1. Illumination and Shading Angel, Chapter 6 slides from AW, etc.
CSCI 6360/4360

2. Overview Photorealism and complexity Rendering equation
Light interactions with a solid
Rendering equation
“infinite scattering and absorption of light”
Local vs. global illumination
Local techniques
Flat, Gouraud, Phong
An illumination model
“describes the inputs, assumptions, and outputs that we will use to calculate illumination of surface elements”
Light
Reflection characteristics of surfaces
Diffuse reflection, Lambert’s law, specular reflection
Phong approximation – interpolated vector shading

3. Angel on Speed for Interactivity
“… our goal is to create realistic shading effects in as close to real time as possible, rather than trying to model the BRDF as accurately as possible. Hence, we use tricks with a local model to simulate effects that can be global in nature.”
P. 298
“Because we cannot solve the full rendering equation, we instead use various tricks in an attempt to obtain realistic renderings, …”
P. 307
Good enough … for “fast” (interactive) graphics
Things change with time
Moore’s law

4. Photorealism and Complexity
Recall, from 1st lecture … examples below exhibit range of “realism”
In general, trade off realism for speed – interactive computer graphics
Wireframe – just the outline
Local illumination models, polygon based
Flat shading – same illumination value for all of each polygon
Smooth shading (Gouraud and Phong) – different values across polygons
Global illlumination models
E.g., Raytracing – consider “all” interactions of light with object
Wireframe
Polygons – Flat shading
Polygons - Smooth shading
Ray tracing

5. Shading So far, just used OpenGL pipeline for vertices
Polygons have all had constant color
glColor(_)
Not “realistic” – or computationally complex
Of course, OpenGL can (efficiently) provide more realistic images
Light-material interactions cause each point to have a different color or shade
Need to consider :
Light sources
Material properties
Location of viewer
Surface orientation
Terminology
“Lighting”
modeling light sources, surfaces, and their interaction
“Shading”
how lighting is done with polygon

6. Rendering Equation Light travels …
Light strikes A
Some scattered, some absorbed, …
Some of scattered light strikes B
Some of this scattered light strikes A
And so on …
Infinite scattering and absorption of light can be described by rendering equation
Bidirectional reflection distribution function
Cannot be solved in general
Ray tracing is a special case for perfectly reflecting surfaces
Rendering equation is global, includes:
Shadows
Multiple scattering from object to object
… and everything
translucent surface
shadow
multiple reflection

7. Elements of Global Illumination
Simulating what happens when other objects effect light reaching a surface element
e.g., ray tracing
Lights and Shadows
Most light comes directly light sources
Light from a source may be blocked by other objects
In “shadow” from that light source, so darker
All Non – global can’t do shadows
Inter-Object Reflection
Light strikes other objects, bounces toward surface element
When that light reaches surface element from other surface elements, brightens surface element (indirect illumination)
Expensive to Compute
Many objects in scene affect light reaching surface elements
But, necessary for some applications
translucent surface
shadow
multiple reflection

8. Global Illumination – Ray Tracing
Image formed from all light reaching view
Ray tracing (or casting)
Basically, “running things backwards, constrained by pixels …”
Follow rays from center of projection until they either are absorbed by objects or go off to infinity
Can handle global effects
Multiple reflections
Translucent objects
Slow
Must have whole data base available at all times
Radiosity
Energy based approach
Very slow

9. Light Interactions with a Solid
Will focus on surface properties and light-material interactions
But, there are complexities in modeling light …
but good enough is good enough…
Below from Watt, “3d Computer Graphics”

10. Light – Material Interactions for CG (quick look)
Will examine each of these in detail
Diffuse surface
Matte, dull finish
Light “scattered” in all directions
Specular surface
Shiny surface
Light reflected (scattered) in narrow range of directions
Translucent surface
Light penetrates surface and emerges in another location on object

11. Physical Model: BRDF Bidirectional Reflectance Distribution Function
Light energy can arrive at any point on a surface from any direction and be reflected and leave from any direction
For every pair of input and output directions, will be a value that is the fraction of incoming light that is reflected and leave in output direction
BDRF – Bidirectional reflectance distribution function
Describes reflectance, absorption, and transmission of light at surface of material
BDRF is a function of
Frequency of light
2 angles to describe light in
2 angles to describe light out

12. Physical Model: BRDF
Light energy can arrive at any point on a surface from any direction and be reflected and leave from any direction
For every pair of input and output directions, will be a value that is the fraction of incoming light that is reflected and leave in output direction
Obtaining BDRF’s empirically
… and how many points are there to consider???

