1 7M836 Animation & Rendering Illumination models, light sources, reflection shading Arjan Kok...

1

7M836 Animation & Rendering

Illumination models, light sources, reflection shading

Arjan Kok

a.j.f.kok@tue.nl

2

Graphics pipeline

Geometric model Viewing

Camera parameters

Light sources,materials

Shading

Visible surface determination

Rasterize

Raster display

3

Illumination

• Illumination model• Illumination (and therefore color) of point on surface is

determined by simulation of light in scene• Illumination model is approximation of real light

transport

• Shading method• determines for which points illumination is computed• determines how illumination for other points is

computed

4

Illumination models

• Model(s) needed for

• Emission of light

• Distribution of light in scene

• Desired model requirement

• Accurate

• Efficient to compute

5

Illumination models

• Local illumination

• Direct illumination

• Emission of light sources

• Scattering at surfaces

• Global illumination

• Shadows

• Refraction

• Interreflection

• (Ray tracing + Radiosity)

6

Light source

• IL (x, y, z, θ, φ, λ)

• Intensity of energy

• of light source L

• arriving at point (x, y, z)

• from direction (θ, φ)

• with wavelength λ

• Complex

• Simpler model needed

(x,y,z)

7

Point light source

• Emits light equally in all directions

• Parameters

• Intensity I0

• Position P (px,py,pz)

•

• Attenuation factor(kc, kl, kq) for distance (d) to light source

• 2

qlc

0L dkdkk

II

d

P

0L II

8

Point light source

9

Direction light source

• Emits light in one direction

• Can be regarded as point light source at infinity

• E.g. sun

• Parameters

• Intenslity I0

• Direction D (dx,dy,dz)

• IL = I0

D

10

Directional light source

11

Spot light source

• Point light source with direction

• E.g. Spot light

• Parameters

• Intensity I0

• Position P (px,py,pz)

• Direction D (dx,dy,dz)

• “Hotspot” angle θ

• Maximum angle φ

• Exponent e

d

PD

γθ

φ

12

Spot light source

• if γ ≤ θ

• if θ < γ ≤ φ

• if φ < γ

• Attenuation factor

)2

(cosII e

0L

0IL θ φ

0L II

2

qlc dkdkk1

13

Spot light source

14

Spot light source

15

Other light sources

• Linear light sources

• Area sources

• Spherical lights

• …

16

Reflection

• Rs (θ, φ, γ, ψ, λ)

• Amount of energy,

• arriving from direction (θ, φ),

• that is reflected in direction (γ, ψ)

• with wavelength λ

• Ideal

• Describe this function for all combinations of θ, φ, γ, ψ and λ

• Impossible, simpler model(s) needed

(θ, φ)(γ, ψ)

λ

17

Reflection model

• Total intensity on point reflected in certain direction is determined by:

• Diffusely reflected light

• Specularly reflected light

• Emission (for light sources)

• Reflection of ambient light

• Intensity not computed for all wavelengths λ, only for R, G and B

18

Diffuse reflection

• Incoming light is reflected equally in all directions

• Amount of reflected light depends only on angle of incident light

viewer

surface

19

Diffuse reflection

• Lambert’ law: Reflected energy from a surface is proportional to the cosine of the angle of direction of incoming light and normal of surface

• Id = kdILcos(θ)

• kd is diffuse reflection coefficient

viewer

surface

20

Specular reflection

• Models reflections of shiny surfaces

21

Specular reflection

• Shininess depends on roughness surface

• Incident light is reflected unequally in all directions

• Reflection strongest near mirror angle

very shiny less shiny

22

Specular reflection / Phong

• Light intensity observed by viewer depends on angle of incident light and angle to viewer

• Phong model: Is = ksILcosn(α)

• ks is specular reflection coefficient

• n is specular reflection exponent

α

23

Specular reflection / Phongin

crea

sing

n

increasing ks

24

Emission

• Emission IE represents light that is emanated directly by surface

• Used for light sources

Emission ≠ 0

25

Ambient light

• Even thought parts of scene are not directly lit by light sources, they can still be visible

• Because of indirect illumination• “Ambient” light IA is an approach to this indirect

illumination• Ambient light is independent of light sources and viewer

position• Conbtribution of ambient light I = kAIA

• kA is ambient reflection coefficient• IA is ambient intensitity (constant over scene)

• Indirect illumination can be computed much better: e.g. radiosity

26

Total illumination Phong model

• Total intensity Itotal at point P seen by viewer is

i

i

n

SiDiAAEtotal )(cosk)cos(kIIkII

α0

θ0

θ1

α1

27

Total illumination Phong model

• In previous formula kA, kD dependent on wavelength (different values for R, G and B)

