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+#### Shading: Implementation Details {#Heading7}
+
+In order to calculate the cosine of the angle between an incoming light
+source and a polygon’s unit normal, we must first have the polygon’s
+unit normal. This could be calculated by generating a cross-product on
+two polygon edges to generate a normal, then calculating the normal’s
+length and scaling to produce a unit normal. Unfortunately, that would
+require taking a square root, so it’s not a desirable course of action.
+Instead, I’ve made a change to X-Sharp’s polygon format. Now, the first
+vertex in a shaded polygon’s vertex list is the end-point of a unit
+normal that starts at the second point in the polygon’s vertex list, as
+shown in Figure 54.3. The first point isn’t one of the polygon’s
+vertices, but is used only to generate a unit normal. The second point,
+however, is a polygon vertex. Calculating the difference vector between
+the first and second points yields the polygon’s unit normal. Adding a
+unit-normal endpoint to each polygon isn’t free; each of those
+end-points has to be transformed, along with the rest of the vertices,
+and that takes time. Still, it’s faster than calculating a unit normal
+for each polygon from scratch.
+
+![](images/54-03.jpg)\
+ **Figure 54.3**  *The unit normal in the polygon data structure.*
+
+![](images/54-04.jpg)\
+ **Figure 54.4**  *The reversed light source vector.*
+
+We also need a unit vector for each directed light source. The directed
+light sources I’ve implemented in X-Sharp are spotlights; that is,
+they’re considered to be point light sources that are infinitely far
+away. This allows the simplifying assumption that all light rays from a
+spotlight are parallel and of equal intensity throughout the displayed
+universe, so each spotlight can be represented with a single unit vector
+and a single intensity. The only trick is that in order to calculate the
+desired cos(theta) between the polygon unit normal and a spotlight’s
+unit vector, the direction of the spotlight’s unit vector must be
+reversed, as shown in Figure 54.4. This is necessary because the dot
+product implicitly places vectors with their start points at the same
+location when it’s used to calculate the cosine of the angle between two
+vectors. The light vector is incoming to the polygon surface, and the
+unit normal is outbound, so only by reversing one vector or the other
+will we get the cosine of the desired angle.
+
+Given the two unit vectors, it’s a piece of cake to calculate
+intensities, as shown in Listing 54.2. The sample program DEMO1, in the
+X-Sharp archive on the listings disk (built by running K1.BAT), puts the
+shading code to work displaying a rotating ball with ambient lighting
+and three spot lighting sources that the user can turn on and off. What
+you’ll see when you run DEMO1 is that the shading is very good—face
+colors change very smoothly indeed—so long as only green lighting
+sources are on. However, if you combine spotlight two, which is blue,
+with any other light source, polygon colors will start to shift abruptly
+and unevenly. As configured in the demo, the palette supports a wide
+range of shading intensities for a pure version of any one of the three
+primary colors, but a very limited number of intensity steps (four, in
+this case) for each color component when two or more primary colors are
+mixed. While this situation can be improved, it is fundamentally a
+result of the restricted capabilities of the 256-color palette, and
+there is only so much that can be done without a larger color set. In
+the next chapter, I’ll talk about some ways to improve the quality of
+256-color shading.
+
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+* * * * *
+
+Graphics Programming Black Book © 2001 Michael Abrash