Lighting and Shading

1
Lighting and Shading
2
Lighting and Shading

• Illumination
• The flux of light energy from light sources to
  objects in the scene via direct and indirect
  paths
• Lighting
• The process of computing the luminous
• intensity reflected from a specified 3-D point
• Shading
• The process of assigning a colors to a pixel

3
Energy and Power of Light

• Light is a form of energy
• measured in Joules (J)
• Power energy per unit time
• Measured in Joules/sec Watts (W)
• Also known as Radiant Flux ( )

4
Point Light Source

• Total radiant flux in Watts
• Energy emitted in unit time
• How to define angular dependence?
• Use solid angle
• Define power per unit solid angle Radiant
  Intensity (I)
• Measured in Watts per steradian (W/sr)

5
Light Emitted from a Surface

• Radiance (L) Power per unit area per unit solid
  angle
• Measured in W/m2sr
• dA is projected area perpendicular to given
  direction
• Radiosity (B) Radiance integrated over all
  directions
• Power from per unit area, measured in W/m2

6
Light Falling on a Surface

• Power falling on per unit area Irradiance (E)
• Measured in W/m2
• Depends on
• Distance from the light source inverse square
  law E 1/r2
• Incident direction cosine law E n.l

7
Irradiance

• The irradiance (E) is an integral of all
  incident radiance.

8
Reflection

• The amount of reflected radiance is proportional
  to the incident radiance.

9
BRDF

• is called Bidirectional
  Reflectance Distribution Function (BRDF)
• Is a surface property
• Relates energy in to energy out
• Depends on incoming and outgoing directions

10
Local Illumination

• Phong illumination model approximates the BRDF
  with combination of diffuse and specular
  components.

11
Energy Balance Equation

• The total light leaving a point is given by the
  sum of two major terms
• Emitted from the point
• Incoming light from other sources reflected at
  the point

12
Rendering Equation

• L is the radiance from a point on a surface in a
  given direction ?
• E is the emitted radiance from a point E is
  non-zero only if x is emissive
• V is the visibility term 1 when the surfaces
  are unobstructed along the direction ?, 0
  otherwise
• G is the geometry term, which depends on the
  geometric relationship between the two surfaces x
  and x
• Its very hard to directly solve this equation.
  Have to use some approximations.

13
Fast and Dirty Approximations (OpenGL)

• Use red, green, and blue instead of full spectrum
  
• Roughly follows the eye's sensitivity
• Forego such complex surface behavior as metals
• Use finite number of point light sources instead
  of full hemisphere
• Integration changes to summation
• Forego such effects as soft shadows and color
  bleeding
• BRDF behaves independently on each color
• Treat red, green, and blue as three separate
  computations
• Forego such effects as iridescence and refraction
  
• BRDF split into three approximate effects
• Ambient constant, non-directional, background
  light
• Diffuse light reflected uniformly in all
  directions
• Specular light of higher intensity in
  mirror-reflection direction
• Radiance L replaced by simple intensity'' I
• No pretense of being physically true

14
Approximate Intensity Equation (single light
source)

•                                                 
                  
•   stands for each of red, green, blue
•    is the intensity of the light source
  (modified for distance)
•         accounts for the angle of the incoming
  light
• the k are between 0 and 1 and represent
  absorption factors
•        accounts for any highlight effects that
  depend on the incoming direction
• use         or constant if there is nothing
  special
•    is the mirror reflection angle for the light
  
• the angle between the view direction and the
  mirror reflection direction
•       accounts for highlights in the mirror
  reflection direction
• the superscripts e, a, d, s stand for emitted,
  ambient, diffuse, specular respectively
• sum over each light l if there are more one

15
OpenGL Lighting Model

• Local illumination model
• Only depends relationship to the light source.
• Dont consider light reflected or refracted from
  other objects.
• Dont model shadow (can be faked)
• A point is lighted only if it can see the light
  source.
• Its difficult to compute visibility to light
  sources in complex scenes. OpenGL only tests if
  the polygon faces to the light source.
• For a point P on a polygon with norm n, P is
  lighted by the light source Q only if

16
Ambient Light Source

• An object is lighted by the ambient light even
  if it is not visible to any light source.
• Ambient light
• no spatial or directional characteristics.
• The amount of ambient light incident on each
  object is a constant for all surfaces in the
  scene.
• A ambient light can have a color.
• The amount of ambient light that is reflected by
  an object is independent of the object's position
  or orientation.
• Surface properties are used to determine how
  much ambient light is reflected.

