taku komuracomputer graphics local illumination and shading computer graphics – lecture 10 taku...

Taku Komura Computer Graphics

Local Illumination and Shading

Computer Graphics – Lecture 10

Taku [email protected]

Institute for Perception, Action & Behaviour


Last Lecture… Hidden Surface Removal

Back face culling Painter’s algorithm BSP Tree Z-buffer


Back Face CullingLight(L), view (V), and normal(N)

Cull faces according to L.N and V.N

Cull if V.N < 0

Cull if L.N > 0

(if only one light,

and no ambient light)


Turning on and off Z-buffer in OpenGL

ON OFF


Today is about calculating the color of objects

The incident light • Position of light source• Direction • Color

The object • Reflectance

Viewer • Position


Overview Illumination (how to calculate the color) Shading (how to color the whole surface)? BRDF (how to simulate the reflection of real objects)


Illumination

Simple 3 parameter model The sum of 3 illumination terms:

• Ambient : 'background' illumination

• Specular : bright, shiny reflections

• Diffuse : non-shiny illumination and shadows

Object

Light source

(here point light source)

surface normal (specifies surface orientation)

'Virtual' camera


Ambient Lighting Light from the environment

light reflected or scattered from other objects

simple approximation to complex 'real-world' process

Result: globally uniform colour for object

— I = resulting intensity

— Ia = light intensity

— ka = reflectance

Object

Uniform Light source

a

a

k

I

ereflectanc

Intensity Light

I

aaIkI

N

camera

Example: sphere


Diffuse Lighting

• Also known as Lambertian reflection– considers the angle of incidence of light on surface

(angle between light and surface normal)

– Result: lighting varies over surface with orientation to light

Object

Infinite point light source

N

Ln

tyreflectivi diffuse:

)(cos

IntensityLight

d

n

p

k

LN

I

I

No dependence on camera angle!

Example: sphere(lit from left)

cosdpkII


Specular Lighting

• Direct reflections of light source off shiny object– specular intensity n = shiny

reflectance of object

– Result: specular highlight on object

Object

N

I = output colorR

n = camera position

α : angle between Rn and S

R (Reflection)

Infinite point light source

Ln

No dependence on object colour.

p Intensity Light Iα

nspkII )cos(


Specular Light


Combined Lighting Models

• Summing it altogether : Phong Illumination Model

+ + =

Ambient(colour)

Diffuse(directional)

Specular(highlights)

Rc

]coscos[ n

sdpaa kkIkII


When you implement it…

Use dot product of the vectors instead of calculating the angles

])()([1

nsd

lights

ppaa RVkLNkIkII

N

L

V

R

,

: Vector from the surface to the viewer

: Normal vector at the colored point

: Reflection vector

: Vector from the light source towards the colored point

Object

N

R

Ln

α

V


Color

• You do the above computation for Red, Green and Blue color

• Finally color the pixel by the RGB color

])()([1

nRs

Rd

lights

p

Rp

Ra

Ra

R RVkLNkIkII

])()([1

nGs

Gd

lights

p

Gp

Ga

Ga

G RVkLNkIkII

])()([1

nBs

Bd

lights

p

Bp

Ba

Ba

B RVkLNkIkII


Demo applets

http://www.cs.unc.edu/%7Eclark/courses/comp14-spr04/code/SphereLightApplet.html

http://www.cs.auckland.ac.nz/~richard/research-topics/PhongApplet/PhongDemoApplet.html


Overview Illumination (how to calculate the color) Shading (how to color the whole surface)?


How often do we do the computation of illumination?

At all the points on the surface?

But usually we have normals only at the vertices

Depends on the shading model

– Flat Shading (once per polygon)

(less computation needed)

– Gouraud shading (for all the vertices of the polygon)

– Phong Shading (all the points)

(heavy computation needed)


Compute the color at the middle of the polygon All points in the same polygon are colored by the

same color

Flat Shading


Compute the color at each vertex first Compute the color inside the polygon by

interpolating the colors of the vertices composing the polygon

Gouraud Shading (Smooth Shading)


interpolating the normal vectors at the vertices Do the computation of illumination at each point in

the polygon

Phong Shading


Gouraud Shaded Floor Phong Shaded Floor

Gouraud shading is not good when the polygon count is low


interpolating the normal vectors at the vertices Do the computation of illumination at each point in

the polygon

Phong Shading


Problems with interpolation shading.

Problems with computing vertex normals.

A,B are shared by all polygons, but C is not shared by the polygon on the left.

-Shading information calculated to the right of C will be different from that to the left.

- Shading discontinuity.

Solution : ?

A

B

C


Problems with interpolation shading.

Problems with computing vertex normals.

Face surface normals and averaged vertex normals shown.

Solution:?


Exercise Draw a picture by Phong Shading by enhancing the

demo program I put up on the web. When doing the rasterization, you do the

computation of the illumination


Overview Illumination (how to calculate the color) Shading (how to color the whole surface)? BRDF (how to simulate the reflection of real objects)


What about real objects?

Phong Illumination model is popular but actually it is not accurate

True photorealism, requires more sophisticated and elaborate models of surface properties


Reflectance of objects

The way the light reflects depends on the physical characteristics of the surface

Its not uniform


Bidirectional Reflectance Distribution Function (BRDF)

The reflectance of an object can be represented by a function of the incident and reflected angles

This function is called the Bidirectional Reflectance Distribution Function (BRDF)

where E is the incoming irradiance and L is the reflected radiance


What affects the BRDF?

The way light reflecting over the surface The smoothness/roughness of the surface

Single reflection : if smooth, specular Multiple reflections : diffusive

The shadowing effect


Isotropic and Anisotropic BRDFs

Isotropic:

Can model by diffuse + specular reflection

Anisotripic

Brushed metal

Cannot model by diffuse + specular reflection


How to get the BRDF?

Measure Data

Use Analytical models Empirical models

Microfacet


Measuring the BRDF

Measured using a device called gonioreflectometer Casting light from various directions to the object, and

capturing the light reflected back


Problems with Measured BRDF

Includes a lot of error

Huge amount of time to capture

The data size is enormous 18 hours acquisition time, 30GB raw data Ngan et al. EGSR ’05

-> Fitting the acquired data into analytical models


Analytical models

Empirical models

Gouraud, Phong models or more complex models

Microfacet models

Assuming the surface is composed of a large number of micro mirrors

Each reflect light back to the specular direction


Microfacet Theory [Torrance & Sparrow 1967]

Surface modeled by tiny mirrors Value of BRDF at

— # of mirrors oriented halfway between and

where is the incoming direction, is the out going direction

— Modulated by Fresnel, shadowing/masking

[Shirley 97]


Examples : Satin


Examples : velvet


Summary Illumination model

Phong model

Shading Flat, Gouraud, Phong Shading

BRDF Measuring Analytical models

— Phong — Microfacet

taku komuracomputer graphics local illumination and shading computer graphics – lecture 10 taku...

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