10-lighting-shading.pdf

Lighting

•

The other side of rendering

•

Computing the light

–

How much

–

Which colour

arriving

–

From a point in the scene

–

To the eye

Lighting: relevant factors

light

eye

object

Trasmission (with rifraction)

absorption

Inner reflection

Absorption by

the environment

(e.g. fog)

Sub-surface scattering

Additional light

shade

Lighting: relevant factors

Multiple reflections

(indirect Lighting)

light

Lighting: global VS local

–

Only takes into account:

•

Light conditions

–

N. lights

–

their position

–

Their color

•

Surface area to lite

–

orientation (normal)

–

Optical charcateristics

»

E.g, color

–

Anything else is ignored

–

Multiple reflections

–

shadows

–

Sub-surface scattering

–

refraction

–

...

Local lighting

Global lighting

Much easier

to do on our

Local lighting

light

eye

object

What can be easily accomplished

•

Local lighting:

–

Light reflections on objects

•

Using simplified optical properties

–

wiht multiple light sources

•

But simplifies: point-sized

•

Global lighting:

–

Multiple reflections

•

VERY simplified

–

Absorption by the environment

•

Simplified case (uniform fog)

–

Everything else only “ad-hoc"

The 3 factors we take into account

total light

=

ambient

+

reflection

+

emission

For any factor we have the

R, G and B components.

Defined for both the

object

,

(vertex attributes)

And for each

light

used

The optical properties of the

object

,

(usually vertex attributes)

Collected together form the

"

material

"

Component emission

•

LEDs, light bulbs...

•

Not related to the lights

–

Only to the object

•

It is only an addittive Component

–

costant for R, G and B

•

Note: it does not send light to nearby objects

–

It isn’t Global lighting

The 3 factors we take into account

total light

=

ambient

+

reflection

+

Component ambient

•

It models (very approximately) the light hitting

the object after multiple reflections

•

Assumption:

“a small amount of light hits any surface from

every direction"

–

Even surfaces in shadow

•

Small additive

constant

Component ambient

•

Product of:

–

“

ambient

” color of the material ( R

_M

G

_M

B

_M

)

–

“

ambient

” color of the light ( R

_L

G

_L

B

_L

)

•

Note: the RGB colors can be different

Component ambient

•

It models (very approximately) the light hitting

the object after multiple reflections

without

The 3 factors we take into account

total light

=

ambient

+

reflection

+

emission

diffuse reflection

+

specular reflection

only

The 4 factors we take into account

total light

=

ambient

+

diffuse reflection

+

specular reflection

+

Component diffuse reflection

•

Effect shown by a few materiale (e.g.):

–

chalk

–

wood (almost)

–

Very opaque materials(not shiny)

•

Also known as

–

diffuse reflection

–

Lambertian reflection

Component diffuse reflection

The light hitting a lambertian

surface is reflected in all

directions (in the half-sphere)

Component diffuse reflection

The light hitting a lambertian

surface is reflected in all

directions (in the half-sphere)

Component diffuse reflection

The light hitting a lambertian

surface is reflected in all

directions (in the half-sphere)

Component diffuse reflection

•

It only depends on:

–

Surface orientation

•

(the "normal")

–

Light direction

Component diffuse reflection

•

It only depends on:

–

Surface orientation

N

•

(the "normal")

–

Light direction

L

•

(Light ray)

θ

cos

⋅

⋅

=

_light

_diff

_material

_diff

diff

I

k

I

R, G, B

(usually white: 1,1,1)

R, G, B

(the "color" of the object)

property of the

"material"

(associated to

the object)

Component diffuse reflection

•

It only depends on:

–

Surface orientation

N

•

(the "normal")

–

Light direction

L

•

(Light ray)

θ

cos

⋅

⋅

=

_light

_diff

_material

_diff

diff

I

k

Component diffuse reflection

•

It only depends on:

–

Surface orientation

N

•

(the "normal")

–

Light direction

L

•

(Light ray)

θ

cos

⋅

⋅

=

_light

_diff

_material

_diff

diff

I

k

Component diffuse reflection

•

It only depends on:

–

Surface orientation

N

•

(the "normal")

–

Light direction

L

•

(Light ray)

