1gr2-00 gr2 advanced computer graphics agr lecture 5 getting started with opengl a simple reflection...

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GR2Advanced Computer

GraphicsAGR

GR2Advanced Computer

GraphicsAGR

Lecture 5Getting Started with OpenGL

A Simple Reflection Model

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What is OpenGL?What is OpenGL?

OpenGL provides a set of routines for advanced 3D graphics– derived from Silicon Graphics GL– acknowledged industry standard, even on

PCs (OpenGL graphics cards available)– integrates 3D drawing into X (and other

window systems such as Windows NT)– draws simple primitives (points, lines,

polygons) but NOT complex primitives such as spheres

– provides control over transformations, lighting, etc

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Geometric PrimitivesGeometric Primitives

Defined by a group of vertices - for example to draw a triangle:

glBegin (GL_POLYGON);

glVertex3i (0, 0, 0);



glEnd(); See Chapter 2 of the OpenGL

Programming Guide

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ViewingViewing

OpenGL maintains two matrix transformation modes– MODELVIEW

to specify modelling transformations, and transformations to align camera

– PROJECTION

to specify the type of projection (parallel or perspective) and clipping planes

See Chapter 3 of OpenGL Programming Guide

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OpenGL Utility Library (GLU)

OpenGL Utility Library (GLU)

Useful set of higher level utility routines to make some tasks easier– written in terms of OpenGL and

provided with the OpenGL implementation

– for example, gluLookAt() is a way of specifying the viewing transformation

See Appendix C of OpenGL Programming Guide

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OpenGL Utility Toolkit (GLUT)

OpenGL Utility Toolkit (GLUT)

Set of routines to provide an interface to the underlying windowing system - plus many useful high-level primitives (even a teapot - glutSolidTeapot()!)

Improved version of the ‘aux’ library described in Appendix E of the Guide

Allows you to write ‘event driven’ applications– you specify call back functions which are

executed when an event (eg window resize) occurs

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How to Get StartedHow to Get Started

Look at the GR2 practicals page:– http://www.scs.leeds.ac.uk/kwb/

GR2/ practicals.html Points you to:

– example programs– information about GLUT– information about OpenGL– a simple exercise

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A Simple Reflection ModelA Simple Reflection Model

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What is a Reflection Model?

What is a Reflection Model?

A reflection modelreflection model (also called lightinglighting or illuminationillumination model) describes the interaction between light and a surface, in terms of:– surface properties– nature of incident light

Computer graphics uses a simplification of accurate physical models– objective is to mimic reality to an

acceptable degree

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Phong Reflection ModelPhong Reflection Model

The most common reflection model in computer graphics is due to Bui-Tuong Phong - in 1975

Has proved an acceptable compromise between simplicity and accuracy

Largely empirical

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Diffuse Reflection and Specular Reflection -

Phong Approach

Diffuse Reflection and Specular Reflection -

Phong Approach

microscopic view

whitelight specular reflection (white)

diffuse reflection(yellow)

yellowpigment particles

Some light reflecteddirectly from surface.

Other light passes intomaterial. Particles ofpigment absorb certainwavelengths fromthe incident light, butalso scatter the lightthrough multiple reflections - somelight emerges backthrough surface as diffuse reflection.

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Ambient ReflectionAmbient Reflection

In addition to diffuse and specular reflection, a scene will also include ambientambient reflection

This is caused by light falling on an object after reflection off other surfaces– eg in a room with a light above a

table, the floor below the table will not be totally black, despite having no direct illumination - this is reflection of ambient light

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Reflection Model - Ambient Light

Reflection Model - Ambient Light

surface

I ( )= Ka ( )Ia()Ia = Intensity of ambient lightKa = Ambient-reflection coefficientI = Reflected intensity= wavelength of light

hemisphereof ambientlight

P

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Reflection Model - Diffuse Reflection


Light reflected equally in all directions - intensity dependent on angle between light source and surface normal

Lambert’s cosine law: I = I* cos where I* is intensity of light source

P

lightsource

P

lightsource

lightsourceN

L

surface

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I = Kd ( cos ) I*

I* = Intensity of light sourceN = Surface normalL = Direction of light sourceKd = Diffuse-reflection

coefficientI = Reflected intensity

lightsourceN

L

surface

Light reflected equallyin all directions, withintensity depending onangle between light andsurface normal:

