使用 c++ opengl 的贝塞尔曲线

Posted 2023-02-14

【中文标题】使用 c++ opengl 的贝塞尔曲线

【英文标题】：Bezier curve using c++ opengl

【发布时间】：2013-07-09 19:53:43

【问题描述】：

我正在使用此代码通过单击一个点来绘制贝塞尔曲线。如果我使用drawBezier 函数中编写的静态公式，它会起作用，并且它会产生正确的曲线。但是如果我用drawBezierGeneralized写的广义公式，最后一点就有问题了。

我做错了什么？

#include <iostream>
#include <stdlib.h>
#include <GL/glut.h>
#include <math.h>

using namespace std;


//Point class for taking the points
class Point 
public:
    float x, y;
    void setxy(float x2, float y2)
    
        x = x2; y = y2;
    
    //operator overloading for '=' sign
    const Point & operator=(const Point &rPoint)
    
        x = rPoint.x;
        y = rPoint.y;
        return *this;
    

;

int factorial(int n)

    if (n<=1)
        return(1);
    else
        n=n*factorial(n-1);
    return n;


float binomial_coff(float n,float k)

    float ans;
    ans = factorial(n) / (factorial(k)*factorial(n-k));
    return ans;





Point abc[20];
int SCREEN_HEIGHT = 500;
int points = 0;
int clicks = 4;


void myInit() 
    glClearColor(1.0,1.0,1.0,0.0);
    glColor3f(0.0,0.0,0.0);
    glPointSize(3);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0.0,640.0,0.0,500.0);



void drawDot(int x, int y) 
    glBegin(GL_POINTS);
     glVertex2i(x,y);
    glEnd();
    glFlush();


void drawLine(Point p1, Point p2) 
    glBegin(GL_LINES);
      glVertex2f(p1.x, p1.y);
      glVertex2f(p2.x, p2.y);
    glEnd();
    glFlush();



//Calculate the bezier point
Point drawBezier(Point PT[], double t) 
    Point P;
    P.x = pow((1 - t), 3) * PT[0].x + 3 * t * pow((1 -t), 2) * PT[1].x + 3 * (1-t) * pow(t, 2)* PT[2].x + pow (t, 3)* PT[3].x;
    P.y = pow((1 - t), 3) * PT[0].y + 3 * t * pow((1 -t), 2) * PT[1].y + 3 * (1-t) * pow(t, 2)* PT[2].y + pow (t, 3)* PT[3].y;

    return P;



//Calculate the bezier point [generalized]
Point drawBezierGeneralized(Point PT[], double t) 
    Point P;
    P.x = 0;P.y=0;
    for(int i=0;i<clicks;i++)
    
        P.x = P.x + binomial_coff((float)clicks,(float)i) * pow(t,(double)i) * pow((1-t),(clicks-i)) * PT[i].x;
        P.y = P.y + binomial_coff((float)clicks,(float)i) * pow(t,(double)i) * pow((1-t),(clicks-i)) * PT[i].y;
    
    //cout<<P.x<<endl<<P.y;
    //cout<<endl<<endl;
    return P;


void myMouse(int button, int state, int x, int y) 
  // If left button was clicked
  if(button == GLUT_LEFT_BUTTON && state == GLUT_DOWN) 
    // Store where mouse was clicked, Y is backwards.
    abc[points].setxy((float)x,(float)(SCREEN_HEIGHT - y));
    points++;

    // Draw the red  dot.
    drawDot(x, SCREEN_HEIGHT - y);


    // If (click-amout) points are drawn do the curve.
    if(points == clicks) 
    
        glColor3f(0.2,1.0,0.0);
        // Drawing the control lines
        for(int k=0;k<clicks-1;k++)
            drawLine(abc[k], abc[k+1]);

        Point p1 = abc[0];
        /* Draw each segment of the curve.Make t increment in smaller amounts for a more detailed curve.*/
        for(double t = 0.0;t <= 1.0; t += 0.02)
        
            Point p2 = drawBezierGeneralized(abc,t);
            cout<<p1.x<<"  ,  "<<p1.y<<endl;
            cout<<p2.x<<"  ,  "<<p2.y<<endl;
            cout<<endl;
            drawLine(p1, p2);
            p1 = p2;
        
        glColor3f(0.0,0.0,0.0);

        points = 0;
    
  



void myDisplay() 
    glClear(GL_COLOR_BUFFER_BIT);
    glFlush();


int main(int argc, char *argv[]) 
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
    glutInitWindowSize(640,500);
    glutInitWindowPosition(100,150);
    glutCreateWindow("Bezier Curve");
    glutMouseFunc(myMouse);
    glutDisplayFunc(myDisplay);
    myInit();
    glutMainLoop();

    return 0;

【问题讨论】：

你能描述最后一点的问题吗？

最后一点总是在左下角，应该是我最后一点的位置

【参考方案1】：

我发现了问题所在。希望这还不算太晚。

另外，感谢您的代码。

Point drawBezierGeneralized(Point PT[], double t) 
    Point P;
    P.x = 0; P.y = 0;   
    for (int i = 0; i<clicks; i++)
    
        P.x = P.x + binomial_coff((float)(clicks - 1), (float)i) * pow(t, (double)i) * pow((1 - t), (clicks - 1 - i)) * PT[i].x;
        P.y = P.y + binomial_coff((float)(clicks - 1), (float)i) * pow(t, (double)i) * pow((1 - t), (clicks - 1 - i)) * PT[i].y;
    
    //cout<<P.x<<endl<<P.y;
    //cout<<endl<<endl;
    return P;

【参考方案2】：

我认为问题在于对原语的调用。

 for(double t = 0.0;t <= 1.0; t += 0.02)
    
        //Point p2 = drawBezierGeneralized(abc,t); -> here is the problem, you call the generalized
         Point p2 = drawBezier(abc,t);
        cout<<p1.x<<"  ,  "<<p1.y<<endl;
        cout<<p2.x<<"  ,  "<<p2.y<<endl;
        cout<<endl;
        drawLine(p1, p2);
        p1 = p2;