reflected - Classes

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reflected - Classes

Computer Graphics (CS551): May 7, 2013

Presenter:

Xianyong Liu

1


Agenda

‣Goals of Lecture

‣Background

• About Rendering

• Light and Color

• Recap Rendering

‣ Light Field

• Flux(Radiant energy)

• Angular Flux Intensity(Radiance)

• Flux Intensity(Irradiance, Radiosity, Radiant intensity)

2


‣Reflection

Agenda

• BRDF (Bidirectional Reflection Distribution Function)

• Diffuse Reflection and Lambertian BRDF

• Specular Reflection and Mirror BRDF

• Glossy reflection

• Real BRDF

‣Rendering Functions

• Local or Direct illumination

• Global or Indirect illumination

• Phong Model: An Empirical Approximation

• The .mtl example for setting model appearance

3


Goals of Lecture

The goal of this lecture is to talk about some stories

about rays. They formed the foundation of rendering in

computer graphics.

THESE STORIES ARE NOT NEW, BUT THEY ARE

HELPFUL TO UNDERSTAND RENDERING.

4


Goals of Lecture

Advanced rendering has been driven by a deeper and better

understanding of the physics of materials and lighting[3].

WHAT ARE THOSE DEEPER AND BETTER

UNDERSTANDINGS?

5


Goals of Lecture

After having this lecture, you are supposed to be here:

What is the light field?

What is the the relationship between reflectance and

albido?

What are those setting in OpenGL for rendering?

6


Background

About Rendering

The aim of almost all OpenGL applications is to draw

color pictures in a window on the screen[1].

The essence of rendering is to royally record down the

color of the scene perceived by the camera.

7


Background

About Rendering

Color is fundamental to both computer graphics

(CG) and image processing.

8


Background

About Rendering

In general, how strong a color is depends on how much

energy you received.

COLOR IS A SORT OF ENERGY.

9


Background

Active counters in image[6]

10


Background

Active counters in image[6]

11


Background

About Rendering

CG is partially different from IP (Image Processing).

IP focuses on understanding images, while CG focuses

on generating images.

12


Background

About Rendering

13


Background

Light and Color

There are two questions listed below. Which one do you

prefer?

1.What is the light?

2.Where is the color?

14


Background

About Light[2]

15


Background

About Color[2]

16


Background

Recap Rendering

Physically based or realistic rendering can be viewed as

the problem of SIMULATING the propagation of light

in an ()environment[3].

I WOULD LIKE TO ADD THE “VIRTUAL” BEFORE

THE “ENVIRONMENT”.

THE KEY WORD OF “SIMULATING ”.

We approach it, but are not exactly the same.

17


Background

Recap Rendering

18


Background

WARNING

In rending, primitive, camera, light and material are

the gang of four. Please keep them in mind lest you

mightbelostinthenextpages.Nomatterhowabstract

or straightforward a rendering method is, it is just

constructing the relationship between the primitive,

camera, light and material

19


Background

WARNING

light incident at surface = light reflected + light

absorbed + light transmitted

20


Find out the gang of four

Light Field

During the introduction, I hope that you’d better KEEP asking

me or yourself a questions: where are the gang of four?

In this way, you will survive from the boring formulations and

concepts.

21


Light Field

We understand the light field as a spatial room where is

full rays.

In physics the study of how “stuff” flows is terms

transport theory, which is of interest to us.

22


Light Field

Geometrical Optics of radiosity

It was not until 1980 that the first global illumination

algorithm was introduced by Whitted. Whitted’s

innovation was the recursive application of ray tracing

to evaluate a simple global illumination model

accounting for mirror reflection, refraction, and

shadows.

More accurate physically based local reflection models

were developed by Blinn[1977] and Cook and

Torrance[1982], using results from the fields of radiative

heat transfer and illumination engineering.

23


Light Field

Photon

Photon is the easiest way to understand light transport

theory.

[5] A photon is an elementary particle, the quantum of

light and all other forms of electromagnetic radiation, and

the force carrier for the electromagnetic force, even when

static via virtual photons.

Photons emitted in a coherent beam from a laser

24


Light Field

Flux

Consider a time slice and a small differential surface

element, how many particles crossing?

25


Light Field

Flux

In general, particles through a point will not be following

with the same speed and in the same direction.

Difference?

26


Light Field

Flux

Given a small perturbation

to direction, the differential

solid angle is the ration

of differential spherical

area to the square of

radius of sphere.

27


Light Field

Radiance and luminance※

In CG rendering, we care more about power than the flux. It

is the radiant energy per unit projected area per unit solid

angle. DIFFERENCE?

28


Light Field

Two Important Rules of Radiance

The radiance in the direction of a light ray remains

constant as it propagates along the ray.

The response of a sensor is proportional to the radiance of

the surface visible to the sensor.

PLEASE REFER TO [3] IF YOU ARE INTERESTED.

