OpenGL切角算法

考虑了很长时间的割圆术的算法，代码实现中遇到了些问题，主要的问题是不知道细分之后的点的坐标。后来将其抽象为对每一个角进行细分，一共细分四次成圆。不过细分的参数不太容易确定，代码如下

m是细分次数，weightValue是角起点的权重，即此值越大越靠近P1，P2。

 

#include "gl/glut.h"#include "windows.h"#include "math.h"int m = -1;//divided coutGLfloat weightValue = 0.29;//point weight value//Control lineGLfloat v[3][2] = {-3.8,-3.8,3.8,3.8,-3.8,3.8 };//p1,p2,q/*GLfloat v1[3][2] = {-1.2,2.0,1.4,1.7,0.0,-0.2};GLfloat v2[3][2] = {0.0,-0.2,0.0,0.7,1.4,1.7};GLfloat v3[3][2] = {1.4,1.7,-2.2,1.0,0.0,-0.2};GLfloat v4[3][2] = {0.0,-0.7,-1.2,2.0,-2.2,-1.0};*///divided linevoid line(GLfloat* p1,GLfloat* p2){glBegin(GL_LINES);{glColor3f(1.0 ,0.0 ,0.0);glVertex2fv(p1);glVertex2fv(p2);}glEnd();//glFlush();}//original linevoid OriLine(GLfloat *a,GLfloat* b, GLfloat* c){glColor3f(0.0 ,1.0 ,0.0);glBegin(GL_LINES);{glVertex2fv(a);glVertex2fv(c);glVertex2fv(c);glVertex2fv(b);}glEnd();}void chaikin(GLfloat * p1,GLfloat * p2,GLfloat * q,int m){GLfloat q1[2];GLfloat q2[2];GLfloat p3[2];GLfloat p4[2];for (int i = 0;i<2;i++){q1[i] = (weightValue)*p1[i]+(1-weightValue)*q[i];p3[i] = (1-weightValue)*p1[i]+(weightValue)*q[i];q2[i] = (weightValue)*p2[i]+(1-weightValue)*q[i];p4[i] = (1-weightValue)*p2[i]+(weightValue)*q[i];}/*for (int i = 0;i<2;i++){q1[i] = (0.33)*p1[i]+(0.66)*q[i];p3[i] = (0.66)*p1[i]+(0.33)*q[i];q2[i] = (0.33)*p2[i]+(0.66)*q[i];p4[i] = (0.66)*p2[i]+(0.33)*q[i];}*/if (m>0){chaikin(p3,q2,q1,m-1);chaikin(q1,p4,q2,m-1);}else{OriLine(p1,p2,q);line(q1,q2);}}void idle(){if (m<7){Sleep(1000);glutPostRedisplay();m++;}}void display(){glClear(GL_COLOR_BUFFER_BIT);//OriLine(v[0],v[1],v[2]);chaikin(v[0],v[1],v[2],m);//OriLine(v1[0],v1[1],v1[2]);//chaikin(v1[0],v1[1],v1[2],m);//OriLine(v2[0],v2[1],v2[2]);//chaikin(v2[0],v2[1],v2[2],m);//OriLine(v3[0],v3[1],v3[2]);//chaikin(v3[0],v3[1],v3[2],m);//OriLine(v4[0],v4[1],v4[2]);//chaikin(v4[0],v4[1],v4[2],m);glFlush();}void init(){glClearColor(0.0 , 0.0 ,0.0 , 0.0);glColor3f(1.0 ,1.0 ,1.0);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(-4.0 ,4.0 ,-4.0 ,4.0);}void reshape(GLsizei w,GLsizei h){glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(-1.5 ,(GLfloat)(1.5/w) ,-1.5 ,(GLfloat)(1.5/h));glutPostRedisplay();}void main(int argc,char** argv){glutInit(&argc,argv);glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);glutInitWindowSize(500,500);glutInitWindowPosition(100,200);glutCreateWindow("chaikin");glutDisplayFunc(display);glutIdleFunc(idle);//glutReshapeFunc(reshape);init();glutMainLoop();}

这里的P1，P2是角的两个起点，即角P1QP2。

 

经过6次细分最终结果