Lighting and Shading - TU Wien€¦ · Lighting and Shading Werner Purgathofer. Shading in the Rendering Pipeline raster image in pixel coordinates 2 clipping + homogenization. object

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

Werner Purgathofer 3

light sourcesbasic model

ambient lightdiffuse shadingspecular highlights

shading interpolationGouraud ShadingPhong Shading

Illumination


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

Light Sources


Surface Lighting Effects

diffuse reflection

specular reflection

transparency

reflections fromother surfaces


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


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

adambdiff IkL =


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


Lambert's Law

L = I ⋅ cos θwhen consideringthe material:

L = kd ⋅ I ⋅ cos θ

kd … diffuse coefficient

I … light source intensityL … pixel color

θθ


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


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


total diffuse reflection

Ambient plus Diffuse Reflection

Ldiff = kaIa + kdI(n⋅l)(ambient only)


Specular Highlights

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


reflection of incident light around specular-reflection angle

empirical Phong model

Specular Reflection Model

Lspec = ks ⋅ I ⋅ cospσ

θl

n

θr

σ v

(1)


Specular Reflection Coefficient p

0° 30° 60° 90°

1

0.5

0

σpcosσcos

(1)8



0° 30° 60° 90°

1

0.5

0

σpcosσcos

(1)864128256



0° 30° 60° 90°

1

0.5

0

σpcosσcos



σcos

σ64cos

σ256cos

σpcosp=1

p=2

p=4

p=16

p=64


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

Werner Purgathofer / Computergraphik 1 21

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


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


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


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


Diffuse and Specular Reflection

[ ]∑ ⋅+⋅+=N

i=1

pisidiaa hnklnkIIkL )()(

ambient ambient + diffuseambient + diffuse

+ specular

© Tong Lai Yu© James Tasker


Diffuse and Specular Reflection

[ ]∑ ⋅+⋅+=N

i=1

pisidiaa hnklnkIIkL )()(

ambient ambient + diffuseambient + diffuse

+ specular


Other Aspects

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


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

single intensity for each polygonflat Gouraud

Polygon-Rendering Methods


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


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


Gouraud Shading

L1 L3

L2

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



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’


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

−−


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


Problems of Gouraud Shading

darkdark

dark


Problems of Gouraud Shading

© Akiyoshi Kitaoka


Gouraud Shading Results

no intensity discontinuitiesMach bands due to linear intensity interpolationproblems with highlights

flat Gouraud

© Camillo Trevisan


Phong Shading

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

darklight

dark

darklight

dark


Phong Shading Principle

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

P


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


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

−−


Phong Shading

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

better highlightsless Mach bandingmore costly

© Camillo Trevisan

Werner Purgathofer / Computergraphik 1 44

Flat/Gouraud/Phong Comparison

© Paul Heckbert© Paul Heckbert

Documents

Lighting and Shading - TU Wien€¦ · Lighting and Shading Werner Purgathofer. Shading in the Rendering Pipeline raster image in pixel coordinates 2 clipping + homogenization. object