Illumination and Shading

1
School of Computing Staffordshire University
3D Computer Graphics
Illumination and Shading
Dr. Claude C. Chibelushi
2
Outline

• Introduction
• Light
• Sources, Propagation
• Illumination Models
• Ambient illumination, Diffuse reflection,
  Specular reflection
• Display of Polygonal Objects
• Polygon Shading
• Constant, Gouraud, and Phong shading
• Summary

3
Introduction

• Photorealism accurate representation of
• shape of object(s) collection of flat / curved
  surfaces
• vertex coordinates, surface equations
• occlusion
• optical properties of object(s) and light
  source(s)
• brightness (shiny / dull), colour, texture,
  transparency (opaque / transparent), shadows, ...

4
Introduction

• Accurate representation of shape, occlusion, and
  optical characteristics
• costly, hence approximations often used, e.g.
• set of polygons for shape approximation
• surface shading based on empirical procedures
  (i.e. not strict physical laws)
• Shading of surfaces
• calculation of intensity of points on surface
• intensity typically calculated using illumination
  (or lighting) model

5
Light

• Propagation
• Light incident onto surface can be
• reflected (bounces off as reflected light
  ray(s))
• transmitted (as observed in glass)
• absorbed (converted to heat or other energy form)
• Visual characteristics of object relate to amount
  and nature of light from object to eye

6
Light

• Propagation
• Amount and direction of light reflected,
  transmitted, or absorbed
• depends on material of object, and light
  wavelength (colour) / intensity / position
• Viewer sees light reflected along rays from
  points on object surface to eye position

7
Light

• Propagation
• Light reaching point often combination of light
  from
• light-emitting sources (commonly called light
  sources) and light-reflecting sources
• Object properties affect light reflected by
  object, hence surface labels describing
• amount of reflected light
• shiny / dull, opaque / transparent
• direction of reflected light
• grainy or rough / smooth

8
Light

• Light emission

Simple light emitters
9
Light

• Light reflection

Diffuse reflection (scatter)
Specular reflection (highlight)
Simple light reflectors
10
Illumination Models
(Parameters position, directionality, colour,
intensity)
(Parameters position, orientation, optical
properties)
(Parameters position, orientation)
(Parameters position, orientation, optical
properties)
Effect of illumination interplay of many factors
11
Illumination Models

• Illumination model

Note Colour representation requires computation
of intensity in each colour band (e.g. R, G, B)
Parameters
12
Illumination Models

• Illumination model
• formula for calculating light intensity seen at
  surface point
• computation based on
• optical properties of surface
• relative positions of surfaces in scene (shadows,
  )
• position, shape, colour and intensity of light
  source(s)
• position and orientation of viewer

13
Basic Illumination Models

• Basic illumination models
• simplified (empirical) methods for calculating
  intensity at given surface point
• calculations based on optical properties of
  surface, lighting and view specifications
• light sources point sources with specified
  position and colour

14
Basic Illumination Models

• Ambient illumination
• Ambient light or background light
• defines general brightness of scene
• models combination of emissions / reflections
  from various sources in scene
• global diffuse lighting effect
• constant throughout scene
• independent of position and direction of object /
  viewer

15
Basic Illumination Models

• Ambient illumination
• Same incident light Ia throughout scene
• but intensity of reflected light depends on
  optical properties of surface
• Fraction of incident light reflected by surface
• determined by ambient-reflection coefficient
  (ka)
• Ir, amb ka Ia 0 ? ka ? 1 (depends on
  surface properties)

16
Basic Illumination Models

• Diffuse reflection
• Independent of viewing direction
• Virtually constant over each surface (for distant
  light source)
• Fraction of incident light reflected by surface
  is determined by
• orientation of surface relative to light source
• diffuse-reflection coefficient (kd)
• 0 ? kd ? 1 (depends on surface properties)

17
Basic Illumination Models

• Diffuse reflection model implementation

Reflected light is Ir, diff kd Ii cos ? If n
and t are unit vectors Ir, diff kd Ii (n ? t )
18
Basic Illumination Models

