Week 10 - Wednesday

 What did we talk about last time?  Shadow volumes and shadow mapping  Ambient occlusion

 I said that shadow maps couldn't be used with point lights, only directional lights  That was incorrect!  The "view" from a point light should be modeled with a perspective projection while a directional light should be modeled with an orthographic projection

 We already talked about reflections!  Environment mapping was our solution  But it only works for distant objects

angle of incidence viewer n angle of reflection reflector

 The reflected object can be copied, moved to reflection space and rendered there  Lighting must also be reflected  Or the viewpoint can bereflected

 Reflector must be partially transparent so that the reflected scene can be viewed  The degree of transparency acts simulates the reflectivity factor  Care must be taken when setting up back face culling for the reflection pass  Also, the scene may be rendered where there is no reflector

 This problem can by solved by using the stencil buffer  The stencil buffer is set to areas where a reflector is present  Then the reflector scene is rendered with stenciling on

 Objects behind the mirror should not be rendered  A user defined clipping plane can solve this problem  Create a clipping plane and place it on the same plane as the mirror

 Reflections can be enhanced by blurring them or fading them to black as the viewer moves away  Objects can be rendered to a texture with a Z- buffer  The Z-buffer can be used to blur or darken objects that are further away  Frosted glass can also be created by blurring

 Ray tracing can be used to create general reflections  Environment mapping can be used for recursive reflections in curved surfaces  To do so, render the scene repeatedly in 6 directions for each reflective object

 How much light gets through your material?  That's transmittance  If your samples are of equal thickness, you can apply a color filter

d

 It's a property of waves (not just light)  Describes the way the path of waves is bent when it changes medium

 Refraction and diffraction results of the Huygens– Fresnel principle  Each point of a medium disturbed by a wave becomes a point of propagation for the disturbance

 Another way of looking at refraction is through the Fermat's Principle of Least Time  The path taken between two points by a ray of light is the path that can be traversed in the smallest amount of time  The light actually bends to spend less time in a slower material

 If the angle of refraction is greater than the critical angle, the light will be reflected back into the initial medium

 If the material has different refractive indices for different polarizations, two images will appear offset from each other  Birefringence  The delta between the refractive indices of different polarizations determines how much the light will be offset  Modern metamaterials exist with a negative refractive index  In those cases, light is refracted on the same side of the normal as the incidence

 Light is focused by reflective or refractive surfaces  A caustic is the curve or surface of concentrated light  The name comes from the Greek for burning Reflective:Refractive:

 First:  The scene is rendered from the view of light  Track the diversion of light and see which locations are hit  Store the result in an image with Z-buffer values called a photon buffer  Second:  Treat each location that received light as a point object called a splat  Transform these to eye viewpoint and render them to a caustic map  Third:  Project the map onto the screen and combine with the shadow map

 Look at each generator triangle  Those that are specular or refractive  Each vertex on each generator triangle has a normal  Create a caustic volume like a shadow volume except that the sides are warped by either reflection or refraction  For receiver pixels in the volume, intensity is computed

 Subsurface scattering occurs when light enters an object, bounces around, and exits at a different point  If the exit point is close to the entrance point (in the same pixel), we can use a BRDF  If it spans a larger distance, we need an algorithm to track photon propagation

 Examples  Pearlescent paint  Human skin ▪ Which matters  Causes  Foreign Particles (pearls)  Discontinuities (air bubbles)  Density variations  Structural changes  We need to know how long light has traveled through the object  Tracking individual photons is impossible, so all algorithms will be statistical

 Subsurface scattering does not affect specular reflection  We often use normal maps to add detail to specular reflection characteristics  Some work suggests that this same normal map should be ignored for diffuse terms  Or the normals can be blurred further since surface direction appears to change slowly if light from other directions is exiting diffusely  More complex models render the diffuse lighting onto a texture and then selectively blur R, G, and B components for more realism This texture space diffusion technique was used in The Matrix Reloaded for rendering skin

 We could cast rays into objects to see where they come out, but it's expensive  An alternative is to use depth maps to record how far the light travels through the object which determines how colored by the object it is  Refraction when the light enters the object is usually ignored  Only exiting refraction is computed

 Radiosity  Ray Tracing  Precomputed lighting  Precomputed occlusion  Precomputed radiance transfer

 Keep working on Project 3  Due next Thursday by midnight  Keep reading Chapter 9