[+F-F-F]","","",22.5f),L_Sys("F[+X]F[-X]+X","X","FF","F[+X]F[-X]+X","",20.0f),L_Sys("F[+X][-X]FX","X","FF","F[+X][-X]FX","",25.7f),L_Sys("F-[[X]+X]+F[+FX]-X","X","FF","F-[[X]+X]+F[+FX]-X","",22.5f),L_Sys("","","","","",0.0)
};/***************************************** myGlutIdle() ***********/void myGlutIdle( void )
{if ( glutGetWindow() != main_window ) glutSetWindow(main_window);  glutPostRedisplay();
}void control_cb( int control )
{if(control == 5){ls[lsSize-1].angle = diyAngle;ls[lsSize-1].startStr = diyS;ls[lsSize-1].replaceF = diyF;ls[lsSize-1].replaceX = diyX;ls[lsSize-1].replaceY = diyY;curr_string = lsSize-1;}
}/**************************************** myGlutReshape() *************/void drawLine(GLfloat x1,GLfloat y1,GLfloat x2,GLfloat y2){glBegin(GL_LINES);glVertex2f(x1,y1);glVertex2f(x2,y2);glEnd();
}void changeSize(int w, int h) {if(h == 0)h = 1;float ratio = 1.0* w / h;glMatrixMode(GL_PROJECTION);glLoadIdentity();glViewport(0, 0, w, h);gluPerspective(45,ratio,1,1000);gluLookAt(0.0,0.0,5.0, 0.0,0.0,-1.0,0.0f,1.0f,0.0f);glMatrixMode(GL_MODELVIEW);
}/***************************************** myGlutDisplay() *****************/
struct tpoint{GLfloat x;GLfloat y;GLfloat delta;
};void fractal(){string resultStr=ls[curr_string].startStr;GLfloat Delta= PI*(ls[curr_string].angle)/180;//生成角度//第一步 得到推进文法for(int i=0; i<depth;++i){string tmpStr;for(int j=0;j<resultStr.size();++j){if(resultStr[j]=='F'){tmpStr=tmpStr+ls[curr_string].replaceF;}else if(resultStr[j]=='X'){tmpStr=tmpStr+ls[curr_string].replaceX;}else if(resultStr[j]=='Y'){tmpStr=tmpStr+ls[curr_string].replaceY;}else{tmpStr=tmpStr+resultStr[j];}}resultStr = tmpStr;}//解析文法，绘制int k=0;tpoint bef={startX,startY,-PI/2},aft;//前一节点 和 后一节点stack<tpoint> s;while(k<resultStr.size()){switch(resultStr[k]) {case 'F':aft.x=bef.x+len*cos(bef.delta);aft.y=bef.y-len*sin(bef.delta);aft.delta = bef.delta;drawLine(bef.x,bef.y,aft.x,aft.y);bef=aft;break;case 'X':aft.x=bef.x+len*cos(bef.delta);aft.y=bef.y-len*sin(bef.delta);aft.delta = bef.delta;drawLine(bef.x,bef.y,aft.x,aft.y);bef=aft;break;case 'Y':aft.x=bef.x+len*cos(bef.delta);aft.y=bef.y-len*sin(bef.delta);aft.delta = bef.delta;drawLine(bef.x,bef.y,aft.x,aft.y);bef=aft;break;case '+':bef.delta += Delta;break;case '-':bef.delta -= Delta;break;case '[':s.push(bef);break;case ']':bef = s.top();s.pop();break;      default:break;}++k;}
}void renderScene(void) {glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);glColor3f(0.0f,1.0f,0.0f);fractal();glutSwapBuffers();
}/**************************************** main() ********************/int main(int argc, char* argv[])
{/****************************************//*   Initialize GLUT and create window  *//****************************************/glutInit(&argc, argv);glutInitDisplayMode( GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH );glutInitWindowPosition( 100, 100 );glutInitWindowSize( 500, 500 );main_window = glutCreateWindow( "OpenGL Fractal " );glutDisplayFunc( renderScene);glutReshapeFunc( changeSize );  glEnable(GL_DEPTH_TEST);GLUI *glui = GLUI_Master.create_glui( "Fractal" );new GLUI_StaticText( glui, "OpenGL Fractal Control Board" );basic_data_panel = new GLUI_Panel(glui,"basic data"); GLUI_Spinner *spinnerX = new GLUI_Spinner( basic_data_panel, "startX:", &startX);spinnerX->set_float_limits(-2.0, 2.0);spinnerX->set_alignment( GLUI_ALIGN_LEFT );GLUI_Spinner *spinnerY = new GLUI_Spinner( basic_data_panel, "startY:", &startY);spinnerY->set_float_limits(-3.0, 3.0);spinnerY->set_alignment( GLUI_ALIGN_LEFT );GLUI_Spinner *spinnerLen = new GLUI_Spinner( basic_data_panel, "lenth:", &len);spinnerLen->set_float_limits(0.0, 3.0);spinnerLen->set_alignment( GLUI_ALIGN_LEFT );GLUI_Spinner *spinnerDepth = new GLUI_Spinner( basic_data_panel, "depth:", &depth);spinnerDepth->set_int_limits(1, 10);spinnerDepth->set_alignment( GLUI_ALIGN_LEFT );data_panel = new GLUI_Panel(glui,"common curve");GLUI_Listbox *list = new GLUI_Listbox( data_panel, "", &curr_string );for(int i=0; i<7; ++i)list->add_item( i, ls[i].name.c_str());tree_panel = new GLUI_Panel(glui,"2D fractal tree");GLUI_Listbox *treeList = new GLUI_Listbox( tree_panel, "", &curr_string );for(int j=7; j<lsSize; ++j)treeList->add_item( j, ls[j].name.c_str());GLUI_Rollout *roll_diy = new GLUI_Rollout(glui, "DIY", false);GLUI_Panel *DIY_panel = new GLUI_Panel( roll_diy, "LS DIY" );textS = new GLUI_EditText( DIY_panel, "start", diyS, 1, control_cb );textF = new GLUI_EditText( DIY_panel, "F->", diyF, 2, control_cb );textX = new GLUI_EditText( DIY_panel, "X->", diyX, 3, control_cb );textY = new GLUI_EditText( DIY_panel, "Y->", diyY, 4, control_cb );textS->set_w(50);textF->set_w(50);textX->set_w(50);textY->set_w(50);textS->set_alignment( GLUI_ALIGN_LEFT);GLUI_Spinner *spinnerAngle = new GLUI_Spinner( DIY_panel, "angle:", &diyAngle);spinnerAngle->set_float_limits(0.0, 90.0);spinnerAngle->set_alignment( GLUI_ALIGN_LEFT );GLUI_Button *ok = new GLUI_Button(DIY_panel,"OK!!",5,control_cb);glui->set_main_gfx_window( main_window );GLUI_Master.set_glutIdleFunc( myGlutIdle ); new GLUI_Button( glui, "iQuit", 0,(GLUI_Update_CB)exit );glutMainLoop();return EXIT_SUCCESS;
}部分截图：