13. “Surface Elements” for Interactive CG (a big idea)
A computer graphics issue/orientation:
Consider everything or just “sampling a scene”?
Again, global view considers all light coming to viewer:
From each point on each surface in scene - object precision
Points are smallest units of scene
Can think of points having no area or infinitesimal area
i.e., there are an infinite number of visible points.
Of course, computationally intractable
Alternatively, consider surface elements
Finite number of differential pieces of surface
E.g., polygon
Figure out how much light comes to viewer from each of these pieces of surface
Often, relatively few (vs. infinite) is enough
Reduction of computation through use of surface elements is at core of tractable/interactive cg

14. Surface Elements and Illumination, 1
Tangent Plane Approximation for Objects
Most surfaces are curved: not flat
Surface element is area on that surface
Imagine breaking up into very small pieces
Each of those pieces is still curved,
but if we make the pieces small enough,
then we can make them arbitrarily close to being flat
Can approximate this small area with a tiny flat area
Surface Normals
Each surface element lies in a plane.
To describe plane, need a point and a normal
Area around each of these vertices is a surface element where we calculate “illumination”
Illumination

15. Surface Elements and Illumination, 2
Tangent Plane Approximation for Objects
Surface Normals
Illumination
Again, light rays coming from rest of scene strike surface element and head out in different directions
Light that goes in direction of viewer from that surface element
If viewer moves, light will change
This is “illumination” of that surface element
Will see model for cg later

16. In Sum: Local vs. Global Rendering
Correct shading requires a global calculation involving all objects and light sources
Recall “rendering equation”
infinite scattering and absorption of light
Incompatible with pipeline model which shades each polygon independently (local rendering)
However, in computer graphics, especially real time graphics, happy if things “look right”
Exist many techniques for approximating global effects
Will see several

17. Light-Material Interaction, 1
Light that strikes an object is partially absorbed and partially scattered (reflected)
Amount reflected determines color and brightness of object
Surface appears red under white light because the red component of light is reflected and rest is absorbed
Can specify both light and surface colors
rough surface
Livingstone, “Vision and Art”

18. Light-Material Interaction, 2
Reflected light is scattered in a manner that depends on the smoothness and orientation of surface to light source
Diffuse surfaces
Rough (flat, matte) surface scatters light in all directions
Appear same from different viewing angles
Specular surfaces
Smoother surfaces, more reflected light is concentrated in direction a perfect mirror would reflected the light
Light emerges at single angle
… to varying degrees – Phong shading will model

19. Light Sources
General light sources are difficult to work with because must integrate light coming from all points on the source
Use “simple” light sources
Point source
Model with position and color
Distant source = infinite distance away (parallel)
Spotlight
Restrict light from ideal point source
Ambient light
A real convenience – recall, “rendering equation” – but real nice
Same amount of light everywhere in scene
Can model (in a good enough way) contribution of many sources and reflecting surfaces

20. Overview: Local Rendering Techniques
Will consider
Illumination (light) models focusing on following elements:
Ambient
Diffuse
Attenuation
Specular Reflection
Interpolated shading models:
Flat, Gouraud, Phong, modified/interpolated Phong (Blinn-Phong)

21. About (Local) Polygon Mesh Shading (it’s all in how many polygons there are)
Angel example of approximation of a sphere…
Recall, any surface can be illuminated/shaded/lighted (in principle) by:
1. calculating surface normal at each visible point and
2. applying illumination model
… or, recall surface model of cg!
Again, where efficiency is consideration, e.g., for interactivity (vs. photorealism) approximations are used
Fine, because polygons themselves are approximation
And just as a circle can be considered as being made of “an infinite number of line segments”,
so, it’s all in how many polygons there are!

22. About (Local) Polygon Mesh Shading (interpolation)
Interpolation of illumination values are widely used for speed
And can be applied using any illumination model
Will see three methods - each treats a single polygon independently of others (non-global)
Constant (flat)
Gouraud (intensity interpolation)
Interpolated Phong (normal-vector interpolation)
Each uses interpolation differently

23. Flat/Constant Shading, About
Single illumination value per polygon
Illumination model evaluated just once for each polygon
1 value for all polygon, Which is as fast as it gets!
As “sampling” value of illumination equation (at just 1 point)
Right is flat vs. smooth (Gouraud) shading
If polygon mesh is an approximation to curved surface,
faceted look is a problem
Also, facets exaggerated by mach band effect
For fast, can (and do) store normal with each surface
Or can, of course, compute from vertices
But, interestingly, approach is valid, if:
Light source is at infinity (is constant on polygon)
Viewer is at infinity (is constant on polygon)
Polygon represents actual surface being modeled (is not an approximation)!

