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Computer Graphics

- Lecture 7
- Illumination and Shading Algorithms
- Lecturer Heather Sayers
- E-mail hm.sayers_at_ulster.ac.uk
- URLhttp//www.infm.ulst.ac.uk/heather

Contents

- Introduction
- The Projective Rendering Pipeline
- Light Sources
- Shading models Flat, Gouraud, Phong

Introduction

- Realistic displays of a scene are obtained by

generating perspective projections of objects and

by applying natural lighting effects to the

visible surfaces - An illumination model (lighting model/shading

model) is used to calculate the intensity of

light that we should see at a given point on the

surface of an object

Introduction

- A surface-rendering algorithm uses the intensity

calculations from an illumination model to

determine the light intensity for all projected

pixel positions - This can be applied in 2 ways
- Applying the illumination model to every visible

surface point - Interpolating intensities across the surfaces

from a small set of illumination-model

calculations - Scan-line, image-space algorithms typically use

interpolation schemes - Ray tracing algorithms invoke the illumination

model at each pixel position

Photorealism

- In Computer Graphics, this involves
- Accurate representations of objects
- Good physical descriptions of the lighting

effects - Lighting effects include
- Light reflections
- Transparency
- Surface texture
- Shadows

Illumination Models

- Given the parameters for
- the optical properties of surfaces,
- the positions of the surfaces in a scene,
- the colour and positions of light sources,
- the position and orientation of the viewing

plane, - illumination models calculate the intensity

projected from a particular surface point in a

specified viewing direction - To minimise intensity calculations, most packages

use empirical models based on simplified

photometric calculations

The Projective Rendering Pipeline

Starts with a mathematical description of the

object The object is transformed from modelling

coordinates into scene (world) coordinates (and

subsequently to device coordinates) Hidden

surfaces are identified and removed The surfaces

are illuminated Surfaces are transformed to view

coordinate space Surfaces which lie outside the

viewing frustrum are clipped Surfaces are

projected to the 2D screen Scan conversion

calculates the colour of the pixels which are

covered by the projected surfaces and writes them

into the frame buffer Video hardware scans the FB

and translates the pixel colours into analogue

signals for the CRT electron guns

Light Sources

- An object that is emitting radiant energy, such

as a light bulb or the sun - The simplest model for a light emitter is a point

source radially diverging paths (good for

sources whose dimensions are small compared to

the size of objects in the scene) - A nearby source is more accurately modelled as a

distributed light source area of the source is

not small compared to the surfaces of the scene

Surface Properties

- Recap on light striking surface a ray of light

strikes a surface how is that light energy

dissipated? - The answer depends on the surface

characteristics perfect reflectors (eg mirrors)

exhibit regular reflection other surfaces

exhibit diffuse reflection - For diffusely reflecting surfaces, light rays are

reflected not just in the perfectly reflected

direction but in all directions (rough, grainy

surfaces).

Two Laws of Reflection

- 1. The reflected ray, incident ray and normal to

the surface at the points of incidence all lie in

the same plane - 2. The angle of incidence angle of reflection

N

R

I

i

r

Specular Reflection

- Polished or shiny surfaces illuminated with a

bright light exhibit specular reflection. At

certain viewing angles the object (or part of the

object) appears to be white (the colour of the

incident light) and not the colour of the object.

- These highlights exist due to the fact that all

incident light has been reflected.

Ambient Light

- A surface that is not exposed directly to a light

source will still be visible if nearby objects

are illuminated - In a basic illumination model, we can set a

general level of brightness for a scene this is

a simple way to model the combination of light

reflections from various surfaces to produce a

uniform illumination called the ambient light or

the background light - No spatial or directional characteristics
- Amount of ambient light incident on each object

is constant for all surfaces and over all

directions - Set the level for ambient light in a scene using

parameter Ia - The intensity of the reflected light for each

surface depends on the surfaces properties

Diffuse Reflection

- Ambient-light reflection is an approximation of

global diffuse lighting effects - Diffuse reflections are constant over each

surface in a scene, independent of the viewing

direction - The fractional amount of the incident light that

is diffusely reflected can be set for each

surface with parameter kd the diffuse

reflection coefficient, or diffuse reflectivity - kd is assigned a constant value between 0 and 1

(highly reflective 1)

Diffuse Reflection

- If a surface is exposed only to ambient light, we

can express the intensity of the diffuse

reflection at any point on the surface as - Iambdiff kdIa
- Scenes are rarely rendered with ambient light

alone (flat, uninteresting shading) - Usually at least one light (a point source at the

viewing position) is included - We assume that the diffuse reflections from the

surface are scattered with equal intensity in all

directions, independent of viewing direction

ideal diffuse reflectors/Lambertian reflectors

Diffuse Reflection

- Even though there is equal light scattering in

all directions from a perfect diffuse reflector,

the brightness of the surface does depend on the

orientation of the surface relative to the light

source - Brighter if surface is perpendicular to the

direction of the incident light - Angle of incidence between the incoming light

direction and the surface normal ? - The projected area of a surface patch

perpendicular to the light direction is

proportional to cos?