)

L

ˆ

N

ˆ

(

⋅

⋅

⋅

=

I

_light

_diff

k

_material

_diff

Angle between

0⁰ and 90⁰

,

otherwise 0,

(object in its own shadow)

θ

cos

⋅

⋅

=

_light

_diff

_material

_diff

diff

I

k

Component diffuse reflection

L

N

Component

diffuse

small

⍬=70⁰

L

N

Component

diffuse

large

⍬=35⁰

L

N

Component

diffuse

Component diffuse reflection

L

N

Component

diffuse

ZERO

⍬=90⁰

L

N

Component

diffuse

ZERO

⍬>90⁰

Component diffuse reflection

•

Properties

–

Accurate model of the optical characteristics

of a number of real materials

☺

–

But only a small number

–

The model is physically coherent

☺

•

As an example, energy is conserved

The 4 factors we take into account

total light

=

ambient

+

diffuse reflection

+

specular reflection

+

Component specular reflection

•

"Specular" reflection

•

For shiny materials

–

With bright reflections

–

("highlights")

Component specular reflection

•

Basic idea:

light

is not

reflected

by

shiny materiale

Component specular reflection

L: light ray

N: normal

R: reflected ray

V: view direction

N

L

_R

V

θ θ

_α

Component specular reflection

•

Phong light model

–

by Bui-Tuong Phong, 1975

in 3D

α

cos

⋅

⋅

=

_light

_spec

_material

_spec

spec

I

k

Component specular reflection

Component specular reflection

•

Phong light model

–

by Bui-Tuong Phong, 1975

in 3D

Belong to the "material"

(properties of the object)

α

n

spec

material

spec

light

spec

I

k

I

=

⋅

⋅

cos

α

cos

⋅

⋅

=

_light

_spec

_material

_spec

spec

I

k

Component specular reflection

•

Phong light model

–

by Bui-Tuong Phong, 1975

in 3D

α

cos

⋅

⋅

=

_light

_spec

_material

_spec

spec

I

k

I

n

spec

material

spec

light

k

R

V

I

⋅

⋅

(

ˆ

⋅

ˆ

)

=

α

n

spec

material

spec

light

spec

I

k

Component specular reflection

1

=

n

n

=

5

n

=

10

n

=

100

Component specular reflection

• Blinn-Phong light model:

• Simplification of the Phong light model

• Similar results, different formula:

n

spec

material

spec

light

spec

I

k

R

V

I

=

⋅

⋅

(

ˆ

⋅

ˆ

)

phong:

blinn-phong:

_I

_spec

=

_I

_light

_spec

⋅

_k

_material

_spec

⋅

₍

_H

ˆ

⋅

_N

ˆ

₎

n

N

L

_R

V

θ θ

_α

Component specular reflection

• Blinn-Phong light model:

• Simplification of the Phong light model

• Similar results, different formula:

Jim Blinn

(MEGA-MEGA-GURU)

phong:

blinn-phong:

n

spec

material

spec

light

spec

I

k

R

V

I

=

⋅

⋅

(

ˆ

⋅

ˆ

)

n

spec

material

spec

light

spec

I

k

H

N

The 4 factors we take into account

total light

=

ambient

+

diffuse reflection

+

specular reflection

+

Complete lighting equation

+

⋅

⋅

⋅

n

specular

material

specular

light

k

H

N

I

(

)

+

⋅

⋅

⋅

k

(

L

N

)

I

_light

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

ambient

light

k

I

emission

material

k

=

tot

I

Lighting equation: lights modeling

emission

materiale

k

=

tot

I

property of the light

L

V

V

L

ˆ

ˆ

)

ˆ

ˆ

(

+

+

+

⋅

⋅

⋅

n

specular

material

specular

light

k

H

N

I

(

)

+

⋅

⋅

⋅

k

(

L

N

)

I

_light

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

ambient

light

k

Lights modeling

•

How does L change ?

