CSC 830 Computer
Graphics
Lecture 5
Shading
Course Note Credit: Some of slides are extracted from the course notes of prof. Mathieu Desburn (USC)
and prof. Han-Wei Shen (Ohio State University).
1
Shading
Determining the light traveling from a point in the
scene to the viewer’s eye
Images courtesy of Watt, Watt & Watt, and Foley & van Dam
2
Shading
Light comes from many sources:
light  emitted  reflected
 transmitted
 scattered  absorbed
reflection
scattering
absorption
transmission
emission
3
Local versus Global
Illumination
 Local Illumination
 Only considers direct
illumination
 No reflection
 No refraction
 Shadows possible
 Global
Illumination
 Considers
indirect
illumination
 Reflection
 Refraction
 Shadows
4
Local versus Global
Illumination
Direct Illumination
P2
P1
Indirect Illumination
We will do local only for this lecture…
5
Local illumination
• Only consider the light, the observer position,
and the object material properties
6
Local versus Global
Illumination
Images courtesy of Francois Sillion
To understand shading properly, we need to
review some basic notions of physics…
7
Basic Illumination Model
• Simple and fast method for calculating
surface intensity at a given point
• Lighting calculation are based on:
– The background lighting conditions
– The light source specification: color, position
– Optical properties of surfaces:
• Glossy OR matte
• Opaque OR transparent (control refection and
absorption)
8
Radiance
Radiance: Power per unit projected area
perpendicular to the ray, per unit
solid angle in the direction of the ray
N
I ( x,  )
d
dA
Think of it as a flux of photons leaving the surface…
9
Irradiance
Irradiance: Radiant energy per unit area
E   dE  I ( x,  ) cos d


I ( x,  )


Think of it as a flux of photons bombarding the surface…
10
BRDF
Bidirectional Reflection Distribution Function
I ( x,  r )
f ( x,  i ,  r ) 
dE ( x,  i )
Determines the fraction of light from an incoming
direction reflected to an outgoing direction
Relates reflected radiance
to incoming irradiance…
11
Image courtesy of Watt, 3D Computer Graphics
Properties of the BRDF
Reciprocity
f ( x, i ,  r )  f ( x,  r , i )
In photography and holography, reciprocity refers to the relationship
between the intensity of the light and duration of the exposure that result
in identical exposure. Within the normal range for intensity and time for the
film, the reciprocity law states that exposure = intensity × time. Outside the
normal range the reciprocity law breaks down, which is known as reciprocity
failure.
12
Properties of the BRDF
Anisotropy
f ( x, i , i , r , r )  f ( x, i , i   , r , r   )
Anisotropy (the opposite of isotropy) is the property of being directionally
dependent.
In the field of computer graphics, an anisotropic surface will change in
appearance as it is rotated about its geometric normal, as is the case with
velvet. Anisotropic scaling occurs when something is scaled by different
amounts in different directions.
13
Reflectance Equation
BRDF allows us to calculate outgoing light,
given incoming light
I from i ( x,  r )  f ( x,  i ,  r ) dE ( x,  i )
Image courtesy of Watt, 3D Computer Graphics
14
Splitting the BRDF
In practice, BRDF can be really funky…
To simplify, we divide the BRDF into 3 components:
f  f ideal diffuse  f directional diffuse  f ideal specular
M
M
L
N
L

N
L

N


15
Reflectance
• 3 forms
16
Slide Courtesy of Dutre et. al on SIGGRAPH 2001
Ideal Specular Reflection
Reflection is only in the mirror direction
M
L
N