Diffuse Reflection

- Thus, the amount of illumination (number of

incident light rays cutting across the surface

patch) depends on cos?

N

A

A cos ?

?

?

Incident light

Diffuse Reflection

- If the incoming light from the source is

perpendicular to the surface, it is fully

illuminated - A surface is illuminated by a point source only

if the angle of incidence is between 0 and 90

degrees (cos ? in the range 0 to 1) - When ? is negative, the light source is behind

the surface

N

L

q

Diffuse Reflection

- If N is the unit normal vector to a surface and L

is the unit direction vector to the point light

source from a position on the surface, then cos?

N . L and the diffuse reflection equation for

single point-source illumination is - Il,diff kdIl (N.L)

Diffuse Reflection

- For general scenes, it is likely that there would

also be some background lighting effects in

addition to that from a direct light source - We can combine the ambient and point-source

intensity calculations to obtain an expression

for the total diffuse reflection - In addition, many graphics packages introduce an

ambient-reflection coefficient ka to modify the

ambient light intensity Ia for each surface,

giving - Idiff ka Ia kd Il (N.L)
- Where both ka and kd depend on surface material

properties and are assigned values in the range 0

to 1

The Phong Model(Introduction)

- A specular reflection model

N

L

R

?

?

V

?

Phong Model(Introduction)

- N unit normal vector, R unit vector in the

direction of ideal specular reflection, L unit

vector directed towards the point light source, V

unit vector pointing to the viewer from the

surface position - The specular-reflection angle equals the angle of

incident light (?) - Angle ? is the viewing angle relative to the

specular-reflection direction for R - For an ideal reflector (perfect mirror), incident

light is reflected only in the specular-reflection

direction (Here, where V and R coincide (? 0))

Phong Model

- If not an ideal reflector, specular reflections

cover a finite range of viewing positions around

vector R shiny surfaces narrow range, dull

surfaces wide range - An empirical model for calculating the

specular-reflection range was developed by Phong

Bui Tuong the Phong Model - Sets the intensity of specular reflection

proportional to cosns ? - Angle can vary between 0 and 90, therefore cos

between 0 and 1 - The value assigned to the specular reflection

parameter ns is determined by the type of surface

to be displayed

Phong Model

- Shiny surface is modelled with a large value for

ns and similarly for a dull value ns has a small

value - In Phong shading, the normal vectors are

interpolated across the scan line - This results in a higher quality of rendering

highlights are visible on shiny surfaces - Phong shading is not (yet) implemented in

hardware, due to the requirement of floating

points arithmetic

Light Source Attenuation

- This refers to the fact that two similar objects

illuminated by a light source should have

different intensities depending on the distance

from the light source - As radiant energy from a point light source

travels through space, its amplitude is

attenuated by the factor 1/d2 where d is the

distance the light has travelled - The intensity of light decreases in inverse

proportion to the square of the distance from the

source - A surface close to the light source (small d)

receives a higher incident intensity than a

distant surface (large d) - To produce realistic lighting effects, our

illumination model should take this intensity

attenuation into account

Attenuation

- A suitable light source attenuation factor is
- fatt 1/Dl2
- where Dl2 is the distance from the point to the

light source - However, this is too drastic, and does not look

realisticIf the light is far away, the function

does not vary very much, if it is close, it

varies greatly - A better approximation is suggested by Rogers,

using a linear attenuation factor - fatt 1/(dK)
- where K is some constant, d is the distance from

the viewer to the object

Shading Models for Polygons

- We can shade any surface by calculating the

surface normal at each visible point and applying

the desired illumination model - Brute-force shading model expensive
- More efficient shading models for surfaces

defined by polygons and polygon meshes

Constant Shading Model

- Simplest model (faceted shading/flat shading)
- An illumination model is applied once to

determine a single intensity value then used to

shade the entire polygon - Assume that a scene is illuminated by a distance

point light source and the viewing is from a

distance. - Calculate a single constant surface normal for

each polygon in the polygon mesh representing the

object

Constant Shading Model

- The result of this is that a faceted appearance

is visible. - Each polygon in the mesh appears distinct

boundaries between adjacent polygons are visible

since two adjacent polygons with different

orientation may have different intensities along

their borders - Curved surfaces (such as spheres) appear very

unrealistic - The simple solution of using a finer mesh is

ineffective, because the perceived difference in

shading between facets is accentuated by the mach

band effect.