17
Directional Light Sources

• All of the rays from a directional light source
  have a common direction, and no point of origin.
• It is as if the light source was infinitely far
  away from the surface that it is illuminating.
• Sunlight is an example of a directional light
  source.
• The direction from a surface to a light source
  is important for computing the light reflected
  from the surface.
• A directional light source has a constant
  direction for every surface. A directional light
  source can be colored.

18
Point Light Sources

• The point light source emits rays in radial
  directions from its source. A point light source
  is a fair approximation to a local light source
  such as a light bulb.
• The direction of the light to each point on a
  surface changes when a point light source is
  used. Thus, a normalized vector to the light
  emitter must be computed for each point that is
  illuminated.

19
Other Light Sources

• Spotlights
• Restricting the shape of light emitted by a point
  light to a cone.
• Requires a color, a point, a direction, and a
  cutoff angle to define the cone.
• Area Light Sources
• Light source occupies a 2-D area (usually a
  polygon or disk)
• Generates soft shadows
• Extended Light Sources
• Spherical Light Source
• Generates soft shadows

20
OpenGL Specifications

• Available light models in OpenGL
• Ambient lights
• Point lights
• Directional lights
• Spot lights
• Attenuation
• Physical attenuation
• OpenGL attenuation
• Default a 1, b0, c0

21
Example of OpenGL Light

• Setting up a simple lighting situation
• GLfloat ambientIntensity4 0.1, 0.1, 0.1,
  1.0
• GLfloat diffuseIntensity4 1.0, 0.0, 0.0,
  1.0
• GLfloat position4 2.0, 4.0, 5.0, 1.0
• glEnable(GL_LIGHTING) // enable lighting
• glEnable(GL_LIGHT0) // enable light 0
• // set up light 0 properties
• glLightfv(GL_LIGHT0, GL_AMBIENT,
  ambientIntensity)
• glLightfv(GL_LIGHT0, GL_DIFFUSE,
  diffuseIntensity)
• glLightfv(GL_LIGHT0, GL_POSITION, position)

22
Ideal Diffuse Reflection

• Ideal Diffuse Reflection an incoming ray of
  light is equally likely to be reflected in any
  direction over the hemisphere.
• An ideal diffuse surface is, at the microscopic
  level a very rough surface. Chalk is a good
  approximation to an ideal diffuse surface.
• The reflected intensity is independent of the
  viewing direction. The intensity does however
  depend on the light source's orientation relative
  to the surface.

23
Computing Diffuse Reflection

• Angle of incidence The angle between the
  surface normal and the incoming light ray
• Lambert's law states that the reflected energy
  from a small surface area in a particular
  direction is proportional to cosine of the angle
  of incidence.

24
Diffuse Lighting Examples

• We need only consider angles from 0 to 90
  degrees. Greater angles (where the dot product is
  negative) are blocked by the surface, and the
  reflected energy is 0.
• Below are several examples of a spherical
  diffuse reflector with a varying lighting angles.
  

25
Specular Reflection

• A specular reflector is necessary to model a
  shiny surface, such as polished metal or a glossy
  car finish.
• We see a highlight, or bright spot on those
  surfaces.
• Where this bright spot appears on the surface is
  a function of where the surface is seen from.
  This type of reflectance is view dependent.
• At the microscopic level a specular reflecting
  surface is very smooth, and usually these
  microscopic surface elements are oriented in the
  same direction as the surface itself.
• Specular reflection is merely the mirror
  reflection of the light source in a surface. An
  ideal mirror is a purely specular reflector.

