使用C ++，OpenGL中的De Casteljau算法绘制Bezier曲线

Question

我正在尝试使用de casteljau算法找到生成贝塞尔曲线的方法，用于我的一项任务。我能够使用常规方法生成贝塞尔曲线，但无法使用上述算法开始生成。如果有人可以向我推荐正确的方向或分享您拥有的任何代码，那将是非常有帮助的。我不只是按原样问。我在它上面做了很多工作并自己编写了下面的代码来生成曲线。 我找到了一个确实需要的网络小程序。 （http://www2.mat.dtu.dk/people/J.Gravesen/cagd/decast.html）。建议我如何实现

#include <iostream>
using std::cerr;
using std::endl;
#include <stdlib.h>
//using std::exit;
#include <GL/glut.h> // GLUT stuff, includes OpenGL headers as well 
#include <windows.h>
#include <math.h>
#include <gl/Gl.h>
#include <gl/Glu.h>


int SCREEN_HEIGHT = 480;
// Keep track of times clicked, on 3 clicks draw.
int NUMPOINTS = 0;

// Point class to keep it a little cleaner.
class Point {
public:
    float x, y, z;
    void setxy(float x2, float y2) { x = x2; y = y2; }
    const Point & operator=(const Point &rPoint) {
         x = rPoint.x;
         y = rPoint.y;
         z = rPoint.z;

         return *this;
      }

};

Point abc[4];

void myInit() {
    glClearColor(0.0,0.0,0.0,0.0);
    glColor3f(1.0,0.0,0.0);
    glPointSize(4.0);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0.0,640.0,0.0,480.0);

}

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

void drawLine(Point p1, Point p2) {
    glBegin(GL_LINES);
      glVertex3f(p1.x, p1.y, p1.z);
      glVertex3f(p2.x, p2.y, p2.z);

    glEnd();
    glFlush();
}

// Calculate the next bezier point.
Point drawBezier(Point A, Point B, Point C, Point D, double t) {
    Point P;




    P.x = pow((1 - t), 3) * A.x + 3 * t * pow((1 -t), 2) * B.x + 3 * (1-t) * pow(t, 2)* C.x + pow (t, 3)* D.x;
    P.y = pow((1 - t), 3) * A.y + 3 * t * pow((1 -t), 2) * B.y + 3 * (1-t) * pow(t, 2)* C.y + pow (t, 3)* D.y;
    P.z = pow((1 - t), 3) * A.z + 3 * t * pow((1 -t), 2) * B.z + 3 * (1-t) * pow(t, 2)* C.z + pow (t, 3)* D.z;

    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 the user clicked, note Y is backwards.
    abc[NUMPOINTS].setxy((float)x,(float)(SCREEN_HEIGHT - y));
    NUMPOINTS++;

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

    // If 3 points are drawn do the curve.
    if(NUMPOINTS == 4) {
        glColor3f(1.0,1.0,1.0);
        // Draw two legs of the triangle
        drawLine(abc[0], abc[1]);
        drawLine(abc[1], abc[2]);
        drawLine(abc[2], abc[3]);
        //drawLine(abc[3], abc[4]);
        Point POld = 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 += 0.1) {
            Point P = drawBezier(abc[0], abc[1], abc[2], abc[3],  t);
            drawLine(POld, P);
            POld = P;
        }
        glColor3f(1.0,0.0,0.0);
        NUMPOINTS = 0;
    }
  }
}

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

int main(int argc, char *argv[]) {
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
    glutInitWindowSize(640,480);
    glutInitWindowPosition(100,150);
    glutCreateWindow("Bezier Curve");

    glutMouseFunc(myMouse);
    glutDisplayFunc(myDisplay);

    myInit();
    glutMainLoop();

    return 0;
}

Answer 1

对我有用，有什么问题？

我不会将此作为答案发布，但我无法在评论中发布图片

Answer 2

关注this link，您可以找到交互式JavaScript实现。

请注意点AB如何使用((1-t)*A + t*B)进行计算，并了解其他点（BC，CD，ABC，{{1}最后BCD}同样计算。

您可以拖动ABCD，A，B和C以及点D以查看构造的工作方式，具体取决于参数{{1 }}