Week 5 - Friday

 What did we talk about last time?  Quaternions  Vertex blending  Morphing  Projections

 [L]ight …travels so fast that it takes most races thousands of years to realise that it travels at all…. Douglas Adams  Light is one of the most complex phenomena in the universe  There are quantum effects, its dual wave/particle nature  We will constantly be approximating the effect of light, since figuring out its real effect is virtually impossible

 We will consider three processes in lighting a scene  Emitting light ▪ From the sun or light bulbs or whatever  Interaction of light ▪ Light is absorbed by and scatters off objects in a scene  Detection by a sensor ▪ A human eye (or a robot eye), camera, piece of film will sense the light  We have to give at least cursory attention to each process to get realistic rendering

 One of the easiest light sources to model are directional lights, such as the sun  With directional lights, all the light travels the same direction, which we can model with a light vector l  We assume that l is a unit vector  l is defined in the opposite direction the light is traveling

 Besides direction, we need to know the amount of light  Radiometry is the science of measuring light, and we'll talk more about it in two weeks  Irradiance is the light's power passing through a unit area surface perpendicular to l  Light can be colored by using RGB components

 Most light is not perpendicular to your surface  The surface irradiance is the perpendicular irradiance times cos θ, where θ is the angle between l and the surface normal n  This is why l is the opposite of the direction of light flowing (so that we don't have to negate it)  Also, we clamp the cos θ to [0,1] (no negative values)

 Real light is coming from many different directions  The final effects of irradiance is additive  Just sum up all the individual light effects  Although we use RGB for light, there is not necessarily a maximum value  Light is perceived logarithmically by humans  High dynamic range displays and floating point color models can allow a better expression of light energy

 Once we know how much and what direction of light we're dealing with, the material it hits impacts the final effect a great deal  These impacts are of two kinds:  Scattering  Absorption

 Scattering is caused by an optical discontinuity  Difference in structure  Change in density  Scattering does not change the amount of light, only its direction  There are two types of scattering  Refraction (or transmission)  Reflection

 With refraction (or transmission) in (partially) transparent objects, the light continues to go through the object and may light other objects  There are light bending effects  Plus the Z-buffer algorithm doesn't work anymore  We won't deal with that now

 Light that is reflected will have a different direction and color than light that was transmitted into the surface, partially absorbed, and scattered back out  We simplify by dividing into two terms  Specular term (the reflected light)  Diffuse term (the re-transmitted light)

 Illumination reaching a surface is irradiance  Illumination leaving a surface is exitance (M)  Although our perception of light is logarithmic, light-matter interaction is linear:  Double the irradiance and you'll double the exitance  The ratio between exitance and irradiance is essentially the surface color that you see back  Surface color c = specular color + diffuse color

 We will often assume that diffuse light has no directionality  Specular light, however, bounces off a surface and spreads out less if the surface is smoother  Color, texture, and the smoothness parameter are not absolute  We may change them depending on how far we are from the object

 We are going to describe mathematical models of sensors  But how did humans investigate the nature of sensors in the first place?  Can you trust your own sensors?  Consider the following slide

 That slide is an example of Mach banding  In Mach banding, a lighter color on the edge of a darker color will appear to grow lighter as you get close to the border between them  The darker color will do the reverse  It's part of our brain's edge detection algorithm

 In general, sensors are made up of many tiny sensors  Rods and cones in the eye  Photodiodes attached to a CCD in a digital camera  Dye particles in traditional film  Typically, an aperture restricts the directions from which the light can come  Then, a lens focuses the light onto the sensor elements

 Irradiance sensors can't produce an image because they average over all directions  Lens + aperture = directionally specific  Consequently, the sensors measure radiance (L), the density of light per flow area AND incoming direction

 In a rendering system, radiance is computed rather than measured  A radiance sample for each imaginary sensor element is made along a ray that goes through the point representing the sensor and point p, the center of projection for the perspective transform  The sample is computed by using a shading equation along the view ray v

 After all this hoopla is done, we need a mathematical equation to say what the color (radiance) at a particular pixel is  There are many equations to use and people still do research on how to make them better  Remember, these are all rule of thumb approximations and are only distantly related to physical law

 Diffuse exitance M diff = c diff  E L cos θ  Lambertian (diffuse) shading assumes that outgoing radiance is (linearly) proportional to irradiance  Because diffuse radiance is assumed to be the same in all directions, we divide by π (explained later)  Final Lambertian radiance L diff =

 Shading  Lambertian  Gouraud  Phong  Anti-aliasing

 Keep working on Project 2, due Friday, March 13  Keep reading Chapter 5  Exam 1 is next Friday in class  Start reviewing everything up to today