–

constant in the scene: "

directional

" light sources

•

Used for light sources very far away, e.g. the sun

–

Variable in the scene: "

positional

" light sources

Lights modeling: positional lights

•

The positional lights, have their intensity

dimmed according to the distance

•

In theory (according to physics)

intensity = 1 / distance

2

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⋅

=

₂

L

1

d

c

Lights modeling: positional lights

•

In practice, it leads to light attenuations that are

too quick

•

We rather use:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

=

min

1

₂

,

1

L

3

L

2

1

c

d

c

d

Lighting equation

=

tot

I

⋅

f

light

attenuatio

n

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

=

min

1

₂

,

1

L

3

L

2

1

c

d

c

d

c

f

_light

_attenuatio

_n

n

specular

material

specular

light

k

H

N

I

⋅

⋅

(

⋅

)

+

⋅

⋅

⋅

k

(

L

N

)

I

_light

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

Kind of lights

•

Kind of lights:

–

positional

–

directional

Spotlights

Lighting equation

effect

spotlight

f

⋅

(

direction

cutoff

Angle

beam

width

)

effect

spotlight

L

spot

spot

spot

f

=

f

,

,

,

=

tot

I

n

attenuatio

light

f

⋅

n

specular

material

specular

light

k

H

N

I

⋅

⋅

(

⋅

)

+

⋅

⋅

⋅

k

(

L

N

)

I

_light

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

ambient

light

k

I

emission

material

k

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

=

min

1

₂

,

1

L

3

L

2

1

c

d

c

d

Lighting: Where?

Lighting & Shading

Computer Graphics Pagina 49

y

z

v

v

v

v

v

v

Final pixels

(filling of the

screen-buffer)

fragments

(candidate pixels)

Ve

rt

ic

e

s

(points in R

3

)

Projected

vertices

_{(points in R}

2

)

Z

Ve

rt

e

x

computations

Fragment

_computations

The 4 factors we take into account

total light

=

ambient

+

diffuse reflection

+

specular reflection

+

Lighting equation

n

specular

material

specular

light

k

H

N

I

⋅

⋅

(

ˆ

⋅

ˆ

)

+

⋅

⋅

⋅

k

(

L

ˆ

N

ˆ

)

I

_luight

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

ambient

light

k

I

emission

material

k

+

=

tot

I

light

attenuatio

n

f

⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

=

min

1

₂

,

1

L

3

L

2

1

c

d

c

d

c

f

_light

_attenuatio

_n

effect

spotlight

f

⋅

(

L

spot

spot

spot

)

f

=

f

,

,

,

^

Normal of a triangle

•

That is its orientation in space

N

v

₀

v

₂

v

₁

)

(

)

(

v

₁

v

₀

v

₂

v

₀

N

=

−

×

−

|

|

ˆ

Lighting face by face

"flat shading"

1.

Initial geometry

For each face,

2.

Compute the normal

3.

Definition

•

Shading

:

–

Recipe to apply

lighting

•

As an example:

flatshading

1.

Apply lighting to each face normal

- (obtaining a color)

Flat shading: problem

When we approximate curved surfaces with

triangles and apply flat shading the result is:

– Edges very visible on curved surfaces

bad

artifact!

Flat shading: problem

Flat shading: problem

•

Increasing the number

of faces, makes the

problem less visible

>10.000 faces,

and we still see

the artifact edges

Flat shading: problem

To make things worse:

the

Mach-band optical effect

The contrast between different

uniform areas catches our eye.

(even when areas are a lot,

and their difference is small).

The brain increases the contrast

between uniform areas.

Idea

"Gouraud" Shading

To apply the lighting, I need to have the normal!

The normal is defined for a face, not for a

vertex

by Henri Gouraud, 1971

Idea

•

Use color interpolation within a face

1- Apply lighting to the 3 vertices of each triangle

•

(obtain a color)

Vertex normals

•

In many cases, the vertex normals are defined

at the same time of the 3D model.

–

As an example,

•

When we model a sphere, a cylinder, a cone...

•

When we compute the surface of a volume

•

When we a triangulated surface sampling a parametric surface

•

...

Vertex normals

Normal of a triangle:

v

₁

v

₂

v

₁

×

v

₂

v

N

ˆ

ˆ

N

ˆ

N

ˆ

N

ˆ

N

ˆ

N

ˆ

N

Normal of a vertex

Shared by

n

triangles:

n

N

N

N

N

=

ˆ

₁

+

ˆ

₂

+

...

