06 lighting

8/6/2019 06 Lighting

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Lighting

Aaron Bloomfield

CS 445: Introduction to Graphics

Fall 2006


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Lighting Sogiven a 3-D triangle and a 3-D viewpoint,

we can set the right pixels

But what color should those pixels be?

If were attempting to create a realistic image, we

need to simulate the lighting of the surfaces inthe scene

Fundamentally simulation of physicsand optics

As youll see, we use a lot of approximations (a.k.ahacks) to do this simulation fast enough


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Definitions Illumination: the transport of energy (in particular,

the luminous flux of visible light) from light sourcesto surfaces & points

Note: includes directand indirect illumination

Lighting: the process of computing the luminousintensity (i.e., outgoing light) at a particular 3-D

point, usually on a surface

Shading: the process of assigning colors to pixels


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Definitions Illumination models fall into two categories:

Empirical: simple formulations that approximateobserved phenomenon

Physically-based: models based on the actual physicsof light interacting with matter

We mostly use empirical models in interactivegraphics for simplicity

Increasingly, realistic graphics are using

physically-based models


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Components of Illumination Two components of illumination: light sources and

surface properties

Light sources (or emitters)

Brightness

Spectrum of emittance (i.e, color of the light) Geometric attributes

Position

Direction

Shape

Directional attenuation


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Components of Illumination Surface properties

Reflectance spectrum (i.e., color of the surface)

Geometric attributes

Position

Orientation

Micro-structure

Common simplifications in interactive graphics

Only direct illuminationfrom emitters to surfaces

Simplify geometry of emitters to trivial case


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Types of lights and light sources Ambient

Diffuse Directional

Point

Area Spot

Specular

Phong

and then onto shading


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Ambient Light Sources Objects not directly lit are typically still visible

E.g., the ceiling in this room, undersides of desks

This is the result of indirect illumination fromemitters, bouncing off intermediate surfaces

Too expensive to calculate (in real time), so weuse a hack called an ambient light source

No spatial or directional characteristics; illuminates allsurfaces equally

Amount reflected depends on surface properties


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Ambient Light Sources For each sampled wavelength, the ambient light

reflected from a surface depends on

The surface properties

The intensity of the ambient light source (constant for allpoints on all surfaces )

Ireflected= kambientIambient


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Ambient Light Sources A scene lit only with an ambient light source:


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Diffuse Directional

Point

Area Spot

Specular

Phong



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Diffuse lighting types There are a number of diffuse lighting models

Minnaert

Toon

Oren-Nayar

Lambert

Etc.

Well belooking onlyat Lambert


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The Physics of Reflection Ideal diffuse reflection

An ideal diffuse reflector, at the microscopic level, isa very rough surface (real-world example: chalk)

Because of these microscopic variations, anincoming ray of light is equally likely to be reflected

in any direction over the hemisphere:

What does the reflected intensity depend on?


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Lamberts Cosine Law Ideal diffuse surfaces reflect according to

Lamberts cosine law:

The energy reflected by a small portion of a surface froma light source in a given direction is proportional to thecosine of the angle between that direction and the

surface normal These are often called Lambertian surfaces

Note that the reflected intensity is independent of

the viewing direction, but does depend on thesurface orientation with regard to the light source


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Lamberts Law


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Computing Diffuse Reflection The angle between the surface normal and the

incoming light is the angle of incidence:

Idiffuse= kd Ilightcos

In practice we use vector arithmetic:

Idiffuse= kd Ilight (n l)

nl


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Diffuse Lighting Examples We need only consider angles from 0 to 90

(Why?)

A Lambertian sphere seen at several differentlighting angles:

An animated gif


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Diffuse Directional

Point

Area Spot

Specular

Phong



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Directional Light Sources For a directional light source we make the

simplifying assumption that all rays of light fromthe source are parallel

As if the source is infinitely far awayfrom the surfaces in the scene

A good approximation to sunlight

The direction from a surface to the light source isimportant in lighting the surface

With a directional light source, this direction isconstant for all surfaces in the scene


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Directional Light Sources The same scene lit with a directional light source


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Diffuse Directional

Point

Area Spot

Specular

Phong



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Point Light Sources A point light source emits light equally in all

directions from a single point

The direction to the light from a point on a surfacethus differs for different points:

So we need to calculate anormalized vector to the lightsource for every point we light:

lplpd

=


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Point Light Sources Using an ambient and a point light source:

How can we tellthe differencebetween a point

light source anda directionallight source ona sphere?


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Point light vs. directional light


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Diffuse

Directional

Point

Area Spot

Specular

Phong



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Area light sources Area light sourcesdefine a 2-D emissive surface (usually a

disc or polygon)

Good example: fluorescent light panels Capable of generating soft shadows(why?)

From http://web.cs.wpi.edu/~emmanuel/courses/cs563/write_ups/zackw/realistic_raytracing.html


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Diffuse

Directional

Point

Area Spot

Specular

Phong



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Spot lights Spotlights are point sources whose intensity falls off

directionally.

Spotlight isjust in frontof the camera

Supported byOpenGL


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Diffuse

Directional

Point

Area Spot

Specular

Phong



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Specular lighting types There are a number of specular lighting models

WardIso

Toon

Blinn

Phong

CookTorr

Etc.