• Often division into color and reflection coefficient of surface

where:• 0 ≤ kA, kD, kS ≤ 1• CA is ambient reflected color of surface• CD is diffuse reflected color of surface• Cs is specular reflected color of surface

i

i

n

ssiDDiAAAEtotaal cosCkcosCkIICkII

28

Only emission and ambient

29

Including diffuse reflection

30

Including specular reflection

31

Illumination model

• More advanced models:

• Allows for angle between incident light and surface normal for specular reflection (Fresnel’s law)

• Better models for surface roughness

• Beter model for wavelength dependent reflection

32

Shading

• Illumination model computes illumination for a point on surface

• But how do we compute the illumination for all points on all (visible) surfaces?

• Shading methods:

• Flat shading

• Gouraud shading

• Phong shading

33

Flat shading

• Determine illumination for one point on polygon

• Use this illumination for all points on polygon

• Disadvantages:

• Does not account for changing direction to light source over polygon

• Does not account for changing direction to eye over polygon

• Discontinuity at polygon boundaries (when curved surface approximated by polygon mesh

34

Flat shading

35

Gouraud shading

• Based on interpolation of illumination values

• Compute illumination for vertices of polygon

• Algorithm

• for all vertices of polygon

• get vertex normal

• compute vertex illumination using this normal

• for all pixels in projection of polygon

• compute pixel illumination by interpolation of vertex illumination

36

Gouraud shading

I1

I2

I3

ys

IA IB

21A II1I

21B II1I

21

s1

yyyy

31

s1

yyyy

IP

BAP II)1(I

BA

PA

xxxx

37

Gouraud shading

38

Gouraud shading

• Advantages

• Interpolation is simple, hardware implementation

• Continuous shading over curved surfaces possible

• Disadvantages

• Subtle illumination effects (e.g. highlights) require high subdivision of surface in very small polygons

39

Phong shading

• Based on normal interpolation

• Compute illumination for each point of polygon

• Algorithm

• for each vertex of polygon

• get vertex normal

• for each pixel in projection of polygon

• compute point normal by interpolation of vertex normals

• compute illumination using interpolated normal

40

Phong shading

41

Phong shading

• Advantages

• Nice highlights

• Disadvantages

• Computational expensive

• Normal interpolation and application of illumination model for each pixel

42

Shading samengevat

43

Shading

• Flat shading

• 1x application of illumination model per polygon

• 1 color per polygon

• Gouraud shading

• 1x application of illumination model per vertex

• Interpolated colors

• Phong shading

• 1x application of illumination model per pixel

• Nice highlightsIncrease computation time

Increase quality

44

Grafische pijplijn

Geometric model Viewing

Camera parameters

Light sources,materials

Shading

Visible surface determination

Rasterize

Raster display

45

Z-buffer & Gouraud shading

modelingtransformation

viewingtransformation

trivialaccept/reject

z-bufferprojection

lighting

clipping display

46

Z-buffer & Phong shading

modelingtransformation

viewingtransformation

trivialaccept/reject

z-bufferlighting

projectionclipping display

47

What is still missing?

• Shadows

• Area light sources

• “Real” mirroring

• Transparency

• Indirect diffuse reflection

• Influence of atmosphere

48

Shadow

• Illumination with shadows

• Si = 0 if light of source i is blocked= 1 if light of source i is not blocked

• Several methods to compute shadow

• Shadow buffer

• Ray casting

• Shadow volumes

• ..

i

i

n

ssiDDiiAAAEtotaal cosCkcosCkSIICkII

49

Shadow buffer

• Based on z-buffer algorithm

• Rendering in 2 steps

• Z-buffer from light source (= shadow buffer) to compute shadows

• During “normal” rendering, when computing illumination of point read from shadow buffer if point is lit by light source

50

Shadow buffer – step 1

• “Render” scene with light source position as viewpoint and store depth results in depth buffer

• sbuffer(x,y) = minimum z-value after projection of all polygons on (x,y)

3 3 5 _5_

z

3

0

5

51

Shadow buffer – step 2

• At rendering, when computing illumination of point (x,y,z), transform point into light source coordinate system, resulting in point (x’,y’,z’)

• Si = 1 als z’ <= sbuffer(x’,y’)= 0 als z’ > sbuffer(x’,y’)

3 3 5 _5_

S=0

S=1 S=1

S=1

52

What is still missing?

• Area light sources

• “Real” mirroring

• Transparency

• Indirect diffuse reflection

• Influence of atmosphere