Lighting and Shading - TU Wien€¦ · Lighting and Shading Werner Purgathofer. Shading in the...

Einführung in Visual Computing186.822

Lighting and Shading

Werner Purgathofer

Shading in the Rendering Pipeline

2raster image in pixel coordinates

clipping + homogenization

object capture/creation

modelingviewing

projection

rasterizationviewport transformation

shading

vertex stage(„vertex shader“)

pixel stage(„fragment shader“)

scene in normalized device coordinates

transformed vertices in clip space

scene objects in object space

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light sourcesbasic model

ambient lightdiffuse shadingspecular highlights

shading interpolationGouraud ShadingPhong Shading

Illumination

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directional lightpoint light source (sometimes directional)distributed light source (“area light source”)

Light Sources

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Surface Lighting Effects

diffuse reflection

specular reflection

transparency

reflections fromother surfaces

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Basic Illumination Models

empirical modelslighting calculations

surface properties (glossy, matte, opaque,…)background lighting conditionslight-source specificationreflection, absorption

ambient light (background light) Iaapproximation of global diffuse lighting effects

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Ambient Light Reflectionconstant over a surfaceindependent of viewing directiondiffuse-reflection coefficient kd (0≤ kd ≤1)

adambdiff IkL =

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shaded surfaces generate a spatial impression

the flatter light falls on a surface,the darker it will appear

therefore:we need the incident light direction

or the position of the (point) light source

Illumination and Shading

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Lambert's Law

L = I ⋅ cos θwhen consideringthe material:

L = kd ⋅ I ⋅ cos θ

kd … diffuse coefficient

I … light source intensityL … pixel color

θθ

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ideal diffuse reflectors (Lambertian reflectors)brightness depends on orientation of surface

Lambert’s cosine law

Lambertian (Diffuse) Reflection

Ldiff = kd ⋅ I ⋅ (n⋅l)l

n

θ cos θ= n∙l

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varying kd

Diffuse Reflection Coefficient

result for varying values of kd ( Ia = 0 )

kd=0 kd=0.3 kd=0.7 kd=1

12

total diffuse reflection

(sometimes kafor ambient light)

Ambient plus Diffuse Reflection

Ldiff = kaIa + kdI(n⋅l)

ka=1

ka=0.6

ka=0.2

ka=0

kd=0 kd=0.3 kd=0.7 kd=1

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total diffuse reflection

Ambient plus Diffuse Reflection

Ldiff = kaIa + kdI(n⋅l)(ambient only)

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Specular Highlights

this area must be lighter than the shading model calculates, because the light source is reflected directly into the viewer's eye

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reflection of incident light around specular-reflection angle

empirical Phong model

Specular Reflection Model

Lspec = ks ⋅ I ⋅ cospσ

θl

n

θr

σ v

(1)

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Specular Reflection Coefficient p

0° 30° 60° 90°

1

0.5

0

σpcosσcos

(1)8

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Specular Reflection Coefficient p

0° 30° 60° 90°

1

0.5

0

σpcosσcos

(1)864128256

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Specular Reflection Coefficient p

0° 30° 60° 90°

1

0.5

0

σpcosσcos

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Specular Reflection Coefficient p

σcos

σ64cos

σ256cos

σpcosp=1

p=2

p=4

p=16

p=64

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Specular Reflection Coefficient

empirical Phong modelp large ⇒ shiny surfacep small ⇒ dull surface

Lspec = ks ⋅ I ⋅ cospσ

shiny surface (large p) dull surface (small p)

θl n

θr

θl n

θr

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Fresnel Specular Reflection Coefficient

Fresnel’s laws of reflectionspecular reflection coefficient W(θ)

σθ plspec IWL cos)(=

specular reflection coefficient as a function of angle of incidence for different materials

silver

gold

dielectric (glass)

W(θ)

θ

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calculation of R:

