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7M836 Animation & Rendering

Illumination models, light sources, reflection shading

Arjan Kok

a.j.f.kok@tue.nl

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Graphics pipeline

Geometric model Viewing

Camera parameters

Light sources,materials

Shading

Visible surface determination

Rasterize

Raster display

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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

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Illumination models

• Model(s) needed for

• Emission of light

• Distribution of light in scene

• Desired model requirement

• Accurate

• Efficient to compute

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Illumination models

• Local illumination

• Direct illumination

• Emission of light sources

• Scattering at surfaces

• Global illumination

• Shadows

• Refraction

• Interreflection

• (Ray tracing + Radiosity)

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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)

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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

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Point light source

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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

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Directional light source

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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

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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

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Spot light source

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Spot light source

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Other light sources

• Linear light sources

• Area sources

• Spherical lights

• …

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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

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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

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Diffuse reflection

• Incoming light is reflected equally in all directions

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

viewer

surface

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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

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Specular reflection

• Models reflections of shiny surfaces

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Specular reflection

• Shininess depends on roughness surface

• Incident light is reflected unequally in all directions

• Reflection strongest near mirror angle

very shiny less shiny

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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

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Specular reflection / Phongin

crea

sing

n

increasing ks

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Emission

• Emission IE represents light that is emanated directly by surface

• Used for light sources

Emission ≠ 0

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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

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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

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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

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Only emission and ambient

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Including diffuse reflection

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Including specular reflection

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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

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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

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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

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Flat shading

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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

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Gouraud shading

I1

I2

I3

ys

IA IB

21A II1I

21B II1I

21

s1

yyyy

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s1

yyyy

IP

BAP II)1(I

BA

PA

xxxx

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Gouraud shading

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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

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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

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Phong shading

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Phong shading

• Advantages

• Nice highlights

• Disadvantages

• Computational expensive

• Normal interpolation and application of illumination model for each pixel

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Shading samengevat

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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

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Grafische pijplijn

Geometric model Viewing

Camera parameters

Light sources,materials

Shading

Visible surface determination

Rasterize

Raster display

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Z-buffer & Gouraud shading

modelingtransformation

viewingtransformation

trivialaccept/reject

z-bufferprojection

lighting

clipping display

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Z-buffer & Phong shading

modelingtransformation

viewingtransformation

trivialaccept/reject

z-bufferlighting

projectionclipping display

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What is still missing?

• Shadows

• Area light sources

• “Real” mirroring

• Transparency

• Indirect diffuse reflection

• Influence of atmosphere

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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

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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

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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

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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

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What is still missing?

• Area light sources

• “Real” mirroring

• Transparency

• Indirect diffuse reflection

• Influence of atmosphere