1. Visual Appearance (Shading & Texture mapping)
Course Note Credit: Some of slides are extracted from the course notes of prof. J. Lee (SNU),
prof. M. Desbrun (USC) and prof. H.-W. Shen (OSU) and others.

2. Shading (Local illumination)

3. Photorealism in Computer Graphics
Photorealism in computer graphics involves
Accurate representations of surface properties, and
Good physical descriptions of the lighting effects
Modeling the lighting effects that we see on an object is a complex process, involving principles of both physics and psychology
Physical illumination models involve
Material properties, object position relative to light sources and other objects, the features of the light sources, and so on

4. Illumination and Rendering
An illumination model in computer graphics
also called a lighting model or a shading model
used to calculate the color of an illuminated position on the surface of an object
Approximations of the physical laws
A surface-rendering method determine the pixel colors for all projected positions in a scene

5. Light Sources Point light sources Infinitely distant light sources
Emitting radiant energy at a single point
Specified with its position and the color of the emitted light
Infinitely distant light sources
A large light source, such as sun, that is very far from a scene
Little variation in its directional effects
Specified with its color value and a fixed direction for the light rays

6. Light Sources Directional light sources Area light sources
Produces a directional beam of light
Spotlight effects
Area light sources

7. Light Sources Radial intensity attenuation
As radiant energy travels, its amplitude is attenuated by the factor
Sometimes, more realistic attenuation effects can be obtained with an inverse quadratic function of distance
The intensity attenuation is not applied to light sources at infinity because all points in the scene are at a nearly equal distance from a far-off source

8. Light Sources Angular intensity attenuation
For a directional light, we can attenuate the light intensity angularly as well as radially

9. Surface Lighting Effects
An illumination model computes the lighting effects for a surface using the various optical properties
Degree of transparency, color reflectance, surface texture
The reflection (phong illumination) model describes the way incident light reflects from an opaque surface
Diffuse, ambient, specular reflections
Simple approximation of actual physical models

10. Diffuse Reflection
Incident light is scattered with equal intensity in all directions
Such surfaces are called ideal diffuse reflectors (also referred to as Lambertian reflectors)

11. Lambert’s Cosine Law
The reflected luminous intensity in any direction from a perfectly diffusing surface varies as the cosine of the angle between the direction of incident light and the normal vector of the surface.
Intuitively: cross-sectional area of the “beam” intersecting an element of surface area is smaller for greater angles with the normal.

12. Diffuse Reflection : the intensity of the light source
Ideally diffuse surfaces obey cosine law.
Often called Lambertian surfaces.
: the intensity of the light source
: diffuse reflection coefficient,
: the surface normal (unit vector)
: the direction of light source, (unit vector)

13. Ambient Light
Multiple reflection of nearby (light-reflecting) objects yields a uniform illumination
A form of diffuse reflection independent of the viewing direction and the spatial orientation of a surface
Ambient illumination is constant for an object
: the incident ambient intensity
: ambient reflection coefficient, the proportion reflected away from the surface

14. Ambient + Diffuse

15. Specular Reflection
Perfect reflector (mirror) reflects all lights to the direction where angle of reflection is identical to the angle of incidence
It accounts for the highlight

16. Specular Reflection Phong specular-reflection model
Note that N, L, and R are coplanar, but V may not be coplanar to the others
: intensity of the incident light
: color-independent specular coefficient
: the gloss of the surface

17. Specular Reflection
Glossiness of surfaces

18. Specular Reflection
Specular-reflection coefficient ks is a material property
For some material, ks varies depending on q
ks =1 if q =90°
Calcularing the reflection vector R

19. Specular Reflection Simplified Phong model using halfway vector
H is constant if both viewer and the light source are sufficiently far from the surface

20. Ambient+Diffuse+Specular Reflections
Single light source
Multiple light source

21. Parameter Choosing Tips
For a RGB color description, each intensity and reflectance specification is a three-element vector
The sum of reflectance coefficients is usually smaller than one
Try n in the range [0, 100]
Use a small ka (~0.1)
Example
Metal: n=90, ka=0.1, kd=0.2, ks=0.5

23. Atmospheric Effects
A hazy atmosphere makes colors fade and objects appear dimmer
Hazy-atmosphere effect is often simulated with an exponential attenuation function such as
Higher values for r produce a denser atmosphere

