Paper Summaries Any takers? Material Properties 2 Assignments - - PDF document

1 Material Properties 2

Paper Summaries

• Any takers?

Assignments

• Checkpoint 2

– Due tonight

• Well….maybe Tuesday

– Any questions?

Projects

• Proposals

– Should receive feedback via e-mail by Monday. – Grading

• ACCEPTED
• CONDITIONALLY ACCEPTED
• PLEASE RESUBMIT WITH MORE INFO

Plan for today

• Material Properties

– Bi-directional reflectance distribution functions (BRDFs) – Advanced Illumination Models – Beyond BRDFs

• Checkpoint 3 of the ray tracer
• Ray tracer problem session

Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

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Shading

• Computing the light that leaves a point
• Shading point - point under investigation
• Illumination model - function or algorithm used to

describe the reflective characteristics of a given surface.

• Shading model – algorithm for using an illumination

model to determine the color of a point on a surface.

• For efficiency’s sake, most illumination models are

approximations.

BRDF

• Bi-directional Reflectance Function

) , , , (

r r i i r

f BRDF θ φ θ φ =

At a given point, gives relative reflected illumination in any direction with respect to incoming illumination coming from any direction; Note: The θ’s are elevation, ϕ’s are measured about the surface normal. The i’s refer to the incident ray; the r’s to the reflected ray.

BRDF Geometry BRDF

• Can return any positive value.
• Generally wavelength specific.

) , , , , ( λ θ φ θ φ

r r i i r

f BRDF =

Anisotropic Models

• Anisotropy

– Isotropic - surfaces reflect equally from any direction of view – Anisotropic - reflection varies not only with angle of incidence, but also with the angle of the incident light w.r.t some viewing angle.

• Surfaces considered to possess an intrinsic grain
• Examples: satin, velvet, hair, brushed aluminum

Anisotropic Models

• Anisotropic reflection -- example

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Anisotropic Models

• Ward Model [Ward92]

– Designed for both accuracy and ease of use – Includes model for anisotropic reflection

Anisotropic Models

• Ward Model - Isotropic

specular 2 / ) (tan diffuse

) 4 cos cos 1 (

2 2

πα δ θ ρ π ρ ρ

α γ −

• +

= e

s d

Anisotropic Model

• Ward Model

– ρd - Diffuse reflectance coefficient (can vary with wavelength) – ρs - Specular reflectance coefficient (can vary with wavelength) – α - Standard deviation of surface slope

Anisotropic Models

• Ward Model -- anisotropic

specular )) / sin / (cos (tan diffuse

) 4 cos cos 1 (

2 2 2 2 2

y x s d

y x

e α πα δ θ ρ π ρ ρ

α φ α φ γ + −

• +

=

Anisotropic Models

• Ward Model w/ ansiotropy

– αx - Standard deviation of surface slope in x- direction – αy - Standard deviation of surface slope in y- direction

Ward’s Anisotropic Model

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Anisotropic Models

• Ward Model - example

Photo Isotropic Anisotropic

Anisotropic Models

• Other anisotropic models (all based on

physics)

– [Kajia85] – [Poulin90] – [He91]

BRDF

• Simplifying Assumptions wrt the BRDF

– Light enters and leaves from the same point.

• Not necessarily true
• Subsurface scattering
• Skin, marble

– Light of a given wavelength will only reflect back light of that same wavelength

• Not necessarily true
• Light Interference
• Oily patches, peacock feathers

Subsurface Scattering

Jensen, et al 2001

Subsurface Scattering

• Example: Skin

Blevins,2001

bidirectional surface scattering distribution function (BSSDF)

• Relates outgoing reflectance in a given

direction (at a given point) to the incoming luminance arriving at another point.

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bidirectional surface scattering distribution function (BSSDF)

Outgoing luminance at xo in the direction

• f wo

incoming luminance at xi in the direction

• f wi

BSSDF When xo = = xi the BSSDF is simply a BRDF

BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

Summary

• Advanced models of reflection

– Anisotropic Models – BSSDF – subsurface scattering – Break.