24. Flat/Constant Shading, Light Source
In cg lighting, often don’t account for angle of rays
Approach is valid, if …
Light source is at infinity (is constant on polygon)
Viewer is at infinity (is constant on polygon)
Polygon represents actual surface being modeled (is not an approximation)
Consider point light sources at right
Close to surface: L1 <> L2 <> L3
Farther from surface: L1 <> L2 <> L3, but closer 
At “infinity” can consider: L1 = L2 = L3! – same for V!,
so and are constant on polygon

25. But, … Mach Banding
May or may not be apparent here …

26. Mach Banding (Chevreul illusion)

27. Mach Banding Mach banding In fact, physiological cause
Exaggerated differences in perceived intensities
At adjacent edges of differing gintensities
Non-intuitive and striking
An “illusion” in sense that perception not veridical (true)
In fact, physiological cause
Actual and perceived intensities due to cellular bilateral inhibition
sensation (response of retinal cells) depends on how cell neighbors are stimulated
Eye’s photoreceptors responds to light
according to intensity of light falling on it minus the activation of its neighbors
Great for human edge detection
A challenge for computer graphics
Ernst Mach

28. Mach Bands and Receptor Fields
Point where uniform area meets luminance ramp, bright band is perceived
Another way, appear where abrupt change in 1st derivative of brightness profile
Particularly a problem for uniformly shaded polygons in computer graphics
Hence, various methods of smoothing are applied
… any number of “unintended” things can happen with perception

29. Simultaneous Brightness Contrast fyi
Gray patch on a dark background looks lighter than the same patch on a light background

30. Simultaneous Brightness Contrast fyi
Background removed! (honest, no change in foreground)

31. Gouraud Shading, About
Recall, for flat/constant shading, single illumination value per polygon
Gouraud (or smooth, or interpolated intensity) shading overcomes problem of discontinuity at edge exacerbated by Mach banding
“Smooths” where polygons meet
H. Gouraud, "Continuous shading of curved surfaces," IEEE Transactions on Computers, 20(6):623–628, 1971.
Linearly interpolate intensity along scan lines
Eliminates intensity discontinuities at polygon edges
Still have gradient discontinuities,
So mach banding is improved, but not eliminated
Must differentiate desired creases from tessellation artifacts
(edges of a cube vs. edges on tesselated sphere)

32. Gouraud Shading, About
To find illumination intensity, need intensity of illumination and angle of reflection
Flat shading uses 1 angle
Gouraud estimates
…. Interpolates
1. Use polygon surface normals to calculate “approximation” to vertex normals
Average of surrounding polygons’ normals
Since neighboring polygons sharing vertices and edges are approximations to smoothly curved surfaces
So, won’t have greatly differing surface normals
Approximation is reasonable one
2. Interpolate intensity along polygon edges
3. Interpolate along scan lines
i.e,, find:
Ia, as interpolated value between I1 and I2
Ib, as interpolated value between I1 and I3
Ip, as interpolated value between Ia and Ib
formulaically, next slide

33. (S) Gouraud Shading, Formulaically
What goes in (firmware) - straightforward
3: interpolate along scan lines
e.g., find:
Ia, as interpolated value between I1 and I2
Ib, as interpolated value between I1 and I3
Ip, as interpolated value between Ia and Ib
i.e., formulaically: or

34. (S) Gouraud Shading Can also interpolate color
Though less straightforward
Summary: Interpolating intensity
Gouraud shading
Gouraud versus constant shading
integrates nicely with scan line algorithm:
constant along polygon edge:

35. What Gouraud Shading Misses
Misses specular highlights in specular objects
because interpolates vertex colors instead of vertex normals
interpolating normal comes closer to what actual normal of surface being “polygonally” approximated would be
Illumination model following, and its implementation in Phong shading, does handle
Below:
Flat/constant, Gouraud/interpolated intensity, Phong