26
Reflection

• The incoming ray, the surface normal, and the
  reflected ray all lie in a common plane.
• According to Snells Law, The incident angle is
  equal to the reflection on a perfect reflective
  surface.

27
Non-ideal Reflectors

• Snell's law, however, applies only to ideal
  mirror reflectors. Real materials tend to deviate
  significantly from ideal reflectors. At this
  point we will introduce an empirical model that
  is consistent with our experience, at least to a
  crude approximation.
• In general, we expect most of the reflected
  light to travel in the direction of the ideal
  ray. However, because of microscopic surface
  variations we might expect some of the light to
  be reflected just slightly offset from the ideal
  reflected ray. As we move farther and farther, in
  the angular sense, from the reflected ray we
  expect to see less light reflected.

28
Phong Illumination

• One function that approximates this fall off is
  called the Phong Illumination model. This model
  has no physical basis, yet it is one of the most
  commonly used illumination models in computer
  graphics.
• The cosine term is maximum when the surface is
  viewed from the mirror direction and falls off to
  0 when viewed at 90 degrees away from it. The
  scalar nshiny controls the rate of this fall off.

29
Effect of the nshiny coefficient

• The diagram below shows the how the reflectance
  drops off in a Phong illumination model. For a
  large value of the nshiny coefficient, the
  reflectance decreases rapidly with increasing
  viewing angle.

30
Computing Phong Illumination

• The V vector is the unit vector in the direction
  of the viewer and the R vector is the mirror
  reflectance direction. The vector R can be
  computed from the incoming light direction and
  the surface normal

31
Blinn Torrance Variation

• Jim Blinn introduced another approach for
  computing Phong-like illumination based on the
  work of Ken Torrance. His illumination function
  uses the following equation
• In this equation the angle of specular
  dispersion is computed by how far the surface's
  normal is from a vector bisecting the incoming
  light direction and the viewing direction.
• On your own you should consider
• how this approach and the previous
• one differ. OpenGL implements this
• model.

32
Phong Examples

• The following spheres illustrate specular
  reflections as the direction of the light source
  and the coefficient of shininess is varied.

33
Putting it all together

• Phong Illumination Model

34
Colored Lights and Surfaces

• for each light Ii
• for each color component
• reflectance coefficients kd, ks, and ka scalars
  between 0 and 1 may or may not vary with color
• nshiny scalar integer 1 for diffuse surface,
  100 for metallic shiny surfaces

35
Where do we Illuminate?

• To this point we have discussed how to compute
  an illumination model at a point on a surface.
  But, at which points on the surface is the
  illumination model applied? Where and how often
  it is applied has a noticeable effect on the
  result.
• Lighting can be a costly process involving the
  computation of and normalizing of vectors to
  multiple light sources and the viewer.
• For models defined by collections of polygonal
  facets or triangles
• Each facet has a common surface normal
• If the light is directional then the diffuse
  contribution is constant across the facet. Why?
• If the eye is infinitely far away and the light
  is directional then the specular contribution is
  constant across the facet. Why?

36
Flat Shading

• The simplest shading method applies only one
  illumination calculation for each primitive. This
  technique is called constant or flat shading. It
  is often used on polygonal primitives.
• Drawbacks
• the direction to the light source varies over the
  facet
• the direction to the eye varies over the facet
• Nonetheless, often illumination is computed for
  only a single point on the facet. Usually the
  centroid.

37
Facet Shading

• Even when the illumination equation is applied
  at each point of the facet, the polygonal nature
  is still apparent.
• To overcome this limitation normals are
  introduced at each vertex.
• different than the polygon normal
• for shading only (not backface culling or other
  computations)
• better approximates smooth surfaces

38
Vertex Normals

• If vertex normals are not provided they can
  often be approximated by averaging the normals of
  the facets which share the vertex.
• This only works if the polygons reasonably
  approximate the underlying surface.

39
Gouraud Shading

• The Gouraud shading method applies the
  illumination model at each vertex and the colors
  in the triangles interior are linearly
  interpolated from these vertex values.

• Implemented in OpenGL as Smooth Shading.
• Notice that facet artifacts are still visible.

40
Phong Shading

• In Phong shading (not to be confused with the
  Phong illumination model), the surface normal is
  linearly interpolated across polygonal facets,
  and the Illumination model is applied at every
  point.
• A Phong shader assumes the same input as a
  Gouraud shader, which means that it expects a
  normal for every vertex. The illumination model
  is applied at every point on the surface being
  rendered, where the normal at each point is the
  result of linearly interpolating the vertex
  normals defined at each vertex of the triangle.
• Phong shading will usually result in a very
  smooth appearance, however, evidence of the
  polygonal model can usually be seen along
  silhouettes.

41
Gouraud and Phong Shading
42
OpenGL Specifications

• Each light has ambient, diffuse, and specular
  component.
• Each light can be a point light, directional
  light, or spot light.
• Directional light is a point light positioned at
  infinity
• Shading Models flat and smooth
• glShadeModel()
• GL_FLAT, GL_SMOOTH
• Smooth model uses Gouraud shading

43
OpenGL Examples

• We have shown how to set up lights in OpenGL
• Set surface material properties
• glMaterialf(GLenum face, GLenum pname, GLfloat
  param)
• glMaterialfv(GLenum face,GLenum pname,GLfloat
  param)
• Face can be GL_FRONT, GL_BACK, or
  L_FRONT_AND_BACK
• Pname can be GL_AMBIENT, GL_DIFFUSE, GL_SPECULAR,
  GL_SHINESS, and GL_EMISSION
• GLfloat mat_specular 1.0, 1.0, 1.0, 1.0
• GLfloat low_shininess 5.0
• glMaterialfv(GL_FRONT, GL_SPECULAR,
  mat_specular)
• glMaterialfv(GL_FRONT, GL_SHININESS,low_shininess)
  
• Nonzero GL_EMISSION makes an object appear to be
  giving off light of that color
• Refer to OpenGL programming guide for more
  details

44
Triangle Normals

• Surface normals are the most important geometric
  surface characteristic used in computing
  illumination models. They are used in computing
  both the diffuse and specular components of
  reflection.
• On a faceted planar surface vectors in the
  tangent plane can be computed using surface
  points as follows.
• Normal is always orthogonal to the tangent space
  at a point. Thus, given two tangent vectors we
  can compute the normal as followsThis normal
  is perpendicular to both of these tangent vectors.

45
Normals of Curved Surfaces

• Not all surfaces are given as planar facets. A
  common example of such a surface a parametric
  surface. For a parametric surface the three-space
  coordinates are determined by functions of two
  parameters u and v.
• The tangent vectors are computed with partial
  derivatives and the normal with a cross product

46
Normals of Implicit Surfaces

• Normals of implicit surfaces S are even simpler
• This is often called the gradient vector

47
Texture Mappings
48
Mapping Techniques

• Consider the problem of rendering a sphere in the
  examples
• The geometry is very simple - a sphere
• But the color changes rapidly
• With the local shading model, so far, the only
  place to specify color is at the vertices
• To get color details, would need thousands of
  polygons for a simple shape
• Same things goes for an orange simple shape but
  complex normal vectors
• Solution Mapping techniques use simple geometry
  modified by a mapping of some type

49
textures
The concept is very simple!
50
Texture Mapping

• Texture mapping associates the color of a point
  with the color in an image the texture
• Each point on the sphere gets the color of mapped
  pixel of the texture
• Question to address Which point of the texture
  do we use for a given point on the surface?
• Establish a mapping from surface points to image
  points
• Different mappings are common for different
  shapes
• We will, for now, just look at triangles
  (polygons)

51
Basic Mapping

• The texture lives in a 2D space
• Parameterize points in the texture with 2
  coordinates (s,t)
• These are just what we would call (x,y) if we
  were talking about an image, but we wish to avoid
  confusion with the world (x,y,z)
• Define the mapping from (x,y,z) in world space to
  (s,t) in texture space
• To find the color in the texture, take an (x,y,z)
  point on the surface, map it into texture space,
  and use it to look up the color of the texture
• With polygons
• Specify (s,t) coordinates at vertices
• Interpolate (s,t) for other points based on given
  vertices

