1. Week 9 - Monday

2.  What did we talk about last time?  BRDFs  Texture mapping and bump mapping in shaders

6.  Fresnel reflectance is an ideal mathematical description of how perfectly smooth materials reflect light  The angle of reflection is the same as the angle of incidence and can be computed:  The transmitted (visible) radiance L t is based on the Fresnel reflectance and the angle of refraction of light into the material:

7.  The angle of refraction into the material is related to the angle of incidence and the refractive indexes of the materials below the interface and above the interface:  We can combine this identity with the previous equation:

9.  Reflectance is obviously dependent on angle  Perpendicular (0°) gives essentially the specular color of the material  Higher angles will become more reflective  The function R F (θ i ) is also dependent on material (and the light color)

10.  Because it's non-linear, Schlick gives an approximation that works for most substances:  We can use a table of R F (0°) values

11.  External reflection needs to be modeled more often than internal reflection  Modeling internal reflection is the same except that the higher optical density can cause total internal reflection

12.  Usually is not as complex as specular light  We can measure a value ρ that gives the ratio between light escaping a surface relative to light entering a surface  ρ is called the scattering albedo  Because of conversation of energy, the more light that is reflected through Fresnel reflection, the less there is to be reflected diffusely  Thus, a simple approximation for diffuse light is

14.  The cause of many lighting effects is microgeometry  The smoother the surface, the tighter (and brighter) the reflections are

15.  Glancing angles can minimize the impacts of surface roughness, making rough surfaces reflective at very high angles  Most surfaces are isotropic (symmetrical) in the way they are rough  Anisotropic surfaces like brushed metal have directional blurring

17.  The book gives a number of BRDF equations  It is also possible to samples materials (from every angle, at every color of light) to measure a BRDF of your own  Once you've got such a model, how do you implement it?

18.  The shader will use the following equation:  The cosine term is found with the dot product  Most BRDFs contain a 1/π term  Many systems pre-divide E L by π  Make sure you don't double divide (or double multiply)  If some value is computed repeatedly, consider putting it in a texture for lookup  Mipmapping may not work for non-linear BRDFs

19.  It may be expensive to compute the shading based on all the light sources  Also, many APIs (and various graphics cards) limit the number of light sources  Some lights must be averaged into each other for performance reasons

20.  Shading is usually done while z-buffer testing is done  It's possible to do all the z-buffer testing and then go back and shade only those fragments that contribute to the final scene

22.  A great deal of graphics research deals with rendering real scenes  Don't cameras do that?  Sure, but these graphics guys couldn't publish papers if the stuff wasn't hard for some reason:  Reconstructing novel viewpoints  Walkthroughs with user controlled paths  Introducing synthetic objects into real scenes  Re-lighting real scenes with new light sources  I would be remiss if I didn't mention these topics even though they usually have nothing to do with video games and often cannot be rendered in real time

24.  Although the research is old now, Daniel Aliaga et al. produced an impressive system for recreating real scenes in real time in which a user can control the path he or she takes  A robot records thousands and thousands of omnidirectional images and its location when it takes them  Then, images are merged together to create a novel view for the current location and orientation

25.  Rendering the images in real time isn't hard  Knowing the robot's position for all images is surprisingly difficult  Storing and loading the next images that will be needed in reconstruction is a huge caching and compression problem  Getting the robot to walk around and scan a scene automatically ended up being too hard  Some of these ideas were used for Google Street View, which is neither real time nor allows for arbitrary locations

27.  Synthetic objects can be rendered using a BRDF based on measurements of real-world materials  Alternatively, we could sample a real-world object from many different directions and get enough information to re-light it  You can also capture lighting from the real world using a mirrored ball  Then you can re-light:  A real image with a different set of real lights  Synthetic objects with realistic real light

30.  Area lighting  Environment mapping

31.  Work on Assignment 4  Due this Friday, March 20  Start working on Project 3  Due April 2  Keep reading Chapter 8