Download Illumination Models

Steve Sterley
Real World Lighting
Physical objects tend to interact with light in
three ways:
• Absorption (black body)
• Reflection (mirror)
• Transmission (glass)
Lighting in OpenGL
Simulates absorption and reflection through 3
different types of light:
• Diffuse
• Specular
• Ambient
Components of Colour
All colours in the spectrum can be represented
through the combination of intensities of 3
distinct colours, namely:red, green, blue
1.
In coming light carries
information about the intensity
of each of its 3 components.
2.
The reflected intensity of each
component is calculated
individually.
3.
The resulting colour of the
reflected light is then the
combination of the 3 reflected
components.
1. Incoming light
3. Reflected light
2. Surface colour
Diffuse Light
• Does not originate from the source!!
• Originates from atoms on the surface being
excited by incident radiation
• Therefore Light emitted in all directions
(moving the camera relative to the surface and light source will not change
how much the face is lit)
The amount of diffuse light emitted, does depend on orientation of surface to
the light source.
A surface  to light
source emits the
most light

Intensity  n  r
Or…
Intensity  cos 

Intensity  n  r
A surface // to light
source emits no light
r  nˆ
I d  I s d
r
I d  I s  d cos
A surface at some arbitrary
angle to the source emits
light whose intensity is
dependent on the angle
Id – Intensity of emitted light
Is – Intensity of light source
d – diffuse reflection
coefficient (for material)

Intensity  n  r
Or…
Intensity  cos 
r  nˆ
I d  I s d
r
I d  I s  d cos
Id – Intensity of emitted light
Is – Intensity of light source
d – diffuse reflection
coefficient (for material)
Note:
Its not possible to have a negative intensity!! When  > 90 or  < -90  Id = 0
We could then rewrite the
formula above as follows :
 r  nˆ 
I d  I s  d max  
,0 
r


Note:
This is not a physically accurate model:
1.
2.
True light is not composed of three components, but an entire spectrum
of frequencies.
In reality, Light intensity is inversely proportional to the distance from
the source squared.
Why does OpenGL not stick to a physically
accurate lighting model?
Realistically, objects emit diffuse light from all points on their
surface, which once again should fall incident on every
other object in the room.
Practically, OpenGL allows only eight light sources to be
used.
Specular Light
•
•
•
•
Originates from the source, not the material!!
Material colour should not influence it
Causes highlights to appear on shiny surfaces
Light is emitted in specific directions
(moving the camera relative to the surface and light source is expected to
change which portions of the face are lit)
Phong Model
• Method used by OpenGL to simulate specular lighting
• Best for modeling plastic or glassy materials, not very good for metals
Perfect Mirror
i r
Light is only reflected in the
direction where i = r
Phong Model
i
i
For one particular angle of incidence,
light is reflected in a number of
directions, but is most intense in the
direction where i = r.
On either side of this angle, the
intensity drops off to 0.
Phong Model
The intensity varies as some complicated
function of , but in the Phong Model, it is
made to vary according to the following
function: cosf(), where f should range
somewhere in the region between 0 and
200.
Intensity  r  v 
f
Or…
Intensity  cos f 
I sp
 r v 

 I s  s 

rv
r
i r
f
I sp  I s  s cos f 

v
Isp – Intensity of reflected light
Is – Intensity of specular light
source
d – specular reflection
coefficient (for material)
 - angle between viewing
vector and maximum
reflection vector
Intensity  r  v 
f
Or…
Intensity  cos f 
I sp
 r v 

 I s  s 

rv
f
I sp  I s  s cos f 
Isp – Intensity of reflected light
Is – Intensity of specular light
source
d – specular reflection
coefficient (for material)
 - angle between viewing
vector and maximum
reflection vector
Note:
Its not possible to have a negative intensity!! When  > 90 or  < -90  Isp = 0
We could then rewrite the
formula above as follows :
I sp
 r v  f 
 ,0 
 I s  s max  
 r v