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The angle between two vectors is given by their dot product: cos = L . N (assume L, N are unit length)

The coefficient Kd depends on the wavelength of the incoming light

lightsourceN

L

surface

I ( ) = Kd() ( L . N ) I*()

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Reflection Model - Specular ReflectionReflection Model -

Specular Reflection

In perfect specular reflection, light is onlyreflected along the unique direction symmetricto the incoming light

P

lightsource

N

R

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Specular Reflection

P

lightsource

N

R

In practice, light is reflected within a small angle ofthe perfect reflection direction - the intensity of thereflection tails off at the outside of the cone. Thisgives a narrow highlight for shiny surfaces, and abroad highlight for dull surfaces.

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Specular Reflection

Thus we want to model intensity, I, as a function of angle between viewer and R, say , like this:

I

with a sharper peak for shinier surfaces, and broader peakfor dull surfaces.

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Specular Reflection

Phong realised this effect can be modelled by:

(cos )n

with a sharper peak for larger n

I

n=1

n=10

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Specular Reflection

I = Ks( cos )n I*

I* = Intensity of light sourceV = View directionR = Direction of perfect

reflected lightKs = Specular-reflection

coefficientI = Reflected intensity

n varies with materiallarge n : shinysmall n : dull

Intensity depends onangle between eye andreflected light ray:

V

lightsourceN

LR

eye

surface

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Specular Reflection

V

lightsourceN

LR

eye

surface

Using cos = R . V (R, V unit vectors), we have:

I () = Ks ( R . V )n I()*

Note: Ks does not depend on the wavelength - hencecolour of highlight is same as source

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Reflection Model -Ambient, Diffuse and

Specular

Reflection Model -Ambient, Diffuse and

Specular

lightsource

I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*()

N

LR

Veye

surface

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Reflection Model - Effect of Distance

Reflection Model - Effect of Distance

lightsource

surface

d

The intensity of light reaching a surface decreases with distance - so we use typically:

I*

K1 + K2*d + K3*d2K1, K2, K3 constant- often K2=1, K3=0

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Final Reflection ModelFinal Reflection Model

lightsourceN

LR

Veye

surfaced

I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*()

K1 + K2*d + K3*d2

This needs to be applied for every light source in the scene

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Phong Model in PracticePhong Model in Practice

In practice, some simplifications are made to the model for sake of efficiency

For example, ambient light is sometimes assumed to be a constant

Other simplifications are:– lights at infinity– simple colour model

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Practicalities - Effect of Distance

Practicalities - Effect of Distance

There are advantages in assuming light source and viewer are at infinity– L and V are then fixed for whole

scene and calculations become simpler

Lights at infinity are called directionaldirectional lights

Lights at a specified position are called positionalpositional, or point point, lights

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Practicalities - Calculating R


R + L = 2 ( N.L ) NhenceR = 2 ( N.L )N - L In practice,

implementations often compute H = ( L + V ) / 2

and replace (R.V) with (H.N) – these are not the same,

but compensation is made with choice of n (angle between N and H is half angle between R and V)

N

LR

R

L

V

R

H

N

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As noted, if viewer and light source both sufficiently far from surface, then V and L are constant over scene - and also H

Then, for nonplanar surfaces, the calculation:

N . His faster than R . V because R

needs to be evaluated at each point in terms of N.

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Practicalities - Effect of Colour

Practicalities - Effect of Colour

The Phong reflection model gives reflection for each wavelength in visible spectrum

In practice, we assume light to be composed as a mixture of RGB (red, green, blue) components - and reflection model is applied for each component

Coefficients of ambient-reflection (Ka) and diffuse-reflection (Kd) have separate components for RGB

Coefficient of specular-reflection (Ks) is independent of colour

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Example - Ambient Reflection

Example - Ambient Reflection

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Example - Ambient and Diffuse

Example - Ambient and Diffuse

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Ambient, Diffuse and Specular

Ambient, Diffuse and Specular

1gr2-00 gr2 advanced computer graphics agr lecture 5 getting started with opengl a simple reflection...

Documents

ambient reflection n

surface light

incoming light light

intensity of light source

phong reflection model

ambient reflection ambient

light passes

simple reflection model