Well be

looking onlyat Phong


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Specular Reflection Shiny surfaces exhibit specular reflection

Polished metal

Glossy car finish

A light shining on a specular surface causes abright spot known as a specular highlight

Where these highlights appear is a function of theviewers position, so specular reflectance is view-dependent


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The Physics of Reflection

At the microscopic level a specular reflectingsurface is very smooth

Thus rays of light are likely to bounce off themicro-geometry in a mirror-like fashion

The smoother the surface, the closer it becomes toa perfect mirror

Polishing metal example (draw it)


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The Optics of Reflection

Reflection follows Snells Laws:

The incoming ray and reflected ray lie in a plane with the

surface normal

The angle that the reflected ray forms with the surfacenormal equals the angle formed by the incoming ray and

the surface normal:

l=

r


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Non-Ideal Specular Reflectance

Snells law applies to perfect mirror-likesurfaces, but aside from mirrors (and chrome)

few surfaces exhibit perfect specularity

How can we capture the softer reflections of

surface that are glossy rather than mirror-like?

One option: model the micro-geometry of thesurface and explicitly bounce rays off of it

Or


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Types of lights and light sources

Ambient

Diffuse

Directional

Point

Area Spot

Specular

Phong



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An Empirical Approximation

In general, we expect most reflected light to travelin direction predicted by Snells Law

But because of microscopic surface variations,some light may be reflected in a direction slightly

off the ideal reflected ray

As the angle from the ideal reflected ray increases,we expect less light to be reflected


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An Empirical Approximation

An illustration of this angular falloff:

How might we model this falloff?


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Phong Lighting

The most common lighting model in computergraphics was suggested by Phong:

( ) shinynlightsspecular IkI = cos

The nshiny term is a purelyempirical constant thatvaries the rate of falloff

Though this model has nophysical basis, it works(sort of) in practice


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Phong Lighting: The nshiny

Term

This diagram shows how the Phong reflectanceterm drops off with divergence of the viewing angle

from the ideal reflected ray:

What does this term control, visually?


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Calculating Phong Lighting

The cos term of Phong lighting can be computedusing vector arithmetic:

Vis the unit vector towards the viewer

Common simplification: Vis constant (implying what?)

Ris the ideal reflectance direction

An aside: we can efficiently calculate R

( ) shinynlightsspecular RVIkI =

LNLNR 2 =


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Calculating TheR Vector

This is illustrated below:

LNLNR 2 =

NLNLR 2 =+


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Phong Examples

These spheres illustrate the Phong model as L andnshinyare varied:


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The Phong Lighting Model

Our final empirically-motivated model for theillumination at a surface includes ambient, diffuse,

and specular components:

Commonly called Phong lighting

Note: once per light Note: once per color component

Do ka, kd, and ksvary with color component?

( ) ( )=

++=lights

i

n

sdiambientatotal

shiny

RVkLNkIIkI#

1


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Phong Lighting: Intensity Plots


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Phong Lighting in OpenGL

The final Phong model as we studied it:

OpenGL variations: Every light has an ambient component

Surfaces can have emissive component to simulateglow Added directly to the visible reflected intensity

Not actually a light source (does not illuminate other surfaces)

See Nate Robins OpenGL Lighting tutors

( ) ( )=

++=

lights

i

n

sdiambientatotal

shiny

RVkLNkIIkI

#

1

( ) ( )#

1

shiny

lights n

total e a a d d s s

i

I k I k I k N L I k V R=

= + + + +


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Types of lights and light sources

Ambient

Diffuse

Directional

Point

Area Spot

Specular

Phong



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Applying Illumination

We now have an illumination model for a point ona surface

Assuming that our surface is defined as a mesh ofpolygonal facets, which points should we use?

Keep in mind:

Its a fairly expensive calculation

Several possible answers, each with differentimplications for the visual quality of the result


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Applying Illumination

With polygonal/triangular models:

Each facet has a constant surface normal

If the light is directional, the diffuse reflectance isconstant across the facet

If the eyepoint is infinitely far away (constant V), the

specular reflectance of a directional light is constantacross the facet


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Flat Shading

The simplest approach, flat shading, calculatesillumination at a single point for each polygon:

If an object really is faceted, is this accurate?

No:

For point sources, the direction to light variesacross the facet

For specular reflectance, direction to eye variesacross the facet


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Flat Shading

We can refine it a bit by evaluating the Phonglighting model at each pixel of each polygon, but

the result is still clearly faceted: To get smoother-looking surfaces

we introduce vertex normalsat each

vertex Usually different from facet normal

Used onlyfor shading (as opposed to what?)

Think of as a better approximation of the real surfacethat the polygons approximate (draw it)

V N l


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Vertex Normals

Vertex normals may be

Provided with the model

Computed from first principles

Approximated by averaging the normals of the facetsthat share the vertex

F l i Bl d


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Face normals in Blender

G d Sh di


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Gouraud Shading

This is the most common approach

Perform Phong lighting at the vertices

Linearly interpolate the resulting colors over faces

This is what OpenGL does

Demo at:

http://www.cs.virginia.edu/~gfx/Courses/2000/intro.spring00.html/vrml/tpot.wrl

Requires a VRML browser or plug-in

Does this eliminate the facets? No: were still subsamplingthe lighting parameters

(normal, view vector, light vector)

Ph Sh di


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Phong Shading

Phong shadingis not the same as Phong lighting,though they are sometimes mixed up

Phong lighting: the empirical model weve beendiscussing to calculate illumination at a point on asurface

Phong shading: linearly interpolating the surface normalacross the facet, applying the Phong lighting model atevery pixel

Same input as Gouraud shading

Usually very smooth-looking results: But, considerably more expensive

A A id T f i N l


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An Aside: Transforming Normals

Irritatingly, the matrix for transforming a normalvector is not the same as the matrix for the

corresponding transformation on points In other words, dont just treat normals as points:

Transforming Normals


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Transforming Normals

Some not-too-complicated affine analysis shows:

If A is a matrix for transforming points, then (AT)-1 is the

matrix for transforming normals

When is this the same matrix?

What is the homogeneous representation of a

vector (as opposed to a point?)

Can use this to simplify the problem: only upper3x3 matrix matters, so use only it

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