Q:

opengl dynamic bezier curve has gaps - glEvalCoord1f();

I like to have a program where you can pick ten points and then a bezier curve is calculated for that points. It seems to work pretty perfect, but the shown curve has some gaps. I used GL_LINE_STRIP how is it possible that the points are not connected?
I figured out, that a very small u in glEvalCoord1f(u); makes the gaps smaller.
How is u depending on controlpoints and window propperties in glEvalCoord1f(u); ?

[Edit] Added Screen with thicker lines:

#include <iostream>
#include <stdlib.h>
#include <string>
#include <fstream>
#include <math.h>
#include <time.h> 
#include <GL/glut.h> //added GL prefix for Ubuntu compatibility

#define MAXP 10

GLint nNumPoints = 0;

GLfloat ctrlpoints[10][3];
GLdouble mouseOgl[3] = {0.0,0.0,0.0};
GLint mouseX, mouseY;
bool mousePressed = false;
void GetOGLPos(int x, int y);

void init(void)
{
   glClearColor(1.0, 1.0, 1.0, 0.0);
   glShadeModel(GL_FLAT);
    // Enable the evaluator
    glEnable(GL_MAP1_VERTEX_3);
    glEnable(GL_DEPTH);
}

void display(void)
{
   int i;
   glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
   glColor3f(0.0, 0.0, 1.0);

    if(mousePressed && nNumPoints < MAXP){
        GetOGLPos(mouseX, mouseY);
        std::cout
            << mouseOgl[0] << " # "
            << mouseOgl[1] << " # "
            << mouseOgl[2] << " # "
            << std::endl;   
        nNumPoints++;
        ctrlpoints[nNumPoints-1][0] = mouseOgl[0];
        ctrlpoints[nNumPoints-1][3] = mouseOgl[1];
        ctrlpoints[nNumPoints-1][2] = mouseOgl[2];
    }
    //Curves
    if( nNumPoints == MAXP ){
        glMap1f(GL_MAP1_VERTEX_3,   // Type of data generated
            0.0f,                       // Lower u range
            1.0f,                       // Upper u range
            3,                          // Distance between points in the data 3: ...Z-X-Y-Z...
            nNumPoints,                 // number of control points
            &ctrlpoints[0][0]);         // start point

        glBegin(GL_LINE_STRIP);
            float max = pow(MAXP,4)*2;  //accuracy of pint calulation?
            for (i = 0; i <= max; i++) 
                glEvalCoord1f((GLfloat) (i/max));   //high value to avoid gaps?!?
        glEnd();
    }
    //Controllpoints:
    glPointSize(5.0);
    glColor3f(1.0, 0.0, 0.0);
    glBegin(GL_POINTS);
        for (i = 0; i < nNumPoints; i++) 
            glVertex3fv(&ctrlpoints[i][0]);
    glEnd();
    //Lines
    glColor3f(0.0, 1.0, 0.0);
    glBegin(GL_LINE_STRIP);
        for (i = 0; i < nNumPoints; i++) 
            glVertex3fv(&ctrlpoints[i][0]);
    glEnd();
    if( nNumPoints == MAXP ){nNumPoints = 0;}
   glFlush();
}

void reshape(int w, int h)
{
   glViewport(0, 0, (GLsizei) w, (GLsizei) h);
   glMatrixMode(GL_PROJECTION);
   glLoadIdentity();
   //keep aspect ratio:
   if (w <= h)
      glOrtho(-2.0, 2.0, -2.0*(GLfloat)h/(GLfloat)w, 
               2.0*(GLfloat)h/(GLfloat)w, -2.0, 2.0);
   else
      glOrtho(-2.0*(GLfloat)w/(GLfloat)h, 
               2.0*(GLfloat)w/(GLfloat)h, -2.0, 2.0, -2.0, 2.0);
   glMatrixMode(GL_MODELVIEW);
   glLoadIdentity();
}

//handle click events of the mouse
void myMouse(int button, int state, int x, int y)
{
    //mouse coords to gl coords

    mouseX = x;
    mouseY = y;
    switch (button)
    {
        case GLUT_LEFT_BUTTON:
            if(state == GLUT_UP){   //on release left mouse button
                std::cout << x << " * "<< y << std::endl;
                mousePressed = true;
                glutPostRedisplay(); //redisplay and calculate gl coords
            } else {    
                mousePressed = false;
            } 
        break;
    }
}
// detailed information: 
// http://nehe.gamedev.net/article/using_gluunproject/16013/
void GetOGLPos(int x, int y)
{
    //init vars:
    GLint viewport[4];          
    GLdouble modelview[16];     
    GLdouble projection[16];    
    GLfloat winX, winY, winZ;   
    GLdouble posX, posY, posZ;
    //get gl specs
    glGetDoublev( GL_MODELVIEW_MATRIX, modelview );     //get Modelmatrix   
    glGetDoublev( GL_PROJECTION_MATRIX, projection );   //get projection matrix
    glGetIntegerv( GL_VIEWPORT, viewport );             //get viewport values
    //calculate the gl mouseposition
    winX = (float)x;
    winY = (float)viewport[3] - (float)y;
    glReadPixels( x, int(winY), 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ );

    gluUnProject( winX, winY, winZ, modelview, projection, viewport, &posX, &posY, &posZ);
    mouseOgl[0] = posX;
    mouseOgl[1] = posY;
    mouseOgl[2] = posZ;
}

int main(int argc, char** argv)
{
   glutInit(&argc, argv);
   glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);
   glutInitWindowSize (600, 600);
   glutInitWindowPosition (100, 100);
   glutCreateWindow (argv[0]);
   init ();
   glutDisplayFunc(display);
   glutReshapeFunc(reshape);
   glutMouseFunc(myMouse);
   glutMainLoop();
   return 0;
}

