this code draws bezier curves properly when the window is used on its original size (640 x 480) but renders the control points incorrectly when its resized.

on the click mouse function there is:

```
   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);

```

I don't understand how the coordinate system is being handled. 

Why using the SCREEN\_HEIGHT conversion works on 640x480 but not in other window sizes? How can it be made universal? 

On my own apps, I had been working without glutOrtho2d and just using a calculation for each X,Y but I have read this approach is better. I'd appreciate a detailed explanation to it. 

**MODIFIED CODE:**

```
/* bezier.cpp by detour@metalshell.com
 *
 * Create a bezier curve by defining the three points
 * with your mouse.
 *
 * http://www.metalshell.com/
 *
 */

#include <windows.h>
#include <math.h>
#include <gl/Gl.h>
#include <gl/Glu.h>
#include <gl/glut.h>

// CREEN_WIDTH = 640, SCREEN_HEIGHT=480;

int SCREEN_WIDTH=640;

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;
    void setxy(float x2, float y2) { x = x2; y = y2; }
    const Point & operator=(const Point &rPoint) {
         x = rPoint.x;
         y = rPoint.y;

         return *this;
      }

};

Point abc[3];

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,(float)SCREEN_WIDTH,0.0,(float)SCREEN_HEIGHT);

}

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

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

    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)(y));
    abc[NUMPOINTS].setxy((float)x,(float)(SCREEN_HEIGHT - y));

    // abc[NUMPOINTS] es un arreglo de objetos Point, su contraparte en Casteljau es 

    NUMPOINTS++;

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

    // If 3 points are drawn do the curve.
    if(NUMPOINTS == 3) {
        glColor3f(1.0,1.0,1.0);
        // Draw two legs of the triangle
        drawLine(abc[0], abc[1]);
        drawLine(abc[1], abc[2]);
        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], 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(SCREEN_WIDTH,SCREEN_HEIGHT);
    glutInitWindowPosition(100,150);
    glutCreateWindow("Bezier Curve");

    glutMouseFunc(myMouse);
    glutDisplayFunc(myDisplay);

    myInit();
    glutMainLoop();

    return 0;
}

```

**ORIGINAL CODE:**

```
 /* bezier.cpp by detour@metalshell.com
     *
     * Create a bezier curve by defining the three points
     * with your mouse.
     *
     * http://www.metalshell.com/
     *
     */

    #include <windows.h>
    #include <math.h>
    #include <gl/Gl.h>
    #include <gl/Glu.h>
    #include <gl/glut.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;
    void setxy(float x2, float y2) { x = x2; y = y2; }
    const Point & operator=(const Point &rPoint) {
         x = rPoint.x;
         y = rPoint.y;

         return *this;
      }

};

Point abc[3];

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);
      glVertex2f(p1.x, p1.y);
      glVertex2f(p2.x, p2.y);
    glEnd();
    glFlush();
}

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

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

    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 == 3) {
        glColor3f(1.0,1.0,1.0);
        // Draw two legs of the triangle
        drawLine(abc[0], abc[1]);
        drawLine(abc[1], abc[2]);
        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], 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;
}

```