Mach Banding

- The Mach band effect exaggerates the intensity

change at any edge where there is a discontinuity

in magnitude or slope of intensity the dark

facet looks darker, and the light facet looks

lighter - Mach banding is caused by lateral inhibition of

the receptors in the eye. The more light a

receptor receives, the more that receptor

inhibits the response of adjacent receptors - The response of a receptor to light is inhibited

by its adjacent receptors in inverse relation to

the distance to the adjacent receptor - This is known as Mach banding, and can be

overcome by adding more polygons with smaller

intensity changes between them

Polygon shading models

- So far, the models described determine the shade

of each polygon individually - Two basic shading models take advantage of the

information provided by adjacent polygons to

simulate a smooth surface - Gouraud shading
- Phong shading

Gouraud Shading

- Also called intensity interpolation shading or

color interpolation shading - It eliminates intensity discontinuities
- Here intensities are calculated at each vertex in

the mesh - The normal at each vertex is required.
- this is performed by averaging the surface

normals of all the polygons for which the vertex

is a member (shared vertices) - The intensity is then calculated at every vertex

of the polygon by applying the appropriate

illumination algorithm - The vertex intensities are linearly interpolated

over the surface of the polygon

Normal Calculation

Scan Conversion

Gouraud Shading

- The result is removal of the intensity

discontinuities present in the Constant Shading

Model - It does, however, have some deficiencies
- Highlights in the surface are sometimes displayed

with anomalous shapes - The linear intensity interpolation can cause

bright or dark intensity streaks (Mach bands) - These effects can be reduced by dividing the

surface into a greater number of polygon faces or

by using other methods, such as Phong shading,

which require more calculations - Gouraud shading is the algorithm most commonly

implemented in hardware (fixed point arithmetic)

Gouraud Shading

- When averaging surface normals they may turn out

to be parallel (same direction and

intensity)this results in the surface appearing

flat in that area, - .can be solved by introducing additional

polygons (subdividing the original polygons)

before computing the normals - Mach Banding is evident
- No highlights are visible
- unless they coincide with a vertex

Phong Shading

- More accurate method for rendering a polygon

surface - In Phong shading (normal-vector interpolation

shading), the normal vectors are interpolated

across the scan line and then the illumination

model is applied to each surface point - This results in a higher quality of rendering

highlights are more realistic on shiny surfaces

greatly reduces the Mach band effect - Phong shading is not (yet) implemented in

hardware, due to the requirement of floating

points arithmetic

Issues

- Number of problems in interpolated shading

models - Perspective Distortion
- Shared Vertices
- Orientation Dependency
- Unrepresentative Vertex Normals

Perspective Distortion

- Due to the fact that interpolation is performed

in screen space and not world space we have lost

information - As we move from scanline to scanline a constant

incrementing factor is applied - This is inappropriate since although the y-values

may well be simple averages of 2 vertices, the

z-values are unlikely to be this simple (due to

perspective foreshortening) - Result is a (potentially visible)distortion of

the object

Shared Vertices

- Shading discontinuities can arise whenever there

is a vertex lying along an edge shared by two

polygons and this vertex is not common to the

polygons. - Consider vertex V, lying on edge AB. This vertex

is shared by surfaces S2 and S3, but not S1.

A

S2

S1

V

S3

B

Shared Vertices

- Shading information determined directly for V

(via surface S1) will typically be different from

that interpolated from A and B via surfaces S2

and S3 - This presents a discontinuity in the shading
- May be overcome by inserting an extra vertex on

surface S1

Orientation Dependency

- The results of interpolated shading models are

not independent of the orientation of the polygon - Since values are interpolated between vertices

and across horizontal scan lines, the results may

differ when the polygon is rotated

Orientation Dependency

B

A

P

A

D

B

P

C

D

C

- Interpolated values for P depend (on left) on

values arrived at from AB and AD - Same point on same object (differently oriented)

depends on values arrived at from AB and BC

Unrepresentative Vertex Normals

- When the averaged normals computed along the

edges are unrepresentative of the component

surfaces comprising the object the resultant

shading values are unsatisfactory - For example, should averaged surface normals

produce vertex normals which are parallel to each

other then there will be little or no variation

in the resultant shading over the polygon (appear

flat shaded)

Summary

- Illumination models and importance of surface

normals - Three polygon shading models
- flat/constant
- Gouraud
- Phong
- Problems with shading models discussed
- Reading Foley and van Dam Chapter 16

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