A:

Try zeroing out your control point Z coords:
#include <GL/glut.h>
#include <cmath>

const unsigned int MAXP = 10;

GLint nNumPoints = 0;

GLfloat ctrlpoints[10][3];
GLdouble mouseOgl[3] = {0.0,0.0,0.0};
GLint mouseX, mouseY;
bool mousePressed = false;
void GetOGLPos(int x, int y);

void display(void)
{
    glClearColor(1.0, 1.0, 1.0, 0.0);
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    int w = glutGet( GLUT_WINDOW_WIDTH );
    int h = glutGet( GLUT_WINDOW_HEIGHT );
    glViewport(0, 0, w, h);

    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    double ar = w / (double)h;
    glOrtho(-2.0*ar, 2.0*ar, -2.0, 2.0, -2.0, 2.0);

    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();

    if(mousePressed && nNumPoints < MAXP)
    {
        GetOGLPos(mouseX, mouseY);
        nNumPoints++;
        ctrlpoints[nNumPoints-1][0] = mouseOgl[0];
        ctrlpoints[nNumPoints-1][1] = mouseOgl[1];
        // this is where the magic happens:
        ctrlpoints[nNumPoints-1][2] = 0;
    }

    //Curves
    glColor3f(0.0, 0.0, 1.0);
    if( nNumPoints == MAXP )
    {
        glMap1f(GL_MAP1_VERTEX_3,   // Type of data generated
            0.0f,                       // Lower u range
            1.0f,                       // Upper u range
            3,                          // Distance between points in the data 3: ...Z-X-Y-Z...
            nNumPoints,                 // number of control points
            &ctrlpoints[0][0]);         // start point

        glBegin(GL_LINE_STRIP);
        float max = pow(MAXP,4.0)*2;  //accuracy of pint calulation?
        for (int i = 0; i <= max; i++) 
            glEvalCoord1f((GLfloat) (i/max));   //high value to avoid gaps?!?
        glEnd();
    }

    //Controllpoints:
    glPointSize(5.0);
    glColor3f(1.0, 0.0, 0.0);
    glBegin(GL_POINTS);
    for (int i = 0; i < nNumPoints; i++) 
        glVertex3fv(&ctrlpoints[i][0]);
    glEnd();
    //Lines
    glColor3f(0.0, 1.0, 0.0);
    glBegin(GL_LINE_STRIP);
    for (int i = 0; i < nNumPoints; i++) 
        glVertex3fv(&ctrlpoints[i][0]);
    glEnd();
    if( nNumPoints == MAXP ){nNumPoints = 0;}
    glFlush();
}

//handle click events of the mouse
void myMouse(int button, int state, int x, int y)
{
    //mouse coords to gl coords

    mouseX = x;
    mouseY = y;
    switch (button)
    {
    case GLUT_LEFT_BUTTON:
        if(state == GLUT_UP){   //on release left mouse button
            mousePressed = true;
            glutPostRedisplay(); //redisplay and calculate gl coords
        } else {    
            mousePressed = false;
        } 
        break;
    }
}

// detailed information: 
// http://nehe.gamedev.net/article/using_gluunproject/16013/
void GetOGLPos(int x, int y)
{
    //init vars:
    GLint viewport[4];          
    GLdouble modelview[16];     
    GLdouble projection[16];    
    GLfloat winX, winY, winZ;   
    GLdouble posX, posY, posZ;
    //get gl specs
    glGetDoublev( GL_MODELVIEW_MATRIX, modelview );     //get Modelmatrix   
    glGetDoublev( GL_PROJECTION_MATRIX, projection );   //get projection matrix
    glGetIntegerv( GL_VIEWPORT, viewport );             //get viewport values
    //calculate the gl mouseposition
    winX = (float)x;
    winY = (float)viewport[3] - (float)y;
    glReadPixels( x, int(winY), 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ );

    gluUnProject( winX, winY, winZ, modelview, projection, viewport, &posX, &posY, &posZ);
    mouseOgl[0] = posX;
    mouseOgl[1] = posY;
    mouseOgl[2] = posZ;
}

int main(int argc, char** argv)
{
    glutInit(&argc, argv);
    glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);
    glutInitWindowSize (600, 600);
    glutInitWindowPosition (100, 100);
    glutCreateWindow (argv[0]);

    glShadeModel(GL_FLAT);
    // Enable the evaluator
    glEnable(GL_MAP1_VERTEX_3);
    glEnable(GL_DEPTH);

    glutDisplayFunc(display);
    glutMouseFunc(myMouse);
    glutMainLoop();
    return 0;
}

