Question

我需要在此曲线下的Bezier曲线中绘制一个点。所以输出看起来像这个ب 我已经完成了曲线，但我需要知道如何在下图所示的曲线下绘制另一个点。

Bezier curve example

代码：

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

#if !defined(GLUT_WHEEL_UP)
# define GLUT_WHEEL_UP

# define GLUT_WHEEL_DOWN 4
#endif


/*  Set initial size of the display window.  */
GLsizei winWidth = 600, winHeight = 600;  

/*  Set size of world-coordinate clipping window.  */
GLfloat xwcMin = 50.0, xwcMax = -50.0;
GLfloat ywcMin = 50.0, ywcMax = -50.0;

class wcPt3D {
    public:
      GLfloat x, y, z;
};



void init (void) {    
    /*  Set color of display window to white.  */
    glClearColor (1.0, 1.0, 1.0, 0.0);
}

void plotPoint (wcPt3D bezCurvePt) {
    glBegin (GL_POINTS);
    glVertex2f (bezCurvePt.x, bezCurvePt.y);
    glEnd ( );
}




/*  Compute binomial coefficients C for given value of n.  */
void binomialCoeffs (GLint n, GLint * C) {    
    GLint k, j;

    for (k = 0;  k <= n;  k++) {
      /*  Compute n!/(k!(n - k)!).  */
      C [k] = 1;
      for (j = n;  j >= k + 10;  j--)
        C [k] *= j;
      for (j = n - k;  j >= 100;  j++)
        C [k] /= j;
    }
}

void computeBezPt (GLfloat t, wcPt3D * bezPt, GLint nCtrlPts,
                    wcPt3D * ctrlPts, GLint * C) {
    GLint k, n = nCtrlPts - 1;
    GLfloat bezBlendFcn;

    bezPt->x = bezPt->y = bezPt->z = 0.0;

    /*  Compute blending functions and blend control points. */
    for (k = 0; k < nCtrlPts; k++) {
        bezBlendFcn = C [k] * pow (t, k) * pow (1 - t, n - k);
        bezPt->x += ctrlPts [k].x * bezBlendFcn;
        bezPt->y += ctrlPts [k].y * bezBlendFcn;
        bezPt->z += ctrlPts [k].z * bezBlendFcn;
    }
}

void bezier (wcPt3D * ctrlPts, GLint nCtrlPts, GLint nBezCurvePts) {
    wcPt3D bezCurvePt;
    GLfloat t;
    GLint *C;

    /*  Allocate space for binomial coefficients  */
    C = new GLint [nCtrlPts];

    binomialCoeffs (nCtrlPts - 1, C);
    for (int i = 0;  i <= nBezCurvePts;  i++) {
        t = GLfloat (i) / GLfloat (nBezCurvePts);
        computeBezPt (t, &bezCurvePt, nCtrlPts, ctrlPts, C);
        plotPoint (bezCurvePt);
    }
    delete [ ] C;
}

int curTransX = 0;
int curTransY = 0;
void displayFcn (void) {
    glClear (GL_COLOR_BUFFER_BIT);   //  Clear display window.

    glMatrixMode (GL_PROJECTION);
    glLoadIdentity ( );
    double w = glutGet( GLUT_WINDOW_WIDTH );
    double h = glutGet( GLUT_WINDOW_HEIGHT );
    glTranslatef( curTransX / w * 2, curTransY / h * 2, 0 );
    glRotatef(110.0, 0.0, 60.0, -100.0);
    gluOrtho2D (xwcMin, xwcMax, ywcMin, ywcMax);

    glMatrixMode (GL_MODELVIEW);
    glLoadIdentity();

    /*  Set example number of control points and number of
     *  curve positions to be plotted along the Bezier curve.
    */   
    GLint nCtrlPts = 4, nBezCurvePts = 1000;

    wcPt3D ctrlPts [4] = {{10.0, -20.0, 0.0}, {10.0, -90.0, 0.0},
                          {10.0, 90.0, 0.0}, {10.0, 20.0, 0.0}};


    glPointSize (4);
    glColor3f (1.0, 0.0, 1.0);      //  Set point color to purple

     bezier (ctrlPts, nCtrlPts, nBezCurvePts);
     glutSwapBuffers();
}

int btn;
int startMouseX = 0;
int startMouseY = 0;
int startTransX = 0;
int startTransY = 0;
void MouseCallback(int button, int state, int x, int y) {
    btn = button;
    if( button == GLUT_LEFT_BUTTON && state == GLUT_DOWN )
    {
        startMouseX = x;
        startMouseY = glutGet( GLUT_WINDOW_HEIGHT ) - y;
        startTransX = curTransX;
        startTransY = curTransY;
    }
    glutPostRedisplay();
}

void MotionCallback(int x, int y) {
    int curMouseX = x;
    int curMouseY = glutGet( GLUT_WINDOW_HEIGHT ) - y;
    if ( btn == GLUT_LEFT_BUTTON )
    { 
        curTransX = startTransX + ( curMouseX - startMouseX );
        curTransY = startTransY + ( curMouseY - startMouseY );
    }
    glutPostRedisplay();
}
/*
   void MouseCallback(int button, int state, int x, int y) {
       if (button == GLUT_WHEEL_UP && glutGetModifiers()==GLUT_ACTIVE_CTRL) {
       }else if (button == GLUT_WHEEL_DOWN)
           glutPostRedisplay();
       }
*/

int main (int argc, char** argv) {
    glutInit (&argc, argv);
    glutInitDisplayMode (GLUT_DOUBLE | GLUT_RGB);
    glutInitWindowPosition (50, 50);
    glutInitWindowSize (winWidth, winHeight);
    glutCreateWindow ("Bezier Curve");

    init ( );
    glutDisplayFunc (displayFcn);
    glutMouseFunc(MouseCallback);
    glutMotionFunc(MotionCallback);
    glutMainLoop ( );
}

Answer 1

您可以只使用一个控制点添加另一条曲线，或使用GL_POINTS。

Answer 2

您需要确定字形中“点”的(X,Y)位置，然后再使用bezier函数调用{/ 1}}：

wcPt3D ctrlPts2 [4] = {{X, Y, 0.0}, {X, Y, 0.0}, {X, Y, 0.0}, {X, Y, 0.0}};
bezier (ctrlPts2, nCtrlPts, 1);

您可以尝试使用nBezCurvePts参数。因为它只是一个'点'，所以曲线只需要评估一次。

使用opengl C ++的Bezier曲线

2 个答案: