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Computer Graphics
If L, N, R, and V are all unit vectors then L * N = cos(θ) and R * V= cos (φ). We can re-write the above
formula as
k
I=Iaka+Ip (kd L * N + ks(R * V) )
The value of R can be calculated with the term L * N.
The above mentioned formulae can be generally used along with the RGB color model. Thus, the
intensity of a light can be written in the form of an RGB color vector which can be represented as I = (I r,
I g, I b). The reflection co-efficients can also be expressed as 3-D vectors.
The reflection coefficient k d = (0.7, 0.7, 0.3) defines a surface that appears
yellowish when illuminated with white light.
The ambient reflection coefficient I c, can simply be similar to the reflection co-efficient k d. The three
components of I c are often made equal since the color of the reflection of a light source is usually the
same as the color of the light source itself. When white light is used the formula for a single point source
can be written as
Ir=Iakar + Ip (kdr L * N + ks ( R *V) )
k
k
l g= I ak ag + I p (k dg L * N + k s (R * V) )
Ib,= I ak ab + I p,( k dp L * N + k s (R * V) )
k
12.3 Interpolative Shading Methods
Interpolation is nothing but the identification of new values that exist between known values
determined for the vertices of a polygon. Interpolative shading methods use interpolation at the vertices
of the faces of polygons.
Surface color can be calculated using an illumination model such as the usage of a formula at any point
of the surface. It can be more costly and it is even unnecessary when the image is used to preview the
scene. To avoid this problem, it is suggested to apply the formula at full scale only at selected surface
points. Then other surface points can be shaded with the help of any other techniques such as color
interpolation and surface normal interpolation.
In the following sub sections we will discuss about some interpolative shading methods that are used to
shade a polygon.
Constant Shading
Constant shading is the easiest shading model for a polygon.
Did you know? Faceted shading or flat shading is the other name for constant shading.
Constant shading method applies an illumination model once to produce a single intensity value. The
single intensity value can be used to shade the polygon completely and to regenerate the polygon's
shade. This method is useful only when the following assumptions are true.
1. The light source should be at infinite distance so that L * N becomes constant through out the
polygon face.
2. The view point should be at infinite distance so that N * V becomes constant throughout the
polygon face.
3. The polygon should signify the actual surface being considered and it should not be an
approximation to a curved surface.
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