+

ˆ

Where do we compute lighting?

x

y

z

v

v

v

v

v

v

Final pixels

(filling of the

screen-buffer)

fragments

(candidate pixels)

Ve

rt

ic

e

s

(points in R

3

)

Projected

vertices

_{(points in R}

2

)

Z

Ve

rt

e

x

computations

Fragment

_computations

Fundamental decision

•

In our rendering paradigm, the (vertex) normal:

• Is NOT

computed in the pipeline

•

Is introduced as an

ATTRIBUTE

of each

VERTEX

•

The normale “is in the model"

•

Exactly similar to vertex position

•

When necessary, the normals computation is tipically a

pre-processing

Final pixels

(filling of the

screen-buffer)

fragments

(candidate pixels)

Ve

rt

ic

e

s

(points in R

3

)

Projected

vertices

_{(points in R}

2

)

Z

Ve

rt

e

x

computations

Fragment

_computations

set-up

set-up

set-up

rasterizer

triangoli

Segments

rasterizer

rasterizer

punti

Triangles

rasterizer

Points

rasterizer

Gouraud shading

including:

property of

the

material

and

normal

Gouraud shading

How to improve the result

•

Rather than interpolating the

color

after

the

lighting

, we interpolate the

normal

before

of the

lighting

!

•

Be careful:

interpolating two normal vectors, the result is

not always a normal:

How to improve the result

•

Rather than interpolating the

color

after

the

lighting

, we interpolate the

normal

before

of the

lighting

!

"Phong" Shading

_{by Bui-Tuong Phong , 1973}

1- Interpolate the normal in the face

2- Normalize

3- Compute lighting

Final pixels

(filling of the

screen-buffer)

fragments

(candidate pixels)

Ve

rt

ic

e

s

(points in R

3

)

Projected

vertices

_{(points in R}

2

)

Z

Ve

rt

e

x

computations

Fragment

_computations

set-up

set-up

set-up

rasterizer

triangoli

Segments

rasterizer

rasterizer

punti

Triangles

rasterizer

Points

rasterizer

Phong shading

including:

property of

the

material

and

normal

Projection

of vertices

and

normals

Normal

interpola

tion

including:

interrpolated

normal

including:

Transformed

normal

Normalize and

compute

lighting

Gouraud vs Phong shading

•

Goraud Shading

-

lighting per vertex much less

computationally expensive:

Compute the lighting once per vertex!

•

Phong Shading

-

lighting per fragment offers better results

Especially suited for bright and small highlights (high shiness)

Gouraud and Phong shading

flat shading

Goraud shading

Gouraud and Phong shading

•

Goraud and Phong suited for curved surfaces

–

They hide the artifact edges

–

Also hide the REAL edges

Gouraud or Phong shading?

•

The OpenGL specifications

do not recommend

which one should be used

–

In most cases (at least now) Gouraud

•

It dipends on the HW implementation

–

There are no OpenGL commands that switch from

Its use in OpenGL

•

Turn on lighting:

( currbet color – that is

glColor3f

–

is now ignored. Only the current material!)

glEnable(GL_LIGHTING);

Normals

•

We set the “current normal". Similarly to colors:

glNormal3d(x,y,z);

What happens to the normals?

world Coordinates

x

y

z

v

v

v

y

-z

v

v

v

view Coordinates

(a.k.a. eye Coordinates)

y

x

-z

v

v

v

v

v

v

Normalized Device

Coordinates

1

-1

1

-1

x

x

y

z

v

v

v

object Coordinates

modeling

view

_projection

v

v

v

screen Space

viewport

Modeling + View transformations:

(keep the angles)

Projection:

All angles are modified

answer: normals are multiplied by the

Are normals preserved in the Transform?

•

Only when the modeling-view transformations

are rigid

modeling-view = V ‧ M

rotations,

translations

(always rigid)

rotations,

translations

Are normals preserved in the Transform?