17
Ideal Diffuse Reflection
Reflection is equal in all directions
f ( x,  i ,  r )   diffuse
L
N
18
Directional Diffuse
Reflection
Reflection is concentrated around the mirror direction
M
L
N
19
Ambient Light
If a surface is visible from the eye, but not a
light, it will be rendered black (if indirect light is
not considered).
Ambient light is an approximation to indirect light
 Difficult to compute
 Approximate this as a constant
 Or a light source at the eye
20
Phong Reflection
Assume point lights and direct illumination only
I  I ambient  I diffuse  I specular
21
Diffuse Light
• The illumination that a surface receives from
a light source and reflects equally in all
directions
• This type of reflection is called Lambertian
Reflection (thus, Lambertian surfaces)
• The brightness of the surface is indepenent
of the observer position (since the light is
reflected in all direction equally)
22
Lambert’s Law
• How much light the surface receives from a
light source depends on the angle between
its angle and the vector from the surface point
to the light (light vector)
• Lambert’s law: the radiant energy ’Id’ from a
small surface da for a given light source is:
Id = IL * cos()
IL : the intensity of the light source
 is the angle between the surface
normal (N) and light vector (L)
23
Phong Diffuse Component
Diffuse component depends only on incident angle.
I diffuse  I l k d cos 
 I l k d ( N  L)
Note: L and N are unit…
Image courtesy of Watt, 3D Computer Graphics
24
Examples
Sphere diffusely lighted from various angles !
25
Specular Light
 These are the bright spots on objects (such as
polished metal, apple ...)
 Light reflected from the surface unequally to all
directions.
 The result of near total reflection of the incident
light in a concentrated region around the specular
reflection angle
26
Specular Highlights
• Shiny surfaces change appearance
when viewpoint is changed
• Specularities are caused by
microscopically smooth surfaces.
• A mirror is a perfect specular
reflector
27
Phong Specular
Component
Phong combines directional diffuse & ideal specular
n
specular
l s
I
 I k cos 
 I l k s ( R V )
Image courtesy of Watt, 3D Computer Graphics
n
28
Half Vector
• An alternative way of computing phong
lighting is: Is = ks * Is * (N*H)n
• H (halfway vector): halfway between V and L:
(V+L)/2
• Fuzzier highlight
• Check
http://www.lighthouse3d.com/opengl/glsl/in
N
H
dex.php?ogldir2
L
V
29
Phong Illumination
Moving Light
Change n
30
Phong Ambient
Component
Treat it as a constant:
I ambient  I a ka
Where
Ia
is the ambient light in the scene.
31
Adding Color
 I l ,r k d ,r 
 I l ,r k s ,r 
 I r   I a ,r k a ,r 
 I    I k   ( N  L)  I k   ( N  H ) n  I k 
 l,g d ,g 
 l ,g s,g 
 g   a,g a,g 
 I l ,b k d ,b 
 I l ,b k s ,b 
 I b   I a ,b k a ,b 
32
Adding Lights

 I l ,r k d ,r 
 I l ,r k s ,r  
 I r   I a ,r k a ,r 




I   I k  
n
 ( N  L)  I l , g k d , g   ( N  H )  I l , g k s , g  
 g   a , g a , g  l 
 I l ,b k d ,b 
 I l ,b k s ,b  
 I b   I al ,b k a ,b  lights

I  ka I a 
 (k
l lights
n
 Il
(
N

L
)

