Computer Graphics(fall 2009)

School of Computer ScienceUniversity of Seoul

Chap 6: Shading

1. Light and Matter2. Light Sources3. The Phong Reflection Model4. Computation of Vectors5. Polygonal Shading6. Approximation of a Sphere by Recursive Subdivision7. Light Sources in OpenGL8. Specification of Materials in OpenGL9. Shading of the Sphere Model10. Global Illumination

6.1 Light and Matter

Rendering Methods

Rendering equation [Kaj86] Integral eq. resulted by recursive scattering Physics-based, slow to compute

Radiosity, raytracing (Ch.12) and photon mapping Approximation of rendering equation for particular

surfaces Still slow

Phong reflection model Fast!

Rendering Equation

Proposed in “The rendering equation” (by James Kajiya, 1986)

Based on “conservation of energy”

Radiosity

FEM (Finite Element Method) applied to solve the rendering equation

For scenes with diffuse surfaces

Radiosity (cont’d)

Supported by 3D Max, EIAS, etc.

(image courtesy of JCM animation, EIAS)

(image courtesy of David Stoddard, EIAS)

Raytracing

Rendering by tracing rays for each pixel from the viewer (camera)

Suitable for reflective surfaces

(image courtesy of Wikipedia)

Raytracing (cont’d)

Supported by POV-Ray, YafaRay, etc.

(“Glasses” by Gilles Tran, POV-Ray) (“Nikon” by Bert Buchholz, YafaRay)

Photon Mapping

Rays from the light source & camera are traced independently

Image courtesy of Wikipedia)

Light-Surface Interaction

Reflected, absorbed and transmitted Depends on

opaqueness wavelength- “Why does an object look red?” roughness - “Why does an object look shiny?” Orientation etc.

Surface Types

Specular surfaces Diffuse surfaces Translucent surfaces

6.2 Light Sources

General Light Source Model

Can be modeled by an illumination function I(x,y,z,,,)

Each frequency consideredindependently

Total contribution can becomputed by integration

Directional properties canvary with frequency

Too complicated to compute

Simplified Light Sources

Four types: ambient lighting, point sources, spotlights, and distant lights

Light sources with three components, RGB- based on “three-color theory”

Each component calculated independently Intensity or luminance:

b

g

r

III

I

Type #1: Ambient Light

Models uniform illumination Simplified as an intensity that is identical at

every point in the scene:

ab

ag

ar

a

III

I

Type #2: Point Sources

Located at p0:

Intensity received at p: High contrast than surface light Can be made soft by

the distance term:

0

0

0

0

ppp

pI

b

g

r

III

00

0 pIpp

ppi 2

1,

12 cdbda

Type #3: Spotlights

Cone-shaped directional range Distribution of the light within the cone

usually defined by ecos

Type #4: Distant Light Sources

Rays can be assumed parallel Direction instead of location:

1zyx

0p

0zyx

0p

6.3 The Phong Reflection Model

Phong Reflection Model

Introduced by Phong Four vectors used Three types of material-light interactions –

ambient, diffuse, and specular Local model

(image courtesy of Wikipedia)

Phong Reflection Model (cont’d)

i-the light source:

Reflection terms for a material:

Contribution of each light color (e.g., red):

Contribution of all sources (e.g., red):

ibsigbirs

ibdigdird

ibaigaira

LLLLLLLLL

is

id

ia

i

LLL

L

ibsigbirs

ibdigdird

ibaigaira

RRRRRRRRR

is

id

ia

i

RRR

R

irsirdirairsirsirdirdirairair IIILRLRLRI

i

arirsirdirar IIIII

#1: Ambient Reflection

Intensity same at every point on the surface Depends on

Material property Independent of

Location of the light source Location of the viewer

aaa LkI

#2: Diffuse Reflection

Characterized by rough surfaces Assumed to be “perfectly diffuse” Depends on

Material property Location of the light source

Independent of Location of the viewer

#2: Diffuse Reflection (cont’d)

Lambert’s law (for perfectly diffuse surface): cosdR

0,max2 nl

dd

d Lcdbda

kI

#3: Specular Reflection

Characterized by smooth surfaces Depends on

Material property Location of the light source Location of the viewer

“shininess coefficient” ()

0,max2vr

s

ss L

cdbdakI

Phong Reflection Model

aassddsda LkLkLkcdbda

IIII

0,max0,max12

vrnl

Modified Phong Reflection Model

Modified by Blinn a.k.a. “Blinn-Phong Shading Model”

Simplified by halfway angle (h) for faster calcu-lation rv replaced by n h

Faster calculation when the lightand the viewer are at infinity (WHY?) GL_LIGHT_MODEL_LOCAL_VIEWER

Default model in OpenGL

vlvlh

6.4 Computation of Vectors

Computation of Vectors

How to compute the normal vector of a triangle? a (smooth) surface?

How to compute reflection vector? lnnlr 2

6.5 Polygonal Shading

Flat & Gouraud Shading

Flat shading The normal of the first vertex used

Gouraud shading Lighting calculation at vertices Linearly interpolated at each fragment Artifacts for coarse polygon

Phong Shading

Lighting computation at each fragment Not directly supported by OpenGL Can be implemented using GLSL (OpenGL

Shading Language)

6.6 Approximation of a Sphere by Recursive Subdivision

6.7 Light Sources in OpenGL

Setting Lights

Enable/disable: glEnable(GL_LIGHTING); glEnable(GL_LIGHT#);

At least 8 lights

Positional or directional light: glLight*(GL_LIGHT#, GL_POSITION, position);

Ambient, diffuse, specular components: glLight*(GL_LIGHT#, GL_*, value);

GL_AMBIENTGL_DIFFUSEGL_SPECULAR

Setting Lights (cont’d)

Global ambient: glLightModel*(GL_LIGHT_MODEL_AMBIENT, value);

Distance-attenuation model: glLight*(GL_LIGHT#, GL_*, value);

GL_CONSTANT_ATTENUATION (a) GL_LINEAR_ATTENUATION (b) GL_QUADRATIC_ATTENUATION (c)

Spotlight: glLight*(GL_LIGHT#, GL_*, value);

GL_SPOT_DIRECTION GL_SPOT_EXPONENT GL_SPOT_CUTOFF ([0,90] or 180)

2

1cdbda

Setting Lights (cont’d)

Infinite/local viewer: glLightModel*(GL_LIGHT_MODEL_LOCAL_VIEW

ER, value); One/two-sided lighting:

glLightModel*(GL_LIGHT_MODEL_TWO_SIDED, value);

Light sources are transformed by mod-elview matrices!

6.8 Specification of Materials in OpenGL

Setting Materials Material properties are OpenGL states! Ambient, diffuse, specular, emissive:

glMaterial*v(face, GL_*, value); GL_AMBIENT, GL_DIFFUSE, GL_SPECULAR, GL_EMISSION,

GL_DIFFUSE_AND_SPECULAR Emissive property

Does not affect any other surface (it’s not a light!) Simply adds color

Shininess: glMaterial*(face, GL_SHININESS, value);

Front/back/front&back: GL_FRONT, GL_BACK, GL_FRONT_AND_BACK

glColorMaterial Various materials: refer to teapots.c!

Nate Robin’s Tutor

Try yourself!!!

6.9 Shading of the Sphere Model

6.10 Global Illumination