•

Note: if the ModelView includes

scaling

we

need to

normalize

the normals before Lighting

•

Tell OpenGL to normalize:

or not to do it:

(default)

glEnable(GL_NORMALIZE);

Normals as attributes

•

Exactly like the color:

glBegin(GL_TRIANGLES);

glNormal3fv( n );

glVertex3fv( v0 );

glVertex3fv( v1 );

glVertex3fv( v2 );

glBegin(GL_END);

glBegin(GL_TRIANGLES);

glNormal3fv( n0 );

glVertex3fv( v0 );

glNormal3fv( n1 );

glVertex3fv( v1 );

glNormal3fv( n2 );

glVertex3fv( v2 );

glBegin(GL_END);

flat shading !

Normals as attributes

•

Shortcut:

–

When we set:

glShadeModel(GL_FLAT);

glShadeModel(GL_SMOOTH);

The attributes are not interpolated, but are

OpenGL: lights!

•

We have N lights available

–

remember: their effects

(ambient + diffuse + specular) add up

•

How many ?

–

Dependent on the specific OpenGL implementation

–

The OpenGL standard requires at least 8

–

The exact number is the value of the constant

OpenGL: lights!

•

Each light can be on or off

•

where

GL_LIGHT0

,

GL_LIGHT1

etc are costants

–

note:

GL_LIGHTk

is

GL_LIGHT0

+

k

.

useful for the

for

•

By default, the light 0 is the only one on

OpenGL: lights!

•

For each light, we set the colors

glLightfv(GL_LIGHT0, GL_DIFFUSE, v);

glLightfv(GL_LIGHT0, GL_AMBIENT, v);

OpenGL: lights!

•

For each light, we can also set:

–

The spotlight effect:

glLightfv(GL_LIGHT0,GL_SPOT_DIRECTION,v);

glLightf (GL_LIGHT0,GL_SPOT_CUTOFF,v);

glLightf (GL_LIGHT0,GL_SPOT_EXPONENT,v);

default:

(0,0,-1)

180

0.0

glLightf(GL_LIGHT0,GL_CONSTANT_ATTENUATION,a);

glLightf(GL_LIGHT0,GL_LINEAR_ATTENUATION,b);

glLightf(GL_LIGHT0,GL_QUADRATIC_ATTENUATION,c);

– distance attenuation:

default:

OpenGL: lights!

•

For each light, we set the position:

glLightfv(GL_LIGHT0,GL_POSITION,v);

– If it is a positional light,

v = {x,y,z,1}

– If it is a directional light, (“infinite distance")

v = {x,y,z,0}

OpenGL: lights!

•

For each light, we set the position :

•

Note: the position of the lights is multiplied by

the MODEL_VIEW matrix

glLightfv(GL_LIGHT0,GL_POSITION,v);

Lighting equation

n

specular

material

specular

light

k

H

N

I

⋅

⋅

(

ˆ

⋅

ˆ

)

+

⋅

⋅

⋅

k

(

L

ˆ

N

ˆ

)

I

_luight

_diffuse

_material

_diffuse

+

⋅

_material

_ambient

ambient

light

k

I

emission

material

k

+

=

tot

I

light

attenuatio

n

f

⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

=

min

1

₂

,

1

L

3

L

2

1

c

d

c

d

c

f

_light

_attenuatio

_n

effect

spotlight

f

⋅

(

L

spot

spot

spot

)

f

=

f

,

,

,

OpenGL: materials!

•

Let us set the parameters of the materials:

–

the colors:

glMaterialfv(face, GL_AMBIENT, colorvec);

glMaterialfv(face, GL_EMISSION, colorvec);

glMaterialfv(face, GL_DIFFUSE, colorvec);

glMaterialfv(face, GL_SPECULAR, colorvec);

glMaterialf (face, GL_SHININESS, intval);

– The specular exponent:

"GL_FRONT"

shortcut: we can use

asdasdsadasdasd

To set both colors to the same value

Other option: Color - Material

glEnable(GL_COLOR_MATERIAL);

activate:

use:

glColorMaterial(face, mode);

glColorMaterial(GL_FRONT, GL_DIFFUSE);

e.g.: when we set

The diffuse color of the material will be the

(otherwise ignored) current color

Two-sided Lighting

glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,1);

glColorMaterial3f(

GL_BACK

, ... );

glColorMaterial3f(

GL_FRONT

, ... );

glColorMaterial3f(

GL_FRONT_AND_BACK

, ... );

activation: