Computer Graphics

1
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

2
Contents

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

3
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

4
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

5
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

6
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

7
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
8
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

9
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).

10
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
11
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.

12
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

13
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)

14
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

15
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?

16
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
17
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
18
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)

19
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

20
The Phong Model(Introduction)

• A specular reflection model

N
L
R
?
?
V
?
21
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))

22
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

23
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

24
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

25
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

26
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

27
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

28
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.

29
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

30
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

31
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

32
Normal Calculation
33
Scan Conversion
34
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)

35
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

36
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

37
Issues

• Number of problems in interpolated shading
  models
• Perspective Distortion
• Shared Vertices
• Orientation Dependency
• Unrepresentative Vertex Normals

38
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

39
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
40
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

41
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

42
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

43
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)

44
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