CS361Week 10 - Wednesday

Last time

What did we talk about last time? Shadow volumes and shadow

mapping Ambient occlusion

Corrections

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

Questions?

Project 3

Assignment 4

Student Lecture:Reflections

Reflections

Environment mapping

We already talked about reflections!

Environment mapping was our solution

But it only works for distant objects

Planar reflections

The simplest reflections to deal with are planar reflections Reflections off of a flat surface like a mirror

An ideal reflector follows the law of reflection Angle of incidence is the angle of reflection Reputedly discovered by Hero of Alexandria between

10 and 70 AD Vector form: where is the reflected vector, is the

incoming vector, is the surface normal

angle ofincidence

viewer

n

angle of reflectionreflector

Reflection rendering

The reflected object can be copied, moved to reflection space and rendered there

Lighting must also be reflected

Or the viewpoint can be reflected

Transparency

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

Hiding incorrect reflections

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

Hiding things behind the mirror

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

Visual improvements

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

Curved Reflections

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

Transmittance

Transmittance

How much light gets through your material?

That's transmittance

If your samples are of equal thickness, you can apply a color filter

Beer-Lambert Law

The Beer-Lambert law says how much light gets through an object of varying thickness

Transmittance is:

where is the absorption coefficient, c is the concentration of the material and d is the thickness d

Refractions

What is refraction?

It's a property of waves (not just light)

Describes the way the path of waves is bent when it changes medium

What causes refraction?

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

Principle of Least Time

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

Snell's Law

Snell's Law allows us to calculate the amount of refraction

Total internal reflection

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

Exotic effects

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

XNA Reflection and Refraction Examples

Caustics

It’s burning!

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:

Image space rendering

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

Object Space Rendering

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

Some other examples

Global Subsurface Scattering

Subsurface scattering

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

Subsurface scattering

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

Blurring normals and lighting 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

Depth map techniques

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

Quiz

Upcoming

Next time…

Radiosity Ray Tracing Precomputed lighting Precomputed occlusion Precomputed radiance transfer

Reminders

Keep working on Project 3 Due next Thursday by midnight

Keep reading Chapter 9