An effective way to deal with predators is to
taste terrible

Concept 9.2 : Effect of Normals on Lighting
===========================================
The top left rendering window should show
you a yellow box, with the window titled
'The Magicbox - IllConceived Normals'
The bottom left rendering window should
show you the same yellow box with the 
window titled 'The Magicbox - Normals 
Corrected'

Clicking the two boxes starts the animation.
Look at the top box carefully. Do you think the 
lighting on the box flaps is correct?  Compare it
to the bottom box.

The reason for this difference is that for
the box on the top the normals have been
incorrectly specified before rendering them.
The bottom box has the normals corrected
for.

The actual pieces of code which render the
flaps for the two boxes is provided below.

The Magicbox - Illconceived Normals
===============================
Press the 'w' key to view the triangles which
make up the top.
glBegin(GL_TRIANGLES);
   /* normals specified incorrectly . i.e. 
    * they are all set for the  positive y 
    * direction even though the top flips open.  
    */
     glNormal3f(0.0, 1.0, 0.0);
     
     /* draw the top rear triangle */
     glVertex3f( 0.0,   Y,   Z);   
     glVertex3f(1.0, 1.0,-1.0);
     glVertex3f( -1.0, 1.0,-1.0);
     
     /* draw the top front triangle*/
     glVertex3f(0, Y, Z1);         
     glVertex3f(-1.0, 1.0, 1.0);
     glVertex3f(1.0, 1.0, 1.0); 
     
     /* draw the top left triangle*/
     glVertex3f(X, Y, 0.0);          
     glVertex3f(-1.0, 1.0, -1.0);
     glVertex3f(-1.0, 1.0, 1.0);
     
     /* draw the top right triangle */
     glVertex3f(X1, Y, 0.0);       
     glVertex3f(1.0, 1.0, 1.0);
     glVertex3f(1.0, 1.0, -1.0);

glEnd();

In the closed condition the normal to the top face
and hence the four rectangles is in deed the positive
Y axis.  
When the top four triangles (the flap of the box) start
to open the normals are also changing.  Our code above
does not account for this and hence the incorrect
lighting.

The Magicbox - Normals Corrected:
=================================
Now lets take a look at the corrected code :

angle = ((float)step/120) * PI;
   Y = 1 + sin(angle);
   Z = -1 + cos(angle);
   Z1= 1 - cos(angle);
   X = -1 + cos(angle);
   X1 = 1 - cos(angle);
   NY = cos(angle);
   NZ = -sin(angle);
   NX= -sin(angle);
   glBegin(GL_TRIANGLES);

     /* draw the top rear triangle */
     glNormal3f(0, NY, NZ);
     glVertex3f( 0.0,   Y,   Z);   
     glVertex3f(1.0, 1.0,-1.0);
     glVertex3f( -1.0, 1.0,-1.0);
     
     /* draw the top front triangle*/
     glNormal3f(0.0,NY, -NZ);
     glVertex3f(0, Y, Z1);         
     glVertex3f(-1.0, 1.0, 1.0);
     glVertex3f(1.0, 1.0, 1.0); 

     /* draw the top left triangle*/     
     glNormal3f(NX, NY, 0.0);
     glVertex3f(X, Y, 0.0);          
     glVertex3f(-1.0, 1.0, -1.0);
     glVertex3f(-1.0, 1.0, 1.0);
     
     /* draw the top right triangle */
     glNormal3f(-NX, NY, 0.0);
     glVertex3f(X1, Y, 0.0);       
     glVertex3f(1.0, 1.0, 1.0);
     glVertex3f(1.0, 1.0, -1.0);

glEnd();

In this case notice how we specify the normals
correctly.  Take for example drawing the top
front flap. In the normal condition this flap
goes from a position of flat to vertical.  In
the flat position the normal vector is the 
+ve Y axis. so far so good.  In the vertical
positon the normal vector is the +ve Z axis.
So through its rotation the normal vector
goes from bein (0,1,0) to (0, 0, 1).  To
accomodate this change we define two
parameters :
NY and NZ which constantly change with the
angle roation. More specifically they are
calculated as follows :

NY = cos(angle)
NZ = -sin(angle)
when the flap is closed and flat angle is
zero giving NY = 1 and NZ = 0
Therefore the Normal vector defined as
(0, NY,-NZ) leads to a vector value of
(0, 1,0)
When the flap is open all the way i.e it
is vertical, the angle is now 90. In this
case NY = 0, and NZ = -1
The normal as specified by (0, NY, -NZ)
now becomes (0, 0, 1) i.e the positive
Z axis, which is what we want.  The inter
mediate normal vectors are similary 
calculated and lighting is achieved properly.
Work through the normal vector calculations
for the other flaps in the box and 
convince yourself on how the whole mechanics
is put together!!