24. Polygon Rendering Methods
We could use an illumination model to determine the surface intensity at every projected pixel position
Or, we could apply the illumination model to a few selected points and approximate the intensity at the other surface positions
Curved surfaces are often approximated by polygonal surfaces
So, polygonal (piecewise planar) surfaces often need to be rendered as if they are smooth

25. Constant-Intensity Surface Rendering
Constant (flat) shading
Each polygon is one face of a polyhedron and is not a section of a curved-surface approximation mesh

26. Intensity-Interpolation Surface Rendering
Gouraud shading
Rendering a curved surface that is approximated with a polygon mesh
Interpolate intensities at polygon vertices
Procedure
Determine the average unit normal vector at each vertex
Apply an illumination model at each polygon vertex to obtain the light intensity at that position
Linearly interpolate the vertex intensities over the projected area of the polygon

27. Intensity-Interpolation Surface Rendering
Normal vectors at vertices
Averaging the normal vectors for each polygon sharing that vertex 4 3 2 1 ) ( N v + =

28. Intensity-Interpolation Surface Rendering
Intensity interpolation along scan lines
I4 and I5 are interpolated along y-axis, and then
Ip is interpolated along x-axis
Incremental calculation is also possible y 3 1 p
scan line 4 5 2 x

29. Intensity-Interpolation Surface Rendering

30. Gouraud Shading Problems
Lighting in the polygon interior is inaccurate
Mach band effect
Optical illusion

31. Mach Band Effect
These “Mach Bands” are not physically there. Instead, they are illusions due to excitation and inhibition in our neural processing
The bright bands at 45 degrees (and 135 degrees) are illusory.
The intensity of each square is the same.

32. Mach Band artifact (Gouraud Shading)
Mach bands:
Caused by interaction of neighboring retinal neurons.
Acts as a sort of high-pass filter, accentuating discontinuities in first derivative.
Linear interpolation causes first deriv. Discontinuities at polygon edges.

33. Normal-Vector Interpolation for Surface Rendering
Phong shading
Interpolate normal vectors at polygon vertices
Procedure
Determine the average unit normal vector at each vertex
Linearly interpolate the vertex normals over the projected area of the polygon
Apply an illumination model at positions along scan lines to calculate pixel intensities n1 n2 n3

34. Gouraud versus Phong Shading
Gouraud shading is faster than Phong shading
OpenGL supports Gouraud shading
Phong shading is more accurate

35. Texture Mapping

36. Can you do this …

37. Visual Realism

38. Texture Mapping Surfaces in real world are very complex
Objects have properties that vary across surface
Cannot model all the fine variations
We need to find ways to add surface detail
How?

39. Texture Mapping
Of course, one can model the exact micro-geometry + material property to control the look and feel of a surface
But, it may get extremely costly
So, graphics use a more practical approach – texture mapping

40. Texture Mapping Texture Mapping
Want a function that assigns a color to each point
The the surface is a 2D domain, so that is essentially an image
can represent using any image representation
raster texture images are very popular

41. Photo-textures

42. OpenGL functions - demo
Usually texture is a (2D/3D) image.
During initialization read in or create the texture image and place it into the OpenGL state.
glTexImage2D (GL_TEXTURE_2D, 0, GL_RGB, imageWidth, imageHeight, 0, GL_RGB, GL_UNSIGNED_BYTE, imageData);
Before rendering your textured object, enable texture mapping and tell the system to use this particular texture.
glBindTexture (GL_TEXTURE_2D, 13);

43. OpenGL functions
During rendering, give the cartesian coordinates and the texture coordinates for each vertex.
glBegin (GL_QUADS);
glTexCoord2f (0.0, 0.0);
glVertex3f (0.0, 0.0, 0.0);
glTexCoord2f (1.0, 0.0);
glVertex3f (10.0, 0.0, 0.0);
glTexCoord2f (1.0, 1.0);
glVertex3f (10.0, 10.0, 0.0);
glTexCoord2f (0.0, 1.0);
glVertex3f (0.0, 10.0, 0.0);
glEnd ();

44. Texture and Texel Each pixel in a texture map is called a Texel
Each Texel is associated with a (u,v) 2D texture coordinate
The range of u, v is [0.0,1.0] due to normalization

45. (u,v) tuple
For any (u,v) in the range of (0-1, 0-1) multiplied by texture image width and height, we can find the corresponding value in the texture map

46. How do we get F(u,v)? We are given a discrete set of values:
F[i,j] for i=0,…,N, j=0,…,M
Nearest neighbor:
F(u,v) = F[ round(N*u), round(M*v) ]
Linear Interpolation:
i = floor(N*u), j = floor(M*v)
interpolate from F[i,j], F[i+1,j], F[i,j+1], F[i+1,j]
Filtering in general !

47. Interpolation
Nearest neighbor
Linear Interpolation

48. Specifying texture coordinates
Texture coordinates needed at every vertex
Hard to specify by hand
Difficult to wrap a 2D texture around a 3D object

49. We would like a constant cost per pixel
Texture Filtering
Resampling using mip mapping
Magnification: Interpolation
Minification: Averaging
Texture
Image
Texture => Image
We would like a constant cost per pixel

50. Mip Mapping MIP = Multim In Parvo = Many things in a small place
Constructs an image pyramid. Each level is a prefilteredversion of the level below resampled at half the frequency.
Whilerasterizing use the level with the sampling rate closest to the desired sampling rate.

51. Trilinear interpolation
Mip Mapping
Used with bilinear/trilinear interpolation R R G B G B
Trilinear interpolation

52. Mip Mapping - Example
Courtesy of John hart
used to save some of the filtering work needed during texture minification

53. Texture Filtering Methods
Nearest Neighbor interpolation
Bilinear Interpolation
Trilinear Interpolation
Anisotropic filtering
Precomputed rectangular(trapezoidal) maps
<anisotropic filtering)

54. example
No mip mapping vs with mip mapping

55. example
Bilinear mip mapping vs trilinear mip mapping

56. Specifying texture coordinates
Texture coordinates needed at every vertex
Hard to specify by hand
Difficult to wrap a 2D texture around a 3D object

57. Planar mapping
Compute texture coordinates at each vertex by projecting the map coordinates onto the model

58. Cylindrical Mapping

59. Spherical Mapping

60. Cube Mapping

61. Modelling Surface Properties
Can use a texture to supply any parameter of the illumination model
ambient, diffuse, and specularcolor
Specular exponent
roughness

62. Environment Maps Use texture to represent reflected color
Texture indexed by reflection vector
Approximation works when objects are far away from the reflective object

63. Spatially variant resolution
Environment Maps
Using a spherical environment map
Spatially variant resolution

64. Environment Maps
Using a cubical environment map

65. Environment Mapping
Environment mapping produces reflections on shiny objects
Texture is transferred in the direction of the reflected ray from the environment map onto the object
Reflected ray: R=2(N·V)N-V
Environment Map
Viewer
Reflected ray
Object

66. Approximations Made
The map should contain a view of the world with the point of interest on the object as the eye
We can’t store a separate map for each point, so one map is used with the eye at the center of the object
Introduces distortions in the reflection, but the eye doesn’t notice
Distortions are minimized for a small object in a large room
The mapping can be computed at each pixel, or only at the vertices

67. Example

68. Refraction Maps
Use texture to represent refraction

69. Use texture to represent opacity
Opacity Maps
Use texture to represent opacity
RGB channels
Use the alpha channel to make portions of the texture transparent. Cheaper than explicit modelling
alpha channels

70. Illumination Maps
Use texture to represent illumination footprint

71. Illumination Maps
Quake light maps

72. Does not change silhouette edges
Bump Mapping
Use texture to perturb normals
Textures are treated as height field
creates a bump-like effect + =
original surface
bump map
modified surface
Does not change silhouette edges

73. Bump mapping

74. Normal Mapping (bump mapping)
Replace normals

75. Bump Mapping
Many textures are the result of small perturbations in the surface geometry
Modeling these changes would result in an explosion in the number of geometric primitives.
Bump mapping attempts to alter the lighting across a polygon to provide the illusion of texture.

76. Bump mapping only affects the normals,
Displacement Mapping
Use texture to displace the surface geometry + =
Bump mapping only affects the normals,
Displacement mapping changes the entire surface (including the silhouette)

77. Displacement Mapping

78. Can simulate an object carved from a material
3D Textures
Use a 3D mapping
Marble or wood
The object is “carved”out of the solid texture
Can simulate an object carved from a material

79. Texture Synthesis
Texture Synthesis

80. Transparency Alpha Blending
a: foreground object , b: background object, o: output
Alpha : opacity , C : color