计算机图形学8——Bezier curve(贝塞尔曲线)

编程实现贝塞尔曲线绘制

核心代码如下：

void Draw_Bezier(int nctrl, CPoint2D *cp, int m)
// nctrl  --- Number of control points
// cp --- Array of control points
// m  --- Number of subdivision
{
    int i;
    float u,x,y;
    CPoint2D bez;
    int c[nctrl];
    binomialCoeffs(nctrl-1,c);
    glBegin(GL_LINE_STRIP);
    glVertex2f(cp[0].x,cp[0].y);

    for(i=0;i<m;++i)
    {
        u=(float)i/(float)m;
        computerBezPt(u,&bez,nctrl,cp,c);
        glVertex2f(bez.x,bez.y);
    }
    glVertex2f(cp[nctrl-1].x,cp[nctrl-1].y);
    glEnd();
}

完整代码如下：

// ====== Computer Graphics Experiment #7 ======
// |              Bezier curve                 |
// =============================================
//
// Requirement:
// (1) Implement algorithm to draw Bezier curve.
// (2)Implement interactive method to specify
//     Bezier curve control points by mouse clicking.
// (3) Implement display callback function

#include <windows.h>
#include <GL/glut.h>
#include <math.h>
#include <stdio.h>

// 2D point class
class CPoint2D
{
public:
	float x, y;
};

int n_cp; // Number of control points
int ic_cp; // Control point counter
int i_cp; // Index of control point being moved
CPoint2D *control_points; // Coordinates of control points

// Program window size
int pw_width, pw_height;

int running_state;
// 0 --- Setting up control points.
// 1 --- Normal state.
// 2 --- Moving control point.

void binomialCoeffs(int n,int *c)//求二项式系数
{
    int k,j;
    for(k=0;k<=n;k++)
    {
        c[k]=1;
        for(j=n;j>=k+1;j--)
            c[k]*=j;
        for(j=n-k;j>=2;j--)
            c[k]/=j;
    }
}

void computerBezPt(float u,CPoint2D *bezPt,int nctrl,CPoint2D *ctrlPts,int *c)
//比例系数 点坐标  控制点数  控制点坐标 二项式系数
{
    int k,n=nctrl-1;//u的多项式次数比控制点少一个
    float bez;
    bezPt->x=bezPt->y=0.0;
    for(k=0;k<nctrl;k++)
    {
        bez=c[k]*pow(u,k)*pow(1-u,n-k);
        bezPt->x+=ctrlPts[k].x*bez;
        bezPt->y+=ctrlPts[k].y*bez;
    }
}
// Draw Bezier curve
void Draw_Bezier(int nctrl, CPoint2D *cp, int m)
// nctrl  --- Number of control points
// cp --- Array of control points
// m  --- Number of subdivision
{
    int i;
    float u,x,y;
    CPoint2D bez;
    int c[nctrl];
    binomialCoeffs(nctrl-1,c);
    glBegin(GL_LINE_STRIP);
    glVertex2f(cp[0].x,cp[0].y);

    for(i=0;i<m;++i)
    {
        u=(float)i/(float)m;
        computerBezPt(u,&bez,nctrl,cp,c);
        glVertex2f(bez.x,bez.y);
    }
    glVertex2f(cp[nctrl-1].x,cp[nctrl-1].y);
    glEnd();
}

void plot(int x,int y)
{
    glBegin(GL_POLYGON);
    glVertex2f(x+2,y);
    glVertex2f(x,y+2);
    glVertex2f(x,y-2);
    glVertex2f(x-2,y);
    glEnd();
}
void display(void)
{
    glClear (GL_COLOR_BUFFER_BIT);//清缓存
    for(int i=0;i<ic_cp;i++)
    {
        plot(control_points[i].x,control_points[i].y);
    }
    glLineStipple(1,0x0f0f);
    glBegin(GL_LINE_STRIP);
    for(int i=0;i<ic_cp;i++)
    {
        glVertex2f(control_points[i].x,control_points[i].y);
    }
    glEnd();
    glLineStipple(1,0xffff);
    if(ic_cp==n_cp)
    Draw_Bezier(n_cp,control_points,1000);
    glutSwapBuffers();
}

// Mouse callback function
void mouse_func(int button, int state, int x, int y)
{
    float dis;

	if (button==GLUT_LEFT_BUTTON)
	{
		if ((state==GLUT_DOWN)&(running_state==0)&(ic_cp<n_cp))
		{
			control_points[ic_cp].x=x;
			control_points[ic_cp].y=pw_height-y;
			ic_cp++;
			if (ic_cp==n_cp)
				running_state=1;
			glutPostRedisplay();
		}
		else if ((state==GLUT_DOWN)&(running_state==1))
		{
            for (int i=0 ;i<n_cp;i++)
			{
				dis=abs((x-control_points[i].x)*(x-control_points[i].x)+(pw_height-y-control_points[i].y)*(pw_height-y-control_points[i].y));
				if (dis<10)
				{
					i_cp=i;
					running_state=2;
					break;
				}
			}
		}
		else if ((state==GLUT_DOWN)&(running_state==2))
		{
			control_points[i_cp].x=x;
			control_points[i_cp].y=pw_height-y;
			glutPostRedisplay();
		}
		else if ((state==GLUT_UP)&(running_state==2))
		{
			running_state=1;
		}
	}
}
// Mouse motion callback function
void motion_func(int x, int y)
{

	if (running_state==2)
	{
		control_points[i_cp].x=x;
        control_points[i_cp].y=pw_height-y;
        glutPostRedisplay();
	}
}
// Initialization function
void init(void)
{
	glClearColor (0.0, 0.0, 0.0, 0.0);
	glEnable(GL_LINE_STIPPLE);

}

// Reshape callback function
void reshape(int w, int h)
{
	pw_width=w;
	pw_height=h;

	glViewport(0, 0,  w,  h);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluOrtho2D (0.0, w, 0.0, h);
}

// Keyboard callback function
void keyboard(unsigned char key, int x, int y)
{
	switch (key) {
		case 27:
			exit(0);
	}
}

// Main program entrance
int main(int argc, char* argv[])
{
	// Input number of control points
	printf("Number of control points = ");
	scanf("%d", &n_cp);
	if (n_cp<2) return 1;
	control_points=new CPoint2D[n_cp];
	running_state=0;
	ic_cp=0;

	glutInit(&argc, argv);
	glutInitDisplayMode (GLUT_RGB | GLUT_DOUBLE);
	glutInitWindowSize(500, 500);
	glutCreateWindow("Bezier Curve");
	init();
	glutReshapeFunc(reshape);
	glutKeyboardFunc(keyboard);
	glutMouseFunc(mouse_func);
    glutMotionFunc(motion_func);
	glutDisplayFunc(display);
	glutMainLoop();

	delete [] control_points;
	return 0;
}