Mapping coordinates from 3D perspective projection to 2D orthographic projection in OpenGL in C++

Question

I have written a simple openGL program in C++. This program draws a sphere in 3D perspective projection and tries to draw a line joining the center of the sphere to the current cursor position in 2D orthographic projection. Now for drawing the line I can't figure out the coordinate of center of the sphere.

This is my code :

#ifdef __APPLE__
#include <GLUT/glut.h>
#else
#include <GL/glut.h>
#endif

void passive(int,int);
void reshape(int,int);
void init(void);
void display(void);
void camera(void);

int cursorX,cursorY,width,height;

int main (int argc,char **argv) {
    glutInit (&argc,argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_DEPTH | GLUT_RGBA);
    glutInitWindowSize(1364,689);
    glutInitWindowPosition(0,0);
    glutCreateWindow("Sample");
    init();
    glutDisplayFunc(display);
    glutIdleFunc(display);
    glutPassiveMotionFunc(passive);
    glutReshapeFunc(reshape);
    glutMainLoop();
    return 0;
}    

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

    //  Render 3D content
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(60,(GLfloat)width/(GLfloat)height,1.0,100.0);    // create 3D perspective projection matrix
    glMatrixMode(GL_MODELVIEW);
    glPushMatrix();
    camera();
    glTranslatef(-6,-2,0);
    glColor3f(1,0,0);
    glutSolidSphere(5,50,50);
    glPopMatrix();

    // Render 2D content
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0, width,height, 0);                 // create 2D orthographic projection matrix
    glMatrixMode(GL_MODELVIEW);
    glColor3f(1,1,1);
    glBegin(GL_LINES);
        glVertex2f( centreX,centreY );          // coordinate of center of the sphere in orthographic projection
        glVertex2f( cursorX,cursorY );
    glEnd();

    glutSwapBuffers();
}    

void camera(void) {
    glRotatef(0.0,1.0,0.0,0.0);
    glRotatef(0.0,0.0,1.0,0.0);
    glTranslated(0,0,-20);
}    

void init(void) {
    glEnable (GL_DEPTH_TEST);
    glEnable (GL_BLEND);
    glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
    glEnable(GL_COLOR_MATERIAL);
}    

void reshape(int w, int h) {
    width=w; height=h;
}    

void passive(int x1,int y1) {
    cursorX=x1; cursorY=y1;
}

I can,t figure out the values for centreX and centreY. Anyway I can get the correct values to draw the line?

Answer 1

You may be interested in using something like gluProject to go from your object coordinates to the actual (projected) position on screen. Once you have the screen coordinates of the object, it's easy to draw a line from one point to another.

In this case, you'll want to project the centre point of the sphere. For more complex objects I've found that it makes sense to project all of the corners of the object's bounding box and then take the extents of the screenspace position of those corners.

You should get the modelview, viewport and projection matrices before you switch to your orthographic projection (2D mode).

Obviously, in order to go from a screen position (say, where you clicked in the window) to a world position, you'll want to use its companion function, gluUnProject .

Note that the coordinates that come out of gluProject do not necessarily correspond directly to the window position; you might have to flip the "Y" coordinate.

Take a look at this GDSE discussion for some other ideas about how to solve the problem.