Simple Specular Reflection

W(θ) ≈ constant for many opaque materials (ks)

r + l = (2n∙l)nr = (2n∙l)n – l

Lspec = ks∙I∙(v∙r)p

θl n

θr

σ v l

nr

n∙l

l

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Specular Reflection Results

Lspec = ks∙I∙(v∙r)p

ks=1

ks=0.7

ks=0.3

ks=0

p=5 p=10 p=40 p=99

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Simplified Specular Reflection

simplified Phong model with halfway vector h→

vlh+=

|| l + v ||

Lspec = ks∙I∙(v∙r)p Lspec = ks∙I∙(n∙h)p

this revised model is called“Blinn-Phong Shading”

ln

rσ v

αh

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Diffuse and Specular Reflection

[ ]∑ ⋅+⋅+=N

i=1

pisidiaa hnklnkIIkL )()(

ambient ambient + diffuseambient + diffuse

+ specular

© Tong Lai Yu© James Tasker

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Diffuse and Specular Reflection

[ ]∑ ⋅+⋅+=N

i=1

pisidiaa hnklnkIIkL )()(

ambient ambient + diffuseambient + diffuse

+ specular

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Other Aspects

intensity attenuation with distanceanisotropic light sourcestransparency (Snell’s law)atmospheric effectsshadows…

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application of illumination model to polygon renderingconstant-intensity shading (flat shading)

single intensity for each polygonflat Gouraud

Polygon-Rendering Methods

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the shading of a polygon is not constant, because it normally is only an approximation of the real surface ⇒ interpolation

Gouraud shading: intensitiesPhong shading: normal vectors

Polygon Shading: Interpolation

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intensity-interpolationdetermine average unit normal vector at each polygon vertexapply illumination model to each vertexlinearly interpolate vertex intensities

Gouraud Shading Overview

∑

∑

=

== N

kk

N

kk

V

n

nn

1

1

V

nV

n4

n3

n2n1

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Gouraud Shading

L1 L3

L2

1. find normal vectors at corners and calculate shading (intensities) there: Li

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1. find normal vectors at corners and calculate shading (intensities) there: Li

2. interpolate intensities along edges linearly: L, L’

Gouraud Shading

L1 L3

L2

L = t·L1 + (1–t)·L2 L’ = u·L2 + (1–u)·L3

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1. find normal vectors at corners and calculate shading (intensities) there: Li

2. interpolate intensities along edges linearly: L, L’3. interpolate intensities along scanlines linearly: Lp

Gouraud Shading

L1 L3

L2

L = t·L1 + (1–t)·L2 L’ = u·L2 + (1–u)·L3

v·L + (1–v)·L’

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Gouraud Shading

interpolating intensities

221

411

21

244 Lyy

yyLyy

yyL −

−+−

−= 5

45

44

45

5 LxxxxLxx

xxL ppp −

−+−

−=

scan line1

2

3

54 p21

41

yyyy

−−

21

24

yyyy

−−

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Gouraud Shading

incremental update

221

11

21

2 Lyyyy

Lyyyy

L −−

+−−

=21

12

yyLL

LL −−

+=′

scan linesL1 L

L2

L´y

y−1

highlights can get lost or grow

corners on silhouette remain

Mach band effect is visible at some edges

darklight

dark

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Problems of Gouraud Shading

darkdark

dark

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Problems of Gouraud Shading

© Akiyoshi Kitaoka

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Gouraud Shading Results

no intensity discontinuitiesMach bands due to linear intensity interpolationproblems with highlights

flat Gouraud

© Camillo Trevisan

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Phong Shading

instead of intensities the normal vectors are interpolated, and for every point the shading calculation is performed separately

darklight

dark

darklight

dark

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Phong Shading Principle

normal-vector interpolationdetermine average unit normal vector at each polygon vertexlinearly interpolate vertex normalsapply illumination model along each scan line

P

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Phong Shading Overview

1. normal vectors at corner points2. interpolate normal vectors along the edges3. interpolate normal vectors along scanlines

& calculate shading (intensities) for every pixel

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Phong Shading Normal Vectors

normal-vector interpolation

221

1 nyyyy

−−

+

121

2 nyyyy

n −−= +

scan line

n1

n

n2

y21

1

yyyy

−−

21

2

yyyy

−−

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Phong Shading

incremental normal vector update along and between scan linescomparison to Gouraud shading

better highlightsless Mach bandingmore costly

© Camillo Trevisan

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Flat/Gouraud/Phong Comparison

© Paul Heckbert© Paul Heckbert