CSC 830 Computer Graphics Lecture 5 Shading

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CSC 830 Computer GraphicsLecture 5Shading
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).
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Shading
Determining the light traveling from a point in
the scene to the viewers eye
Images courtesy of Watt, Watt Watt, and Foley
van Dam
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Shading
Light comes from many sources
reflection
scattering
absorption
transmission
emission
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Local versus Global Illumination

• Global Illumination
• Considers indirect illumination
• Reflection
• Refraction
• Shadows

• Local Illumination
• Only considers direct illumination
• No reflection
• No refraction
• Shadows possible

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Local versus Global Illumination
Direct Illumination
Indirect Illumination
We will do local only for this lecture
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Local illumination

• Only consider the light, the observer position,
  and the object material properties

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Local versus Global Illumination
Images courtesy of Francois Sillion
To understand shading properly, we need to
review some basic notions of physics
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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)

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Radiance
Radiance Power per unit projected area
perpendicular to the ray, per unit solid
angle in the direction of the ray
Think of it as a flux of photons leaving the
surface
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Irradiance
Irradiance Radiant energy per unit area
Think of it as a flux of photons bombarding the
surface
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BRDF
Bidirectional Reflection Distribution Function
Determines the fraction of light from an incoming
direction reflected to an outgoing direction
Relates reflected radiance to incoming
irradiance
Image courtesy of Watt, 3D Computer Graphics
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Properties of the BRDF
Reciprocity Anisotropy
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Reflectance Equation
BRDF allows us to calculate outgoing light, given
incoming light
Image courtesy of Watt, 3D Computer Graphics
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Splitting the BRDF
In practice, BRDF can be really funkyTo
simplify, we divide the BRDF into 3 components
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Ideal Specular Reflection
Reflection is only in the mirror direction
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Ideal Diffuse Reflection
Reflection is equal in all directions
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Directional Diffuse Reflection
Reflection is concentrated around the mirror
direction
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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

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Phong Reflection
Assume point lights and direct illumination only
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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)

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Lamberts 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)
• Lamberts law the radiant energy Id from a
  small surface da for a given light source is
• Id IL cos(q)
• IL the intensity of the light source
• is the angle between the surface
• normal (N) and light vector (L)

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Phong Diffuse Component
Diffuse component depends only on incident angle.
N.B L and N are unit
Image courtesy of Watt, 3D Computer Graphics
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Examples
Sphere diffusely lighted from various angles !
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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

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Specular Highlights

• Shiny surfaces change appearance when viewpoint
  is changed
• Specularities are caused by microscopically
  smooth surfaces.
• A mirror is a perfect specular reflector

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Phong Specular Component
Phong combines directional diffuse ideal
specular
Image courtesy of Watt, 3D Computer Graphics
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Half Vector

• An alternative way of computing phong lighting
  is Is ks Is (NH)n
• H (halfway vector) halfway between V and L
  (VL)/2
• Fuzzier highlight

N
L
H
V
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Phong Illumination
Moving Light
Change n
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Phong Ambient Component
Treat it as a constant
Where is the ambient light in the scene.
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Adding Color
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Adding Lights
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Phong Reflection
Image courtesy of Watt, 3D Computer Graphics
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Aluminium
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Bronze
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Chrome
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Stainless Steel
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OpenGL Materials
GLfloat white8 .8, .8, .8, 1., white2
.2,.2,.2,1.,black0.,0.,0. GLfloat
mat_shininess 50. / Phong
exponent / glMaterialfv( GL_FRON
T_AND_BACK, GL_AMBIENT,
black) glMaterialfv( GL_FRONT_AND_BACK,
GL_DIFFUSE, white8) glMaterialfv( GL_FRON
T_AND_BACK, GL_SPECULAR, white2)
glMaterialfv( GL_FRONT_AND_BACK, GL_SHININESS,
mat_shininess)
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OpenGL Lighting
GLfloat white 1., 1., 1., 1.
GLfloat light0_position 1., 1., 5., 0. /
directional light (w0) /
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_SI
DE, GL_TRUE)/ two-sided lighting/
glEnable(GL_LIGHTING)
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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.
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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?
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Vertex Normals vs. Face Normals
Should use the actual surfaces normals
Usually stored at the vertices of the object Can
calculate as averages of face normals
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Mach Band ?
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Mach Band ?
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• 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

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Interpolation
Given vertex normals, how to color the interior

• Gouraud Interpolation
• Phong Interpolation

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Un-lit
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Flat Shading
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Gouraud Interpolation Interpolated Shading
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Phong Interpolation Per pixel Shading
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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)
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Gouraud Interpolation Problems
Misses some highlights
light
shading will be constant!
Shading is not linear
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Phong Interpolation
Interpolate the normals, then compute the colors
light
Interpolation is usually done component-wise
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• 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.

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Interpolation
Image courtesy of Watt Watt, Advanced Animation
and Rendering Techniques
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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

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Shade Trees
Phong Shade Tree




ka
ks
pow
Il
Ia
dot
n
kd
dot
Il
N
H
N
L
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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 Cs Surface color Os Surface
opacity P Surface point N - Surface normal I
- Direction of viewing (eye ray) L -
Direction to the light source
N
I
L
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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(Kaambient()Kddiffuse(Nf)
specularColorKsspecular(Nf,-I,roughness)
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Light Sources

• Point light source
• Directional light source e.g. sun light
• Spot light

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Spot Light

• To restrict a lights 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

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Light Source Attenuation

• Takes into account the distance of the light from
  the surface
• IL I L fatt (d)
• IL 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 c2d c3d2) , 1)
• C1, C2, C3 are user defined constants associated
  with each light source

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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.