52
Texture Interpolation

• Specify where the vertices in world space are
  mapped to in texture space
• Linearly interpolate the mapping for other points
  in world space
• Straight lines in world space go to straight
  lines in texture space

t
s
Texture map
Triangle in world space
53
Textures

• Two-dimensional texture pattern T(s, t)
• It is stored in texture memory as an nm array of
  texture elements (texels)
• Due to the nature of rendering process, which
  works on a pixel-to-pixel base, we are more
  interested in the inverse map from screen
  coordinates to the texture coordinates

54
Computing Color in Texture mapping

• Associate texture with polygon
• Map pixel onto polygon and then into texture map
• Use weighted average of covered texture to
  compute color.

55
Basic OpenGL Texturing

• Specify texture coordinates for the polygon
• Use glTexCoord2f(s,t) before each vertex
• Eg glTexCoord2f(0,0) glVertex3f(x,y,z)
• Create a texture object and fill it with texture
  data
• glGenTextures(num, indices) to get identifiers
  for the objects
• glBindTexture(GL_TEXTURE_2D, identifier) to bind
  the texture
• Following texture commands refer to the bound
  texture
• glTexParameteri(GL_TEXTURE_2D, , ) to specify
  parameters to use when applying the texture
• glTexImage2D(GL_TEXTURE_2D, .) to specify the
  texture data (the image itself)

MORE
56
Basic OpenGL Texturing (cont)

• Enable texturing glEnable(GL_TEXTURE_2D)
• State how the texture will be used
• glTexEnvf()
• Texturing is done after lighting

57
Controlling Different Parameters

• The texels in the texture map may be
  interpreted as many different things. For
  example
• As colors in RGB or RGBA format
• As grayscale intensity
• As alpha values only
• The data can be applied to the polygon in many
  different ways
• Replace Replace the polygon color with the
  texture color
• Modulate Multiply the polygon color with the
  texture color or intensity
• Similar to compositing Composite texture with
  base color using operator

58
Texture Stuffs

• Texture must be in fast memory - it is accessed
  for every pixel drawn
• If you exceed it, performance will degrade
  horribly
• There are functions for managing texture memory
• Skilled artists can pack textures for different
  objects into one map
• Texture memory is typically limited, so a range
  of functions are available to manage it
• Specifying texture coordinates can be annoying,
  so there are functions to automate it
• Sometimes you want to apply multiple textures to
  the same point Multitexturing is now in some
  hardware

59
Yet More Texture Stuff

• There is a texture matrix in OpenGL apply a
  matrix transformation to texture coordinates
  before indexing texture
• There are image processing operations that can
  be applied to the pixels coming out of the
  texture
• There are 1D and 3D textures
• Mapping works essentially the same
• 3D used in visualization applications, such a
  visualizing MRI or other medical data
• 1D saves memory if the texture is inherently 1D,
  like stripes

60
Procedural Texture Mapping

• Instead of looking up an image, pass the texture
  coordinates to a function that computes the
  texture value on the fly
• Renderman, the Pixar rendering language, does
  this
• Available in a limited form with vertex shaders
  on current generation hardware
• Advantages
• Near-infinite resolution with small storage cost
• Has the disadvantage of being slow in many cases

61
Other Types of Mapping

• Bump-mapping computes an offset to the normal
  vector at each rendered pixel
• No need to put bumps in geometry, but silhouette
  looks wrong
• Displacement mapping adds an offset to the
  surface at each point
• Like putting bumps on geometry, but simpler to
  model
• All are available in software renderers like
  RenderMan compliant renderers
• All these are becoming available in hardware