k
(
N

H
)
d
s
33
Phong Reflection
34
Image courtesy of Watt, 3D Computer Graphics
Aluminium
35
Bronze
36
Chrome
37
Stainless Steel
38
OpenGL Materials
GLfloat white8[] = {.8, .8, .8, 1.}, white2 = {.2,.2,.2,1.},black={0.,0.,0.};
GLfloat mat_shininess[] = {50.};
/* Phong exponent */
glMaterialfv(
GL_FRONT_AND_BACK,
GL_AMBIENT, black);
glMaterialfv(
GL_FRONT_AND_BACK,
GL_DIFFUSE, white8);
glMaterialfv(
GL_FRONT_AND_BACK,
GL_SPECULAR, white2);
glMaterialfv(
GL_FRONT_AND_BACK,
GL_SHININESS, mat_shininess);
39
OpenGL Lighting
GLfloat white[] = {1., 1., 1., 1.};
GLfloat light0_position[] = {1., 1., 5., 0.}; /* directional light (w=0) */
glLightfv(GL_LIGHT0, GL_POSITION, light0_position);
glLightfv(GL_LIGHT0, GL_DIFFUSE, white);
glLightfv(GL_LIGHT0, GL_SPECULAR, white);
glEnable(GL_LIGHT0);
glEnable(GL_NORMALIZE); /* normalize normal vectors */
glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);/* two-sided lighting*/
glEnable(GL_LIGHTING);
40
Vertex Normals vs. Face
Normals
What are the normals to the surface?
Each polygonal face has a normal.
c
N = (b - a) x (c - b)
a
b
We call these face normals.
41
Flat Shading
Assume a constant color across the polygon
c
a
b
Uses face normals
Equivalent to single point sampling…
Polygon mesh is only an approximation.
Can we do better?
42
Vertex Normals vs. Face
Normals
Should use the actual surface’s normals
Usually stored at the vertices of the object
Can calculate as averages of face normals
43
Mach Band ?
44
Mach Band ?
45
Shading Models for Polygons
 Constant Shading (flat shading)
 Compute illumination at any one point on the surface.
Use face or one normal from a pair of edges. Good for
far away light and viewer or if facets approximate
surface well.
 Per-Pixel Shading
 Compute illumination at every point on the surface.
 Interpolated Shading
 Compute illumination at vertices and interpolate color
46
Interpolation
Given vertex normals, how to color the interior:
 Gouraud Interpolation
 Phong Interpolation
47
Un-lit
48
Flat Shading
49
Gouraud Interpolation – Interpolated Shading
50
Phong Interpolation – Per pixel Shading
51
Gouraud Interpolation
Calculate the color at each vertex
C(c)
C(a)
C(b)
Interpolate the colors
C(c)
C = t C(b) + (1 – t) C(c)
C(a)
C(b)
52
Gouraud Interpolation
Problems
Misses some highlights
light
shading will be constant!
Shading is not linear
53
Phong Interpolation
Interpolate the normals, then compute the colors
light
Interpolation is usually done component-wise
54
Phong Shading Model
 Gouraud shading does not properly handle specular highlights,
specially when the n parameter is large (small highlight).
Reason: colors are interpolated.
Solution: (Phong Shading Model)
1. Compute averaged normal at vertices.
2. Interpolate normals along edges and scan-lines. (component by
component)
3. Compute per-pixel illumination.
55
56
Interpolation
Image courtesy of Watt & Watt, Advanced Animation and Rendering Techniques
57
Interpolated Shading - Problems
 Problems at shared vertices – shared by right polygons and
not by one on left and hence discontinuity
 Incorrect Vertex normals – no variation in shade
58
Shade Trees
Phong Shade Tree:
+
*
ka
*
*
Ia
kd Il
ks
Il
dot
dot
N
pow
L
N
n
H
59
Shading Language
A language for implementing shading models
State is passed to/from the shader by global variables
Ci – Outgoing ray color
Oi – Outgoing ray opacity
N
I
Cs – Surface color
Os – Surface opacity
P – Surface point
N - Surface normal
I - Direction of viewing (eye ray)
L - Direction to the light source
L
60
Shading Language
Phong Surface Shader:
surface
plastic(float Ks = .5, float Kd = .5, float Ka = 1,
float roughness = .1, color specularColor = 1)
{
point Nf = faceforward(N,I);
Oi = Os;
Ci = Os*(Cs*(Ka*ambient()+Kd*diffuse(Nf)
+ specularColor*Ks*specular(Nf,-I,roughness);
}
61
Light Sources
• Point light source
• Directional light source: e.g. sun light
• Spot light
62
Spot Light
• To restrict a light’s effects to a limited area of the scene
• Flap: confine the effects of the light to a designed range in
x, y, and z world coordinate
• Cone: restrict the effects of the light using a cone with a
generating angle d
63
Light Source Attenuation
• Takes into account the distance of the light
from the surface
I’L = I L * fatt (d)
I’L: the received light after attenuation
I L: the original light strength
fatt: the attenuation factor
d: the distance between the light source
and the surface point
• fatt = max ( 1/(c1 + c2*d + c3*d2) , 1)
• C1, C2, C3 are user defined constants
associated with each light source
64
Hints for HW4
• Shading can be done in easily in view space or in
world space where all light, view, & surface normal
vectors are described in same coordinate space. –
how can you achieve this effect?
• For normal transformation, use only 3x3 rotation
matrix out of the 4x4 transformation & inverse
transpose of it – remember normal transformation
from the lecture 2?
• For Phong shading, interpolate normal & compute
shading for each pixel. For Gouraud shading,
compute shading at only vertex and interpolate
the color.
65