Lighting and Normal Transformations in Computer Graphics, Slides of Computer Graphics

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Lighting

Triangle Rendering^ „

The main stages in the

traditional graphics

pipeline

are:

„

Transform „

Lighting „

Clipping / Culling „

Scan Conversion „

Pixel Rendering

Lighting^ „

Today, we will mainly focus on vertex lighting „

Each vertex goes through a lighting process whichdetermines its final color „

This color value is then interpolated across the trianglein the scan conversion process „

Usually, each vertex has some sort of initial colorassigned to it, which defines what color it would be if welllit by a uniform white light „

This initial color is then modified based on the positionand normal of the vertex in relation to lights placed in thescene (in other words, a grey vertex dimly lit by red lightswill appear dark red…) „

In GL, you pass in the ‘unlit’ color through glColor3f(). Itwill then compute the ‘lit’ color, which gets interpolated inthe scan conversion process

Normal Transformations^ „^

Lighting requires accurate measurement of distances and angles, so wewant to compute lighting in a regular 3D space (i.e., not 4D un-normalizedview space, or 2.5D device space…) „^

This leaves object space, world space, or camera space as our mostnatural options „^

To light in object space, we would have to transform the lights from worldspace into each object’s space „^

If we are applying shears or non-uniform scales to our object, this will distortthe object which will mean that object space isn’t actually a legitimate placeto do lighting „^

Lighting in world space would be fine, but it would require transforming theobject into world space, which is a step that we usually avoid explicitlydoing „^

Therefore, it makes good sense to light in camera space, as we willprobably want to perform clipping & some culling in this space as well „^

GL does it’s lighting in camera space, which means that we must transformnormals into camera space in addition to the vertex positions

Direction Vector Transformation

z z z y z x z y z y y y x y x z x y x x x

x y z

z

z

z

z

y

y

y

y

x

x

x

x

c n b n a n n c n b n a n n c n b n a n n

n n n

d

c

b

a

d

c

b

a

d

c

b

a

0 1 0 0 0 n M n

Normal Transformations^ „

It’s actually worse than that… „

Let’s say we take the 3 vertices of a triangle andcompute the normal, then we transform the 3 verticesand the normal „

If the transformation contains any shear or non-uniformscaling, then it is possible that the transformed normalwill no longer be perpendicular to the transformedtriangle itself „

To fix this, we should actually transform the normal bythe

inverse transpose

of the matrix, or

M

-1T

„

The transformed normals will also not be unit length anymore, so they must also be renormalized before lighting

Normal Transformations^ „

If we want to compute lighting in camera space,we need to first transform the vertices & normalsinto camera space:

1

1 n n

n

n

M

n

v

M

v

W

C

M

− −

T

[^

]

(^

)

[^

]

(^

) 1 0 z

y

x

z

y

x

n

n

n

v

v

v = = v n

Lighting^ „

Whether we are computing lighting pervertex or lighting per pixel, the basicprocess is the same

„

In either case, we are computing thelighting at some position

v

with some

normal

n

Light Color^ „

However, if we are looking at a white piece ofpaper under uniform light, we can always turnmore lights on, and get more light to reflect off ofthe paper „

There is no upper limit to the intensity of light „

If we want to represent a light intensity (lightcolor), we can store it as red, green, and bluevalues ranging from 0.0 to an arbitrarily highvalue „

In other words, a bright white light bulb mighthave an color of (10, 10, 10)

Color & Intensity^ „

We need to make a distinction between material color and light color „^

Material colors represent the proportion of light reflected „^

Light colors represent the actual intensity of a beam of light „^

We never actually perceive the inherent material color, all we see isthe light reflected off of a material „^

If we shine a red light on a grey surface, the object appears dark redbecause it is reflecting beams of dark red light „^

I will use

m

to represent a material color and

c

to represent an

actual light color

Reflectivity^ „

A white sheet of paper might reflect 95% of thelight that shines on it „

An average mirror might reflect 95% of the lightthat shines on it „

Yet, these two things look completely different,because they reflect light in different directions „

We say that the paper is a

diffuse

reflector,

whereas the mirror is a

specular

reflector

Diffuse Reflection^ „

An

ideal diffuse reflector

will receive light from some

direction and bounce it uniformly in all directions „

Diffuse materials have a dull or matte appearance „

In the real world, materials will not match this behaviorperfectly, but might come reasonably close

Specular (Glossy) Reflection^ „

Sometimes, a material behaves in a specular way, butnot quite perfect like a mirror (like an unpolished metalsurface) „

In CG, this is sometimes referred to as

glossy

reflection

„

Glossy materials look shiny and will show

specular

highlights

Diffuse/Specular Reflection^ „

Many materials have a mixture of diffuse and specularbehavior „

Plastics are a common example of this, as they tend tohave an overall diffuse behavior, but still will catchhighlights