62
Bump Mapping
Textures can be used to alter the surface normal
of an object. This does not change the actual
shape of the surface -- we are only shading it as
if it were a different shape! This technique is
called bump mapping. The texture map is treated
as a single-valued height function. The value of
the function is not actually used, just its
partial derivatives. The partial derivatives tell
how to alter the true surface normal at each
point on the surface to make the object appear as
if it were deformed by the height function.
Since the actual shape of the object does not
change, the silhouette edge of the object will
not change. Bump Mapping also assumes that the
Illumination model is applied at every pixel (as
in Phong Shading or ray tracing).
Swirly Bump Map
Sphere w/Diffuse Texture Bump Map
Sphere w/Diffuse Texture
63
Bump mapping
Compute bump map partials by numerical
differentiation
64
Bump mapping derivation
65
Bump Map Examples
Bump Map
Cylinder w/Diffuse Texture Map
Cylinder w/Texture Map Bump Map
66
Displacement Mapping
We use the texture map to actually move the
surface point. This is called displacement
mapping. How is this fundamentally different than
bump mapping?
The geometry must be displaced before visibility
is determined.
67
Readings

• Textbook 16.1-16.3
• OpenGL Programming Guide Chapter 5 and Chap 9.

68
Better Illumination Models

• Blinn-Torrance-Sparrow (1977)
• isotropic collection of planar microscopic facets
  
• Cook-Torrance (1982)
• Add wavelength dependent Fresnel term
• He-Torrance-Sillion-Greenberg (1991)
• adds polarization, statistical microstructure,
  self-reflectance
• Very little of this work has made its way into
  graphics H/W.

69
Cook-Torrance Illumination

• I?,a - Ambient light intensity
• ka - Ambient surface reflectance
• I?,i - Luminous intensity of light source i
• ks - percentage of light reflected specularly
  (notice terms sum to one)
• kd - Diffuse reflectivity
• li - vector to light source
• n - average surface normal at point
• D - the distribution of microfacet orientations
• G - the masking and shadowing effects between the
  microfacets
• F?(?i) - Fresnel conductance term related to
  materials index of refraction
• v - vector to viewer

70
Microfacet Distribution Function

• Statistical model of the microfacet variation in
  normal direction
• Based on a Beckman distribution function
• Consistent with the surface variations of rough
  surfaces
• m - the root-mean-square slope of the
  microfacets
• Small m (e.g., 0.2) pretty smooth surface
• Large m (e.g., 0.7) pretty rough surface

71
Beckman's Distribution
72
Geometric Attenuation Factor

• The geometric attenuation factor G accounts for
  microfacet shadowing.
• in the range from 0 (total shadowing) to 1 (no
  shadowing).
• There are many different ways that an incoming
  beam of light can interact with the surface
  locally.
• The entire beam can simply reflect.

73
Blocked Reflection

• A portion of the out-going beam can be blocked.
• This is called masking.

74
Blocked Beam

• A portion of the incoming beam can be blocked.
• Cook called this self-shadowing.

75
Geometric Attenuation Factor

• In each case, the geometric configurations can be
  analyzed to compute the percentage of light that
  actually escapes from the surface. The geometric
  factor, chooses the smallest amount of lost light.

76
Fresnel Effect

• At a very sharp angle surfaces like a book, a
  wood table top, concrete and plastic can almost
  become mirrors.

77
Fresnel Reflection

• The Fresnel term results from a complete analysis
  of the reflection process while considering light
  as an electromagnetic wave.
• The behavior of reflection depend on how the
  incoming electric field is oriented relative to
  the surface at the point where the field makes
  contact.

78
Fresnel Reflection

• The Fresnel effect is wavelength dependent. It
  behavior is determined by the index-of-refraction
  of the material
• The Fresnel effect accounts for the color change
  of the specular highlight as a function of the
  angle of incidence of the light source,
  particularly on metals (conductors).
• It also explains why most surfaces approximate
  mirror reflectors when when the light strikes
  them at a grazing angle.

79
Reflectance of Metal
80
Reflectance of Dielectrics

• Non conducting material, e.g., glass, plastics.

81
Schlick Approximation

• To calculate F for every angle, we can use
  measurements of F0, the value of F at normal
  incidence.

82
Index of Refraction
83
Remaining Hard Problems

• Reflective Diffraction Effects
• thin films
• feathers of a blue jay
• Anisotropy
• brushed metals
• strands pulled materials
• satin and velvet cloths