• Specular reflection
• Models highlights or bright spots on illuminated
  shiny surfaces
• Theoretical specular reflection
• single reflected ray
• specular reflection angle is equal to angle of
  incidence
• In reality multiple reflected rays (cone)

19
Basic Illumination Models

• Specular reflection
• Phong specular-reflection model
• Fraction of incident light reflected by surface
  and seen by viewer is determined by
• orientation of surface relative to light source
  and viewer
• specular-reflection coefficient (ks) 0 ? ks ? 1
  (depends on surface properties)
• specular-reflection parameter (ns) high value
  (say ns gt 100) for very shiny surface
• depends on surface properties (ns is also known
  shininess parameter)

20
Basic Illumination Models

• Specular reflection model implementation

Viewed reflected light is Ir, spec ks Ii cosns
?
21
Basic Illumination Models

• Specular reflection model implementation
• If n, t, and v are unit vectors
• Ir, spec ks Ii (v r) ns
• where r (2n t) n t
• Possible geometric simplification
• assume point light source at infinity
• hence t considered constant for scene

22
Basic Illumination Models

• Specular reflection effect of ks and ns

23
Basic Illumination Models

• Combination of reflections
• For single point source
• sum up ambient, specular, and diffuse intensities
• Ir, tot Ir, amb Ir, diff Ir, spec
• where ka kd ks 1
• For multiple point sources
• sum up total intensities (computed as above) for
  all sources

24
Basic Illumination Models

• Colour scenes
• Alternative 1 for each colour component (e.g.
  red, green, blue RGB)
• specify properties of light-source and surface
  material
• specular highlight looks like reflection of light
  source
• hence set proportions of ks across colour
  components to match colour of light source
• apply illumination model(s)

25
Basic Illumination Models

• Colour scenes
• Alternative 2
• surface colour modulates reflection coefficients
  
• e.g. for white light source
• same light-source parameters for RGB components
• same material coefficients / parameters for RGB
  components
• but possibly different RGB components for surface
  colour

surface colour
ambient reflection
diffuse reflection
specular reflection
26
Basic Illumination Models

• Directional light source
• If t and s are unit vectors
• Ispot Ii cosm ? Ii (-t s) m
• use Ispot in place of Ii in reflection formula

27
Basic Illumination Models

• Attenuation of light due to travel distance
• may be modelled by inverse linear or quadratic
  function
• Note reflected light calculated in world or
  viewing coordinates
• i.e. before perspective transformation is applied
• perspective and shear transformation may change
  orientation of surface normals!

28
Display of Polygonal Objects

• Wireframe
• faces represented by line segments connecting
  vertices
• may use colour or broken lines for depth cueing
• Filled solid
• faces filled with single colour
• no illumination model used
• adjacent faces appear as one surface

29
Display of Polygonal Objects

• Shaded solid
• faces shaded with intensity calculated from
  suitable illumination model(s)
• illumination model(s) typically applied to
• single point (calculated intensity used for
  shading whole polygon) constant shading
• some points (calculated intensities interpolated
  to obtain intensity at other points) e.g.
  Gouraud shading
• all polygon pixels e.g. Phong shading

30
Polygon Shading

• Constant / Flat shading
• Face filled with single shade calculated from
  suitable illumination model(s)
• Low realism but better than filled models
• may require smoothing (close to face junctions)
• Pseudocode
• for each face
• apply illumination model to a point on the
  face
• fill face with calculated intensity

31
Polygon Shading

• Gouraud shading
• Intensity-interpolation shading
• calculate intensity at polygon vertices
• interpolate intensity values across surface
• interpolation weighted averaging
• Less intensity discontinuity along edges than in
  flat shading

32
Polygon Shading

• Gouraud shading (ctd.)
• Calculation of intensity at polygon vertices
• compute normal vector at each vertex
• e.g. sum up surface normals of polygons sharing
  vertex
• convert to unit vector
• compute intensity at each vertex
• apply illumination model(s) to vertex

