Environment Mapping CSE - PowerPoint Presentation

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Environment MappingCSE 5542 – Roger Crawfis

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Natural illumination

People perceive materials more easily under natural illumination than simplified illumination.

Images courtesy Ron Dror and Ted Adelson

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Natural illumination

Natural illumination is very expensive compared to using simplified

illumination (take CSE

5543).

directional source

natural illumination

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Environment MappingDetermine reflected ray.

Look-up direction from a sphere-map.

Reflection only depends

on the direction, not the position.

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Environment MappingWe can also encode

the reflected directions using several other formats.Greene, et al suggested a cube. This has the advantage that it can be constructed by six normal renderings.

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Environment MappingCreate six views from the shiny object’s centroid.When scan-converting the object, index into the appropriate view and pixel.

Use reflection vector to index.Largest component of reflection vector will determine the face.

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Environment Mapping

Problems:

Reflection is about object’s centroid.

Okay for small objects and

and distant reflections.

N

N

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Environment MappingLatitude/LongitudeToo much distortion at poles

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Environment MappingCube Maps

Can be created with GPULow distortion

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Environment MappingCube Mapping

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Sphere Mapping

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Indexing Sphere Maps

Given the reflection vector

R

(s,t) on the spherical map

Problems:

Highly non-uniform sampling

Highly non-linear mapping

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Non-linear Mapping

Linear interpolation of texture coordinates picks up the wrong texture pixels

Use small polygons!

Correct

Linear

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Sphere Mapping

Can be easily created by photographing a mirrored sphere.

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Sphere Mapping

Miller and Hoffman, 1984

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Sphere MappingExample

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Parabolic MappingDual Paraboloid

Error

Support Region

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Parabolic Mapping

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Environment MappingApplicationsSpecular highlightsMultiple light sources

Reflections for shiny surfacesIrradiance for diffuse surfaces

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Specular Highlights

Sphere map on top

Result in the middle

Standard OpenGL lighting on the bottom.

Not needed with fragment shaders, … unless …

Still a nice technique for many lights.

View dependent.

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Chrome MappingCheap environment mappingMaterial is very glossy, hence perfect reflections are not seen.

Index into a pre-computed view independent texture.Reflection vectors are still view dependent.

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Chrome MappingUsually, we set it to a very blurred landscape image.Brown or green on the bottom

White and blue on the top.Normals facing up have a white/blue color

Normals facing down on average have a brownish color.

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Chrome MappingAlso useful for things like fire.The major point, is that it is not important what actually is shown in the reflection, only that it is view dependent.

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Diffuse Reflection

radiosity

(image intensity)

reflectance

(albedo/texture)

irradiance

(incoming light)

×

=

quake light map

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Lambertian

Surface

Diffuse Scattering

specular

reflection

diffuse reflection

Light everywhere

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2-Color Hemi-sphere Model

Sky Color

Ground Color

q

The 2-color hemi-sphere model from Lab1 was a very simple environment map for diffuse reflection.

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Model Elements

Sky Color

Final Color

Ground Color

Hemisphere Model

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Distributed Light Model

Hemisphere of possible incident light directions

Surface Normal

Microfacet Normal

- defines axis of hemisphere

q

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Irradiance environment maps

Illumination Environment Map

Irradiance Environment Map

L

n

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Example Hemi-sphere

Map

Environment map

(longitude/latitude)

Irradiance map

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Cube Map And Its Integral

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Spherical HarmonicsRoger CrawfisCSE 781

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Basis Functions are pieces of signal that can be used to produce approximations to a function

Basis

f

unctions

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We can then use these coefficients to reconstruct an approximation to the original signal

Basis

f

unctions

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We can then use these coefficients to reconstruct an approximation to the original signal

Basis

f

unctions

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Orthogonal Basis Functions

Orthogonal Basis Functions

These are families of functions with special properties

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Orthogonal Basis Functions

Space to represent dataDifferent spaces often allow for compression of coefficients

Lets look at one simple example of the following piece of data

Data

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Orthogonal Basis FunctionsStandard Basis

Coefficient for each discrete position

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DCTDiscrete Cosine Transform

Use Cosine waves as basis functions

1

cos

x

cos 2x

cos 3x

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Function Reconstruction with DCT

0.15

+ 0.25

=

- 0.3

=

k

cos x

cos 3x

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Function Reconstruction with DCTOnly needed 3 coefficients instead of 20!

Remaining coefficients are all 0

Most of the time data not perfect

Obtain good reconstruction from few coefficients

Arbitrary function conversion requires projection

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Real spherical harmonics

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Reading SH

diagrams

–

+

Not this

direction

This

direction

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Reading SH

d

iagrams

–

+

Not this

direction

This

direction

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The SH functions

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The SH functions

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Spherical harmonics

-1

-2

0

1

2

0

1

2

m

l

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Examples of reconstruction

Displacement mapping on the sphere

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An example

Take a function comprised of two area light sourcesSH project them into 4 bands = 16 coefficients

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Low frequency light source

We reconstruct the signal

Using only these coefficients to find a low frequency approximation to the original light source

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SH lighting for diffuse objectsAn Efficient Representation for Irradiance Environment Maps

, Ravi Ramamoorthi

and Pat

Hanrahan

, SIGGRAPH 2001

AssumptionsDiffuse surfaces

Distant illumination No shadowing, interreflection

irradiance is a function of surface normal

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Spherical harmonic expansionExpand lighting (L), irradiance (E) in basis functions

= .67

+ .36

+ …

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Analytic irradiance formula

Lambertian surface acts like low-pass filter

0

0

1

2

cosine term

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9 parameter approximation

Exact image

Order 0

1 term

RMS error = 25 %

-1

-2

0

1

2

0

1

2

l

m

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9 Parameter Approximation

Exact image

Order 1

4 terms

RMS Error = 8%

-1

-2

0

1

2

0

1

2

l

m

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9 Parameter Approximation

Exact image

Order 2

9 terms

RMS Error = 1%

For any illumination, average

error < 3% [Basri Jacobs 01]

-1

-2

0

1

2

0

1

2

l

m

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Comparison

Incident

illumination

300x300

Irradiance map

Texture: 256x256

Hemispherical

Integration 2Hrs

Irradiance map

Texture: 256x256

Spherical Harmonic

Coefficients 1sec

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RenderingIrradiance approximated by quadratic polynomial

Surface Normal vector

column 4-vector

4x4 matrix

(depends linearly

on coefficients L

lm

)

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matrix form

c

1

L

22

c

1

L

2-2

c

1

L

21

c

2

L

11

c

1

L

2-2

-c

1

L

22

c

1

L

2-1

c

2

L

1-1

c

1

L

21

c

1

L

2-1

c

3

L

20

c

2

L

10

c

2

L

11

c

2

L

1-1

c

2

L

10

c

4

L

00 –

c

5

L

20

M =

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Complex geometry

Assume no shadowing: Simply use surface normal

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Cool!

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IN4151 Introduction 3D graphics63

Diffuse environment shading

received radiance is function of accessability

specular reflection

diffuse reflection

Need integration over environment map

For diffuse reflection scaled by cosinus

Index in filtered versions of map

ambient occlusion

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A Skin Texture Shader

Skin appears softer than Lambertian

reflectance because of subsurface scattering

Seeliger

lighting model

I

= (N L

) / (

N



L

+ N V )

Implement as a texture shaders = N



L

t

=

N



V

C = s/(s

+t )