29


Light Field

Irradiance and Illumination※

Radiance is direction dependence. It considers the total flux

within a small beam of radiation. The irradiance is the

radiant energy per unit area falling on a surface.

30


Light Field

Radiosity and luminosity※

Whereas irradiance is the energy per unit area incident onto

a surface, radiosity is the energy per unit area that leaves a

surface.

LO is the outgoing radiance.

31


Light Field

Radiant and Luminous Intensity※

Radiance is incapable of describing the energy

distribution of a point light source because of the point

singularity at the source. That is, the face area is

infinitely small.

32


Light Field

Radiant and Luminous Intensity※

For an isotropic point light source:

33


Light Field

Radiant and Luminous Intensity※

The irradiance on a differential surface due to single point

light source can be computed by. You can think about that

the differential surface is on the surface of the sphere

centered by the point light source.

34


Reflection

The last section tells the story about light. The next section

will tell another one, happened when light is incident on

surfaces.

To keep the story short, we only take the reflection as an

example, which is defined as the process by which light

incident on a surface leaves that surface from the same side.

Actually transmission, absorption, spectral and

polarization effects, fluorescence, and phosphorescence are

also important parts of the story.

35


Reflection

Reflection in the nature

36


Reflection

BRDF ※

A well‐known measurement about reflection is BRDF.

BRDF describes how much light is reflected when light

makes contact with a certain material. Similarly, BTDF

describes how much light is transmitted when light makes

contact with a certain material[7].

37


Reflection

BRDF ※

Suppose we are given an incoming light direction, wi

, and an outgoing reflected direction, wr, each defined

relative to a small surface element. A BRDF is defined as

the ratio of the quantity of reflected light in direction wr,

to the amount of light that reaches the surface from

direction wi.

38


Reflection

BRDF ※

A surface element illuminated by a light source

As a result:

s

39


Reflection

BRDF ※

The cosine theta does account for BRDF. See the

Lambertian BRDF example[8].

40


Reflection

Reflectance Equation

Please notice that the radiosities produced by various

incident irradiances are independent to each other.

Herein, we have the reflectance equation:

41


Reflection

Diffuse Reflection and Lambertian BRDF

Surface appears equally bright from ALL directions!

(independent of )

42


Reflection

Diffuse Reflection and Lambertian BRDF

Thus, Lambertian BRDF is simply regarded as a constant.

43


Reflection

Diffuse Reflection and Lambertian BRDF

The relationship between Lambertian BRDF and

reflectance.

44


Reflection

Diffuse Reflection and Lambertian BRDF

Rendered Sphere with Lambertian BRDF[8].

45


Reflection

Specular Reflection and Mirror BRDF

For very SMOOTH surface:

46


Reflection

Specular Reflection and Mirror BRDF

Mirror BRDF is simply a double‐delta function :

47


Reflection

Specular Reflection and Mirror BRDF

ANY PROBLEM? IS the cosine theta is necessary???

48


Reflection

Glossy reflection

Delta Function in mirror BRDF is too harsh. Many

glossy surfaces show broader highlights in addition to

mirror reflection.

49


Reflection

Real BRDF

A real BRDF will thus contain a component between

these limiting cases in which light hitting the surface

from a certain direction is reflected into a complex

distribution of outgoing directions.

50


Reflection

Albedo (Reflectance)

From the delta‐function of mirror BRDF, we see that

BRDF might be an infinite value.

Often, it is more intuitive to work with a quantity that

is bounded between 0 and 1. This value is called albedo,

which measures the possibility that the irradiance

reflects along a direction.

51


Rendering Equation

Local or Direct illumination

The easiest case is one with no occlusion. It is the direct

illumination from simple light source and assumed that

all light arrives at the surface; that is, there is no

shadowing.

52


Rendering Equation

Global or Indirect illumination

In this case, light may come from any surface in the

environment, and it is very important to consider

shadowing.

53


Rendering Equation

Global or Indirect illumination

The two points radiant power transfer equation:

54


Rendering Equation

Global or Indirect illumination

The three points radiant power transfer equation:

55


Phong Model: An Empirical

Approximation

Rendering Equation

56


Phong Model: An Empirical

Approximation

Rendering Equation

57


Rendering Equation

The .mtl example for setting model

apperance

newmtl mat008

Ka 0.5000 0.5000 0.5000

Kd 1.65368e‐029 2.27576e‐038 7.56701e‐044

Tr2.27575e‐038

illum 1

map_Kd

bunnyWithColor7_textures\gauss_curvature.png

58


Rendering Equation

The .mtl example for setting model

appearance

59


Reference

1. OpenGL Programming Guide

2. Google Image

3. Radiosity and Realistic Image Synthesis

4. The Rendering Equation

5. Wikipedia

6. Advanced Color Image Processing and Analysis

7. An Introduction to BRDF‐Based Lighting

8. http://www.cs.cmu.edu/afs/cs/academic/class/15462

‐f09/www/lec/lec8.pdf

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