33
Polygon Shading

• Gouraud shading (ctd.)
• Interpolation of intensities along polygon edges
• compute intensity at intersection of scan-line
  with edge
• interpolate intensities at edge endpoints (2
  vertices)
• compute intensity at interior points
• interpolate intensities at edge points (along
  scan-line)

34
Polygon Shading

• Gouraud shading (ctd.)
• Interpolation of intensities

Shading is often coupled to scan conversion
35
Polygon Shading

• Gouraud shading (ctd.)
• Exploiting coherence
• use incremental computation
• add a constant step to I value of previous point
  to obtain I value of current point (for
  increasing y or x)
• it can be shown that
• along polygon edge
• Icurrent Iprevious (I1 - I2) / (y1 - y2)
  (along edge between 1 and 2)
• Icurrent Iprevious (I1 - I3) / (y1 - y3)
  (along edge between 1 and 3)
• along scan line
• Icurrent Iprevious (I5 - I4) / (x5 - x4)
  (along scan line between 4 and 5)

36
Polygon Shading

• Gouraud shading pseudocode
• for each face
• compute unit normal at each vertex
• apply illumination model(s) to each face
  vertex
• for each scan line
• compute intensity at face edges from relevant
• vertex intensities
• for each interior scan-line pixel compute
  intensity from relevant
• edge intensities

37
Polygon Shading

• Phong shading
• Normal-vector interpolation shading
• calculate unit normal vector at each vertex
• interpolate vertex normals across surface
• apply illumination model(s) along each scan line
• Better realism than Gouraud shading
• but higher computational cost
• vector interpolation illumination model(s)
  applied to each pixel

38
Polygon Shading

• Phong shading (ctd.)
• Calculation of unit normals at polygon vertices
• as in Gouraud shading
• Interpolation of surface normals along polygon
  edges
• compute normal at intersection of scan-line with
  edge
• interpolate normals at edge endpoints (2
  vertices)
• compute normal at interior points
• interpolate normals at edge points (along
  scan-line)

39
Polygon Shading

• Phong shading (ctd.)
• Interpolation of surface normals

Efficiency incremental calculations can be used
40
Polygon Shading

• Phong shading pseudocode
• for each face
• compute unit normal at each vertex
• for each scan line
• compute normal at face edges from relevant
• vertex normals
• for each interior scan-line pixel
• compute normal from relevant edge normals
• apply illumination model(s) to pixel

41
Polygon Shading

• Comparison of techniques
• Constant shading
• Face filled with single shade
• Low realism
• Low computational and storage cost

42
Polygon Shading

• Comparison of techniques
• Gouraud shading
• Vertex intensity interpolation
• Prone to Mach band effect
• May fail to show highlights
• hence surfaces may appear dull / matt
• Slower but better realism than flat shading

43
Polygon Shading

• Comparison of techniques
• Phong shading
• Vertex normal interpolation
• illumination model(s) applied to each pixel
• deals well with highlights
• more rounding of polygon seams than Gouraud
  shading
• Higher computational cost but better realism than
  Gouraud shading

44
Suggested Reading

• Relevant parts of Ch. 9 Ch. 14, D. Hearn, M.P.
  Baker, Computer Graphics, 2nd Ed. in C,
  Prentice-Hall, 1996.
• Relevant parts of Ch. 10 Ch. 12, A. LaMothe,
  Black Art of 3D Game Programming, Waite Group
  Press, 1995.

45
Summary

• Illumination model gives intensity of surface
  points
• calculated intensity is used for shading surface
• Basic illumination models
• ambient illumination, diffuse reflection,
  specular reflection
• combination of intensities sum of contribution
  of models and light sources
• model(s) applied to / modulated by each colour
  component

46
Summary

• Polygon shading illumination model(s) applied
  for
• single pixel (constant / flat shading), vertex
  pixels (Gouraud shading), all surface pixels
  (Phong shading)
• increasing realism and computational cost