36. Illumination Model, Describing Light, 1
Will be looking at model of illumination for cg
Why are things relatively brighter or darker depending on orientation to light source and viewer?
Start with light …
Units of light
light incident on a surface and exiting from a surface is measured in specific terms defined later
for now, consider the ratio:
Light exiting surface from the viewer
Light incident on surface from light
Another way to conceptualize
Quick take ( note diff angle, theta, at right):
Just not as much “light” (energy) per surface area unit – for non “straight on” light
dA “shorter” (less) on left, than right
And can describe quantitatively

37. Describing Light, 2
Factors in computing “light exiting surface” (how bright)
physical properties of the surface (material)
geometric relationship of surface with respect to viewer
geometric relationship of surface with respect to lights
light incident on the surface (color and intensity of lights in the scene)
polarization, fluorescence, phosphorescence
Difficult to define some of these inputs
not sure what all categories of physical properties are …,
and the effect of physical properties on light is not totally understood
polarization of light, fluorescene, phosphorescene difficult to keep track of
Light exiting surface toward viewer
Light incident on surface from lights

38. Simple Illumination Model
One of first models of illumination that “looked good” and could be calculated efficiently
simple, non-physical, non-global illumination model
describes some observable reflection characteristics of surfaces
came out of work done at the University of Utah in the early 1970’s
still used today, as it is easy to do in software and can be optimized in hardware
Later, will put all together with normal interpolation
Components of a simple model
Reflection characteristics of surfaces
Diffuse Reflection
Ambient Reflection
Specular Reflection
Model not physically-based, and does not attempt to accurately calculate global illumination
does attempt to simulate some of important observable effects of common light interactions
can be computed quickly and efficiently

39. Reflection Characteristics of Surfaces, Diffuse Reflection (1/7)
Diffuse (Lambertian) reflection
typical of dull, matte surfaces
e.g. carpet, chalk plastic
independent of viewer position
dependent on light source position
(in this case a point source, again a non-physical abstraction)
Vecs L, N used to determine reflection
Value from Lambert’s cosine law … next slide

40. Reflection Characteristics of Surfaces, Lambert’s Law (2/7)
Lambert’s cosine law:
Specifies how much energy/light reflects toward some point
Computational form used in equation for illumination model
Now, have intensity (I) calculated from:
Intensity from point source
Diffuse reflection coefficient (arbitrary!)
With cos-theta calculated using normalized vectors N and V
For computational efficiency
Again:

41. Reflection Characteristics of Surfaces, Energy Density Falloff (3/7)
Less light as things are farther away from light source
Reflection - Energy Density Falloff
Should also model inverse square law energy density falloff
Formula often creates harsh effects
However, this makes surfaces with equal differ in appearance ¾ important if two surfaces overlap
Do not often see objects illuminated by point lights
Can instead use formula at right
Experimentally-defined constants
Heuristic

42. Reflection Characteristics of Surfaces, Ambient Reflection (4/7)
Diffuse surfaces reflect light
Some light goes to eye, some to scene
Light bounces off of other objects and eventually reaches this surface element
This is expensive to keep track of accurately
Instead, we use another heuristic
Ambient reflection
Independent of object and viewer position
Again, a constant – “experimentally determined”
Exists in most environments
some light hits surface from all directions
Approx. indirect lighting/global illumination
A total convenience
but images without some form of ambient lighting look stark, they have too much contrast
Light Intensity = Ambient + Attenuation*Diffuse

43. Reflection Characteristics of Surfaces, Color (5/7)
Colored Lights and Surfaces
Write separate equation for each component of color model
Lambda - wavelength
represent an object’s diffuse color by one value of for each component
e.g., in RGB
are reflected in proportion to
e.g., for the red component
Wavelength dependent equation
Evaluating the illumination equation at only 3 points in the spectrum is wrong, but often yields acceptable pictures.
To avoid restricting ourselves to one color sampling space, indicate wavelength dependence with (lambda).

44. Reflection Characteristics of Surfaces, Specular Reflection (6/7)
Directed reflection from shiny surfaces
typical of bright, shiny surfaces, e.g. metals
color depends on material and how it scatters light energy
in plastics: color of point source, in metal: color of metal
in others: combine color of light and material color
dependent on light source position and viewer position
Early model by Phong neglected effect of material color on specular highlight
made all surfaces look plastic
for perfect reflector, see light iff
for real reflector, reflected light falls off as increases
Below, “shiny spot” size < as angle view >

45. Reflection Characteristics of Surfaces, Specular Reflection (7a/7)
Phong Approximation
Again, non-physical, but works
Deals with differential “glossiness” in a computationally efficient manner
Below shows increasing n, left to right
“Tightness” of specular highlight
n in formula below (k, etc., next slide)

46. Reflection Characteristics of Surfaces, Specular Reflection (7b/7)
Yet again, constant, k, for specular component
Vectors R and V express viewing angle and so amount of illumination
n is exponent to which viewing angle raised
Measure of how “tight”/small specular highlight is

47. Putting it all together: A Simple Illumination Model
Non-Physical Lighting Equation
Energy from a single light reflected by a single surface element
For multiple point lights, simply sum contributions
An easy-to-evaluate equation that gives useful results
It is used in most graphics systems,
but it has no basis in theory and does not model reflections correctly!

48. Interpolated Vector Shading/Model
Calculating normal at each point is computationally expensive
Can interpolate normal
As interpolated vertices with Gouraud shading
Interpolated Vector Model:
Rather than recalculate normal at each at each step, interpolate normal for calculation
Much more computationally efficient
Bui Tuong Phong, "Illumination for Computer Generated Images," Comm. ACM, Vol 18(6): , June 1975

49. Phong Shading
Normal vector interpolation
interpolate N rather than I
especially important with specular reflection
computationally expensive at each pixel to recompute
must normalize, requiring expensive square root
Looks much better than Gouraud and done in commodity hardware
OpenGL default
Bui Tuong Phong, "Illumination for Computer Generated Images," Comm. ACM, Vol 18(6): , June 1975

50. Demo Program
Calculates Phong shading at each point on sphere

51. End .

52. OpenGL Shading Functions
Polygonal shading
Flat
Smooth
Gouraud
Steps in OpenGL shading
Enable shading and select model
Specify normals
Specify material properties
Specify lights

53. Normals Normal – vector perpendicular to a surface
Recall, typically set by application program for each vertex or polygon
In OpenGL the normal vector is part of the state
Set by glNormal*()
glNormal3f(x, y, z);
glNormal3fv(p);
Usually we want to set the normal to have unit length so cosine calculations are correct
Length can be affected by transformations
Note that scaling does not preserved length
glEnable(GL_NORMALIZE) allows for autonormalization at a performance penalty

54. FYI - Normal for Trianglep0 p1 p2 n p
plane n ·(p - p0 ) = 0
n = (p2 - p0 ) ×(p1 - p0 )
normalize n  n/ |n|
Note that right-hand rule determines outward face

55. Enabling Shading Shading calculations are enabled by
glEnable(GL_LIGHTING)
Once lighting is enabled, glColor() ignored
Must enable each light source individually
glEnable(GL_LIGHTi) i=0,1…..
Can choose light model parameters:
glLightModeli(parameter, GL_TRUE)
GL_LIGHT_MODEL_LOCAL_VIEWER
do not use simplifying distant viewer assumption in calculation
GL_LIGHT_MODEL_TWO_SIDED
shades both sides of polygons independently

56. Defining a Point Light Source
For each light source, can set an RGBA (A for alpha channel)
For diffuse, specular, and ambient components, and
For the position
Code below from Angel, other ways to do it (of course)
GL float diffuse0[]={1.0, 0.0, 0.0, 1.0};
GL float ambient0[]={1.0, 0.0, 0.0, 1.0};
GL float specular0[]={1.0, 0.0, 0.0, 1.0};
Glfloat light0_pos[]={1.0, 2.0, 3,0, 1.0};
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glLightv(GL_LIGHT0, GL_POSITION, light0_pos);
glLightv(GL_LIGHT0, GL_AMBIENT, ambient0);
glLightv(GL_LIGHT0, GL_DIFFUSE, diffuse0);
glLightv(GL_LIGHT0, GL_SPECULAR, specular0);

57. Distance and Direction
Position is given in homogeneous coordinates
If w =1.0, we are specifying a finite location
If w =0.0, we are specifying a parallel source with the given direction vector
Coefficients in distance terms are by default a=1.0 (constant terms), b=c=0.0 (linear and quadratic terms)
Change by:
a= 0.80;
glLightf(GL_LIGHT0, GLCONSTANT_ATTENUATION, a);
GL float diffuse0[]={1.0, 0.0, 0.0, 1.0};
GL float ambient0[]={1.0, 0.0, 0.0, 1.0};
GL float specular0[]={1.0, 0.0, 0.0, 1.0};
Glfloat light0_pos[]={1.0, 2.0, 3,0, 1.0};

