Chaikin细分曲线

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继续初步学习细分曲线曲面阶段，先是细分曲线，首先接触的是Chaikin细分，其计算规则非常简单，就是一个割角过程，其最终收敛到2次B样条曲线

索性我做了点为了以后工作方便的事情。改写了一下之前的2次B样条曲线

#include<GL/GLUT.H>    #include <windows.h>        #include <math.h>        #include <gl/GL.h>        GLfloat ctrlPoints[4][2] ={{ -0.8f, 0.1f }, { -0.4f, 0.6f }, { 0.2f, 0.8f }, { 0.7f, 0.2f }};void myDisplay(void){glClear(GL_COLOR_BUFFER_BIT);glPointSize(3);glColor3f(1.0, 0.0, 0.0);for (int i = 0; i < 4; i++){glBegin(GL_POINTS);glVertex2fv(&ctrlPoints[i][0]);glEnd();}glColor3f(0.0, 0.0, 1.0);glBegin(GL_LINE_STRIP);for (int i = 0; i < 4; i++){glVertex2fv(&ctrlPoints[i][0]);}glEnd();GLfloat ps1[11][2];GLfloat ps2[11][2];GLint i = 0;for (double t = 0.0; t <= 1.0; t += 0.1){double a1 = pow((1 - t), 2) / 2;double a2 = (1 + 2 * t - 2 * t*t) / 2;double a3 = t*t / 2;ps1[i][0] = a1*ctrlPoints[0][0] + a2*ctrlPoints[1][0] + a3*ctrlPoints[2][0];ps1[i][1] = a1*ctrlPoints[0][1] + a2*ctrlPoints[1][1] + a3*ctrlPoints[2][1];ps2[i][0] = a1*ctrlPoints[1][0] + a2*ctrlPoints[2][0] + a3*ctrlPoints[3][0];ps2[i][1] = a1*ctrlPoints[1][1] + a2*ctrlPoints[2][1] + a3*ctrlPoints[3][1];i = i + 1;}glColor3f(1.0, 1.0, 0.0);glBegin(GL_LINE_STRIP);for (int i = 0; i < 11; i++){glVertex2fv(ps1[i]);}glEnd();glBegin(GL_LINE_STRIP);for (int i = 0; i < 11; i++){glVertex2fv(ps2[i]);}glEnd();glFlush();}int main(int argc, char *argv[]){glutInit(&argc, argv);glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);glutInitWindowPosition(100, 100);glutInitWindowSize(400, 400);glutCreateWindow("opengl1");glutDisplayFunc(&myDisplay);glutMainLoop();return 0;}

然后是现在的Chaikin细分

<pre name="code" class="cpp">#include<GL/GLUT.H>    #include <windows.h>        #include <math.h>        #include <gl/GL.h>       #define N 4GLfloat ctrlPoints[4][2] ={{ -0.8f, 0.1f }, { -0.4f, 0.6f }, { 0.2f, 0.8f }, { 0.7f, 0.2f }};void myDisplay(void) {glClear(GL_COLOR_BUFFER_BIT);glPointSize(3);glColor3f(1.0, 0.0, 0.0);for (int i = 0; i < 4; i++) {glBegin(GL_POINTS);glVertex2fv(&ctrlPoints[i][0]);glEnd();}glColor3f(0.0, 0.0, 1.0);glBegin(GL_LINE_STRIP);for (int i = 0; i < 4; i++) {glVertex2fv(&ctrlPoints[i][0]);}glEnd();int n1 = N;//表示之前的顶点数int n = 2 * (N - 2) + 2;//表示细分一次的顶点数GLfloat ps2[4][30][2];for (int i = 0; i < 4; i++){ps2[0][i][0] = ctrlPoints[i][0];ps2[0][i][1] = ctrlPoints[i][1];}for (int i = 0; i < 3; i++){ ps2[i + 1][0][0] = ps2[i][0][0];ps2[i + 1][0][1] = ps2[i][0][1];ps2[i+1][n - 1][0] = ps2[i][n1 - 1][0];ps2[i+1][n - 1][1] = ps2[i][n1 - 1][1];//计算中间的点for (int j = n1 - 2; j > 0; j--){ps2[i+1][2 * j - 1][0] = 3 * ps2[i][j][0] / 4 + ps2[i][j - 1][0] / 4;ps2[i+1][2 * j - 1][1] = 3 * ps2[i][j][1] / 4 + ps2[i][j - 1][1] / 4;ps2[i+1][2 * j][0] = 3 * ps2[i][j][0] / 4 + ps2[i][j + 1][0] / 4;ps2[i+1][2 * j][1] = 3 * ps2[i][j][1] / 4 + ps2[i][j + 1][1] / 4;}if (i==0)glColor3f(1.0, 0.0, 1.0);else{if (i==1){glColor3f(0.75, 0.8, 0.3);}else glColor3f(0.5, 0.8, 0.8);}glBegin(GL_LINE_STRIP);for (int w = 0; w < n; w++){glVertex2fv(ps2[i+1][w]);}glEnd(); n1 = n; n = 2 * (n - 2) + 2;}glFlush();}int main(int argc, char *argv[]){glutInit(&argc, argv);glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);glutInitWindowPosition(100, 100);glutInitWindowSize(400, 400);glutCreateWindow("opengl1");glutDisplayFunc(&myDisplay);glutMainLoop();return 0;}

效果如下

附上和上次2次B样条的对比

Chaikin细分和2次B样条Chaikin细分2次B样条我这里专门没画出来第一个点和最后一个点，为的就是看得出来和2次B样条的对比，经过对比发现还是一样的，之后进入曲面细分部分

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