Note:
This diagram is a polar plot, so the length of
the arrows on the right hand side, represent the
reflected intensity for different camera angles
relative to the normal.
i
f
The graph above, shows how the function: cosf() varies with different values
of f. When f = 1, the shininess of the material is low, and the specular highlight
will be large. When f = 256, the shininess of the material is high (the material is
almost mirror like), and the specular highlight will be small.
Reasons for Ambient Light
• In the real world, light reflecting off walls and other objects
accounts for a lot of the light in a room.
•Physically, if an object were placed in a lit room, even the
faces not directed towards the light would be visible.
• If only diffuse and specular light were applied to a scene,
large areas of it would be left in darkness. (Areas where the
angles between the normal to a face and the light vector were
greater than 90, or less than 0 degrees) (Shadows would
appear unrealistically dark)
Ambient Light
Ambient light has a uniform intensity in all directions, and
serves to increase the overall brightness of the environment.
I  I a a
• Too little – Shadows too harsh
• Too much – picture appears bland
The Overall Picture
The overall light intensity used to shade each face of an
object, is now simply the sum of the three different light
intensities incident on that face
i.e.
Intensity = I a  a
 r v  f 
 r  nˆ 


,0 
 ,0 + I d  d max  
+ I s  s max  

r
r v 





This calculation must then be performed for each of the three
light components (R, G, B) to calculate the overall colour of
that face.
Application of the Model
Intensity = I a  a
 r v  f 
 r  nˆ 


,0 
 ,0 + I d  d max  
+ I s  s max  

r
r v 





This is the very formula used by OpenGL, and its parameters
are set as follows:
Ambient
• Ia : Use glLight, set
GL_AMBIENT to the
desired RGBA value
• a : Use glMaterial, set
GL_AMBIENT to the
desired RGBA value.
Specular
• Is : Use glLight, set
GL_SPECULAR to the
desired RGBA value
• s : Use glMaterial, set
GL_SPECULAR to the
desired RGBA value.
• f : Use glMaterial, set
GL_SHININESS to the
desired floating point value.
Diffuse
• Id : Use glLight, set
GL_DIFFUSE to the
desired RGBA value
• d : Use glMaterial, set
GL_DIFFUSE to the
desired RGBA value.
Shading Models
There are two types of shading available in OpenGL, these
are smooth, and flat shading.
• Flat Shading assigns a
single colour to a face
• Smooth shading applies a
gradient of colours to a face
• Flat shading is best for
modeling objects with flat
faces e.g. a faceted diamond
• Smooth shading is best for
modeling objects with
curved surfaces e.g. sphere,
toroid etc.
Flat Shading
Each vertex for a face has a normal. In flat shading,
OpenGL chooses just one of them to calculate the
lighting for that face.
In order for flat shading to appear correctly, the normals should be set  to
each face, and for any particular face, they should all lie // to each other.
If the normals are simply estimated e.g. modeling a
sphere, through subdividing an icosahedron, the
lighting will not appear accurate.
<digression>
Problem with Flat Shading
• A problem with OpenGL flat shading is that it assumes that
all the normals for a surface are the same. (This is sometimes
not the case)
• An incorrect normal could be chosen, resulting in incorrect
lighting for a surface.
• A simple fix (which would be computationally inexpensive)
would be to average all the normals for a face, and use this
average to calculate the lighting
• Unfortunately OpenGL does not implement this.
Smooth Shading
• Used for objects that aren’t meant to have flat faces.
• In OpenGL, smooth surfaces are estimated by a large number
of flat faces.
• Normals should now be different for each vertex of a polygon
(perpendicular to the underlying surface)
Gourand Shading
• The type of smooth shading used by OpenGL
• A unique colour is calculated for each normal to a polygon
• The face is then coloured in through interpolation
Intensity 4
Intensity 3
I left  ( I 4  I1 )  f  I1
I right  ( I 3  I 2 )  f  I 2
60%
I left
40%
Intensity 1
I right
Scan Line
Intensity 2
Phong Shading
• Not used by OpenGL
• More computationally expensive
• Normals are interpolated across the surface of the polygon,
then the lighting is recalculated for each pixel.
n3
n4
n right  (n 3  n 2 )  f  n 2
n2
n1
n left  (n 4  n1 )  f  n1