Week 6 - Wednesday

 What did we talk about last time?  Light  Material  Sensors

 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

 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 =

 Specular shading is dependent on the angles between the surface normal to the light vector and to the view vector  For the calculation, we compute h, the half vector half between v and l 

 The total specular exitance is almost exactly the same as the total diffuse exitance:  M spec = c spec  E L cos θ  What is seen by the viewer is a fraction of M spec dependent on the half vector h  Final specular radiance  L spec =  Where does m come from?  It's the smoothness parameter

 Final lighting is:  We want to implement this in shaders  The book goes into detail about how often it is computed  Note that many terms can be precomputed, only the ones with angles in them change

 Computing the shading equation more often gives better visual results but takes more time  Flat shading  Computes shading equation once per primitive  Gouraud shading  Computes shading equation once per vertex, linearly interpolates color for pixel values  Phong shading  Computes color per pixel

 When sampling any continuous thing (image, sound, wave) into a discrete environment (like the computer), multiple samples can end up being indistinguishable from each other  This is called aliasing  We can reduce aliasing by carefully considering how sampling and reconstruction of the signal is done

 Ever seen wheels of a car spinning the wrong way?  Without enough samples, it may be impossible to tell which way it's spinning  You need a sampling frequency twice as high as the maximum frequency of the events to reconstruct the original signal  Called the Nyquist limit

 Jaggies are caused by insufficient sampling  A simple method to increase sampling is full- scene antialiasing, which essentially renders to a higher resolution and then averages neighboring pixels together  The accumulation buffer method is similar, except that the rendering is done with tiny offsets and the pixel values summed together

FSAA schemes A variety of FSAA schemes exist with different tradeoffs between quality and computational cost

 For non-interactive render speeds, the A-buffer can be used  The A-buffer generates a coverage mask for each fragment for each pixel  Fragments are thrown away if they have z-buffer values that are higher than fragments with full coverage  Final pixel color is based on fragment merging

 Supersampling techniques (like FSAA) are very expensive because the full shader has to run multiple times  Multisample antialiasing (MSAA) attempts to sample the same pixel multiple times but only run the shader once  Expensive angle calculations can be done once while different texture colors can be averaged  Color samples are not averaged if they are off the edge of a pixel

 Active research is still trying to find techniques with good visual output and good computational performance  Stochastic (random) sampling reduces the visual repetition of some artifacts  Sharing samples between pixels can reduce overall cost

 Review for Exam 1  Review all material covered so far  Exam 1 is Friday in class

 Keep working on Project 2, due Friday, March 1  Keep reading Chapter 5  Start reading Chapter 6