As mentioned in class and labs the order of transformations are important. This example illustrates the differences in composing transformations. It also uses a display list (this is given below).

You should implement transformations and observe the difference in ordering them. Add one transformation at a time to observe cumulative effects.

• First the original object:
  
• We apply some transformations:
  • The first transformations are:

      glPushMatrix();  
        glRotatef(30, 0, 0, 1); //30 degrees around z
        glTranslatef(-1.0, -0.5, 0.0);
        glScalef(0.5, 0.5, 0.5);	 
        glCallList( object ); //drawPattern
      glPopMatrix();

    
    Which gives us:
    
    
    
  • Then add:

      glPushMatrix();  
        glRotatef(30, 0, 0, 1);
        glScalef(0.5, 0.5, 0.5);
        glTranslatef(-1.5, -0.5, 0.0);	 
        glCallList( object ); //drawPattern
      glPopMatrix();

    
    Which gives us:
    
• Now we change the order again, putting translate first:
  • The transformations are:

      glPushMatrix();  
        glTranslatef(-1.0, -0.5, 0.0);
        glRotatef(30, 0, 0, 1); //30 degrees around z
        glScalef(0.5, 0.5, 0.5);	 
        glCallList( object ); //drawPattern
      glPopMatrix();
    

    
    Which gives us:
    
  • Then add:

      glPushMatrix();  
        glTranslatef(-1.0, -0.5, 0.0);
        glScalef(0.5, 0.5, 0.5);
        glRotatef(30, 0, 0, 1);
        glCallList( object ); //drawPattern
      glPopMatrix();
        

    
    Which gives us:
    
• Now we change the order again, putting scale first:
  • The transformations are:

      glPushMatrix();  
        glScalef(0.5, 0.5, 0.5);	 
        glTranslatef(-1.0, -0.5, 0.0);
        glRotatef(30, 0, 0, 1); //30 degrees around z
        glCallList( object ); //drawPattern
      glPopMatrix();
    

    
    Which gives us:
    
  • Then add:

      glPushMatrix();  
        glScalef(0.5, 0.5, 0.5);
        glRotatef(30, 0, 0, 1);
        glTranslatef(-1.0, -0.5, 0.0);
        glCallList( object ); //drawPattern
      glPopMatrix();
        

    
    Which gives us:
    
  
  
• Put them all together and we get:
  
• The display list looks like this:

  GLuint GLBox::drawPattern()
  {
  	GLuint list;
  
    	list = glGenLists( 1 );
  
     glNewList( list, GL_COMPILE );
  
  	glPushMatrix();
  
  	 glBegin(GL_LINE_LOOP);
  	   glVertex3f(-1.3, 0.0, 0.0);
  	   glVertex3f(-1.0, -1.0, 0.0);
  	   glVertex3f(0.0, -1.3, 0.0);
  		glVertex3f(1.0, -1.0, 0.0);
  	   glVertex3f(1.3, 0.0, 0.0);
  		glVertex3f(1.0, 1.0, 0.0);
  	   glVertex3f(0.0, 1.3, 0.0);
  		glVertex3f(-1.0, 1.0, 0.0);
  	 glEnd();
  	 //This is where the object is defined and drawn.
  	 GLfloat y_red = 1.0;
  	 GLfloat y_green = 1.0;
  	 GLfloat y_blue = 0.0;
  	 GLfloat x = 0.1;
  	 GLfloat y = 0.0;
  	 GLfloat z = 0.0;
  	 GLfloat rot = 0.0; 
  	 for(int ct = 0; ct < 100; ct++)
  	 {
  		GLfloat mat_Y[] = {y_red, y_green, y_blue};
  		glPushMatrix();
  		glRotatef(rot, 0.0, 0.0, 1.0);
  		glTranslatef(x, y, z);	
  		glBegin(GL_POLYGON);
  	     glNormal3f(0.0, 0.0, -1.0);
  		  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, mat_Y);
  		  glVertex3f(0.0, 0.0, 0.0);
  		  glVertex3f(0.1, 0.1, 0.0);
  		  glVertex3f(0.15, 0.0, 0.0);
  		  glVertex3f(0.1, -0.1, 0.0);
  		glEnd();
  		glPopMatrix();
  		rot += 137.5; //phylotactic pattern
  		x += 0.01;
  		y_green -= 0.01;
  		
  	 }
  	 glFlush();
  	glPopMatrix();
  	
     glEndList();
  		  
     return list;
  }

• The display list is declared in:

  void GLBox::initializeGL()
  {
    object = drawPattern();	
  ...
  }