58. Spotlights f Use glLightv to set q -q Direction GL_SPOT_DIRECTION
Cutoff GL_SPOT_CUTOFF
Attenuation GL_SPOT_EXPONENT
Proportional to cosaf f -q q

59. Global Ambient Light Ambient light depends on color of light sources
A red light in a white room will cause a red ambient term that disappears when the light is turned off
OpenGL also allows a global ambient term that is often helpful for testing
glLightModelfv(GL_LIGHT_MODEL_AMBIENT, global_ambient)

60. Moving Light Sources
Light sources are geometric objects whose positions or directions are affected by the model-view matrix
Depending on where we place the position (direction) setting function, we can
Move the light source(s) with the object(s)
Fix the object(s) and move the light source(s)
Fix the light source(s) and move the object(s)
Move the light source(s) and object(s) independently

61. Material Properties
Material properties are also part of the OpenGL state and match the terms in the modified Phong model
Set by glMaterialv()
GLfloat ambient[] = {0.2, 0.2, 0.2, 1.0};
GLfloat diffuse[] = {1.0, 0.8, 0.0, 1.0};
GLfloat specular[] = {1.0, 1.0, 1.0, 1.0};
GLfloat shine = 100.0
glMaterialf(GL_FRONT, GL_AMBIENT, ambient);
glMaterialf(GL_FRONT, GL_DIFFUSE, diffuse);
glMaterialf(GL_FRONT, GL_SPECULAR, specular);
glMaterialf(GL_FRONT, GL_SHININESS, shine);

62. Front and Back Faces
The default is shade only front faces which works correctly for convex objects
If we set two sided lighting, OpenGL will shade both sides of a surface
Each side can have its own properties which are set by using
GL_FRONT, GL_BACK, or GL_FRONT_AND_BACK in glMaterialf
back faces not visible
back faces visible

63. Emissive Term
We can simulate a light source in OpenGL by giving a material an emissive component
This component is unaffected by any sources or transformations
GLfloat emission[] = 0.0, 0.3, 0.3, 1.0);
glMaterialf(GL_FRONT, GL_EMISSION, emission);

64. Transparency Material properties are specified as RGBA values
The A value can be used to make the surface translucent
The default is that all surfaces are opaque regardless of A
Later we will enable blending and use this feature

65. Efficiency
Because material properties are part of the state, if we change materials for many surfaces, we can affect performance
We can make the code cleaner by defining a material structure and setting all materials during initialization
typedef struct materialStruct {
GLfloat ambient[4];
GLfloat diffuse[4];
GLfloat specular[4];
GLfloat shineness;
} MaterialStruct;
We can then select a material by a pointer

66. Polygonal Shading Shading calculations are done for each vertex
Vertex colors become vertex shades
By default, vertex shades are interpolated across the polygon
glShadeModel(GL_SMOOTH);
If we use glShadeModel(GL_FLAT); the color at the first vertex will determine the shade of the whole polygon

67. Polygon Normals Polygons have a single normal
Shades at the vertices as computed by the Phong model can be almost same
Identical for a distant viewer (default) or if there is no specular component
Consider model of sphere
Want different normals at each vertex even though this concept is not quite correct mathematically

68. Smooth Shading We can set a new normal at each vertex
Easy for sphere model
If centered at origin n = p
Now smooth shading works
Note silhouette edge

69. Mesh Shading
The previous example is not general because we knew the normal at each vertex analytically
For polygonal models, Gouraud proposed we use the average of the normals around a mesh vertex
n = (n1+n2+n3+n4)/ |n1+n2+n3+n4|

70. Gouraud and Phong Shading
Gouraud Shading
Find average normal at each vertex (vertex normals)
Apply modified Phong model at each vertex
Interpolate vertex shades across each polygon
Phong shading
Find vertex normals
Interpolate vertex normals across edges
Interpolate edge normals across polygon
Apply modified Phong model at each fragment

71. Comparison
If the polygon mesh approximates surfaces with a high curvatures, Phong shading may look smooth while Gouraud shading may show edges
Phong shading requires much more work than Gouraud shading
Until recently not available in real time systems
Now can be done using fragment shaders (see Chapter 9)
Both need data structures to represent meshes so we can obtain vertex normals

72. End .