Page 193 - DCAP504_Computer Graphics

Computer Graphics

The vertices of the polygon mesh in figure 12.10 (a) are on the surface of an
underlying cylinder. The normal vector N at a point on the underlying cylinder
is perpendicular to the axis of the cylinder.

To determine normal vector N at vertex E in figure 12.10 (b), we use the average of the normal vectors
of the polygons that meet at E:
N=N1 + N2 + N3 + N4
The value of N can then be normalized by dividing it by |N|.
Common normal vectors at the vertices of a polygon mesh that are used to shade a curved surface result
in color values that are shared by adjacent polygons and also eliminate abrupt modifications in shading
characteristics across polygon edges. Even when the polygon mesh is relatively coarse, Gouraud
shading is very useful in eliminating abrupt modifications.

Consider a hexagonal polygon, draw a bilinear interpolation diagram and analyze how
you can find out normals at each vertex.

Some of the advantages of Gouraud shading are:
1. Unlike a constant shaded polygon, Gouraud shading allows to use different shade for each vertex
of a polygon.
2. Gouraud shading provides much better image than constant shading.
3. Gouraud shading is not too computationally expensive as it calculates only one illumination
formula for each vertex.
Some of the disadvantages of Gouraud shading are:
Gouraud shading eliminates folds that you may want to retain.

In some cases, it is not appropriate to use Gouraud shading for polygons with three
vertices. Polygons may appear quite different when they have more than three vertices
with different shades for each.
The following figure 12.11 depicts the Gouraud shading of an image.

Figure 12.11: Gouraud Shading of an Image

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