For this paper/pencil/calculator exercise, assume the following:

• There is one positional light, with these properties:
  • Diffuse Intensity (RGB) = (1.0, 0.8, 0.6) ;
    Specular Intensity (RGB) = (0.9, 0.85, 0.2);
    Ambient Intensity (RGB) = (0.6, 0.4, 0.4)
    
    
  • light position (x,y,z) = (4, 12, 2)
    
    
  • eye position (x,y,z) = (-3, 2, 5)
    
    
• There is a global ambient light (RGB) = (0.2, 0.2, 0.2)
  
  
• There is a facet whose color (RGB) will be caculated using the Phong Lighting Model and these facts:
  • a vertex on the facet has coordinates = (0,0,0)
  • the normal vector to the facet at this vertex = <-1, 1, 1>
  • the material of the facet has these properties:
    • material diffuse coefficient (RGB) = (0.8, 0.5, 0.3)
    • material specular coefficient (RGB) = (0.8, 0.5, 0.3)
    • material ambient coefficient (RGB) = (0.8, 0.5, 0.3)
    • material Phong exponent = 57.0

1. What is the vector s from the vertex to the light source?
2. What is the length of vector s ?
3. What is the normalized vector U_s ?
4. What is the vector  v from the vertex to the eye?
5. What is the vector h (the vector halfway between vector s and vector v?
6. What is the length of vector h ?
7. What is the normalized vector U_h?
8. What is the vector  m (the vector normal to the face at the vertex)?
9. What is the length of vector m ?
10. What is the normalized vector U_m ?
    
11. What is the value of Lambert?
    
12. What is the value of I_diffuse (RGB) ?
    
13. What is the value of Phong?
    
14. What is the value of Phong ^f
    
15. What is the value of I_specular (RGB) ?
    
16. What is the value of I_ambient (RGB) ?
    
17. Finally, what is the value of I (RGB) at this vertex?
    
    

Compile and run the program 2spheres_b.cpp.

• Change the materials properties
• Change the light properties (from the default, which is used)
• Change the position of the light

Make sure you understand how the changes affect the spheres.