illumination virendra
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Illumination models are also called
lighting or shading models
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An illumination model is operating on a pixelbasis, while surface rendering works on asurface in its whole
To get realism (summary):
perspective projection and clipping
hidden surface removal
shading/lighting aspects
color/material aspects
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An illumination model is based on optical
properties of surfaces
Typical optical effects (require one or more
light sources): reflection, (can be of different types)
refraction (if transparent objects)
shadows (can be of different types)
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Various optical surface properties have to be
specified, such as:
reflectivity coefficients
degree of transparency index of refraction
For simplicity, we assume opaque (non-
transparent) surfaces
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Point light source
Distributed light
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A cone is illustrating the light spread from a
spotlight
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Illumination is primarily of two kinds:
ambient light (background light) all points on a surface have the same intensity
with only ambient light, no realism (e.g. asphere will look like a circle slice
point source light emphasizes 3D
without ambient light, like a spotlight in a darkroom
a light source in VRP => no shadows
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The intensity (I) of reflected ambient light fora point on an object surface:
I = Ib.Rb
where
Ib=the intensity of the ambient light
Rb=the coefficient of reflectionof ambient light for the surface(a material constant, 0-1)
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Reflected light from a point source is dividedinto:
a) diffuse reflection (especially when dullsurfaces)
* the reflected color is the color of theobject surface
b) specular reflection (especially whenshiny surfaces)
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Reflection is uniform
in all directions
Intensity isproportional to cos,
the angle of
incident light
(Lambert’s cosine
law )
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Adjust the intensity formula:
I = Ib.Rb + Id
.Rd.cos
where
Id=the intensity of the light sourceRd=the coefficient of diffuse reflection forthe surface
Id.Rd
.cos can also be written Id.Rd
.(L.N),
(dot product)
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The intensity of light is known to decrease
with the factor 1/r2 due to energy laws,
where r is the distance from the light source
From experience, the factor 1/r2
is modified to1/(r+k) or something similar, where k is a
constant to prevent the nominator to
approach zero
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The decreasing intensity factor is called the
attenuation factor
Thus, the formula is adjusted to:
I = Ib.Rb + Id.Rd.(L.N)/(r+k)
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Angle of reflection =
angle of incidence
The intensity dependson the position of
the VRP (cp. the
vector V)
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Described by Phong Bui Tuong, the formula nowis:
I = Ib.Rb + Id
.Rd.(L.N)/(r+k) + Id
.Rs.cosn/(r+k),
whereRs=the coefficient of specular reflection forthe surface (not really a constant but afunction of the angle, W())
cosn (in vector form (R.V)n) determines howshiny the surface is; typically 1≤n≤10000,
means from dull (chalk) to very shiny (mirror)
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The understanding of the different values of
the parameter n (or ns) in the factor cosn:
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The factor cosn does not follow any physical law
but is found out to be useful from experience
Rs is always independant of the color of thereflecting surface
If multiple light sources, then by index j, the
formula is extended to:
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In a color model, three versions of the
formula need to be used; one for each
primary color, i.e. one for red, one for
green and one for blue in the RGB modelFurthermore, both the intensities and the
material constants in the formula have to
be given separately for each primary color
In theory, every point on an object surface
has to be computed!
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Usually, several simplifications are used:
assume light sources in an infinite distance
=> parallel light rays and L is constant for all
points the attenuation factor is eliminated
V constant, i.e. VRP at an infinite distance
same model for all three primaries
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An alternative way of
defining the vectors
in the model
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When polygons are used to approximate curved
surfaces (e.g. a sphere), we don’t want to
identify any discontinuities at an edge
between two adjacent polygons.
On the other hand, all surfaces are not curved,
so a simple surface rendering technique may
also be fine.
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1) Flat Surface Rendering - oneintensity/polygon* the selected point is often chosensomewhere in the middle of the polygon
* fast (+)* can give intensity discontinuities (-)* OK if
- the object is a polyhedron
- light sources far away- VRP far away
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2) Gouraud Surface Rendering - intensityinterpolation
* linear interpolation of intensities overeach polygon
* a kind of scan-filling
* eliminates possible intensitydiscontinuities
* so called Mach bands can appear(subdivide polygons)
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For each polygon:
calculate the average normal vector ineach vertex
use an illumination model to obtain theintensities in the vertices, e.g. Phong
interpolate the intensities linearly overthe surface
First, vertically along the edges Then, horizontally along each scan-line
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IqI1y2 ys
y2 y1 I2
ys y1y2 y1
IrI4y3 ys
y3 y4 I3
ys y4
y3 y4
IpIqxr xp
xr xq Ir
xp xq
xr xq
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The normal in vertex
V is calculated as
the average of N1,N2, N3 and N4
Notice that vertex V
then will have the
same normal andintensity for all four
polygons joining in V
Nv Nk
Nk
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Illumination from point light sources
includes generating shadows, i.e. some
objects will shade other objects.
The problem of identifying shaded surfacesdirectly corresponds to the problem of
identifying hidden surfaces; those
surfaces that are hidden when viewed
from the light source position are exactlythose shaded (from that particular light
source!)
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In principle, this means that those surfaces
that are invisible from the light source, but
visible from the view point (VRP), are to be
shaded
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A pixel intensity is determined by following all rays
emitted from a light source (infinitely many!),
adding the intensities of those rays which are passing
through the pixel area on their way to VRP
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A better idea is to start in a pixel position and
trace the rays backwards, since most rays
from the light source will not pass through
the current pixel.
Then, only those rays which are traced back to
a light source will result in a contribution of
the intensity
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A ray intersecting
with a point on
an object surfaceis divided into (in
general):
* a specular
reflected ray* a refracted ray
(if transparency)
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