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[Previous](54-02.html) [Table of Contents](index.html) [Next](54-04.html)
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#### Shading {#Heading4}
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So far, the polygons out of which our animated objects have been built
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have had colors of fixed intensities. For example, a face of a cube
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might be blue, or green, or white, but whatever color it is, that color
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never brightens or dims. Fixed colors are easy to implement, but they
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don’t make for very realistic animation. In the real world, the
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intensity of the color of a surface varies depending on how brightly it
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is illuminated. The ability to simulate the illumination of a surface,
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or shading, is the next feature we’ll add to X-Sharp.
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The overall shading of an object is the sum of several types of shading
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components. *Ambient shading* is illumination by what you might think of
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as background light, light that’s coming from all directions; all
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surfaces are equally illuminated by ambient light, regardless of their
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orientation. *Directed lighting*, producing diffuse shading, is
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illumination from one or more specific light sources. Directed light has
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a specific direction, and the angle at which it strikes a surface
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determines how brightly it lights that surface. *Specular reflection* is
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the tendency of a surface to reflect light in a mirrorlike fashion.
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There are other sorts of shading components, including transparency and
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atmospheric effects, but the ambient and diffuse-shading components are
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all we’re going to deal with in X-Sharp.
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#### Ambient Shading {#Heading5 align="center"}
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The basic model for both ambient and diffuse shading is a simple one.
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Each surface has a reflectivity between 0 and 1, where 0 means all light
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is absorbed and 1 means all light is reflected. A certain amount of
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light energy strikes each surface. The energy (intensity) of the light
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is expressed such that if light of intensity 1 strikes a surface with
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reflectivity 1, then the brightest possible shading is displayed for
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that surface. Complicating this somewhat is the need to support color;
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we do this by separating reflectance and shading into three components
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each—red, green, and blue—and calculating the shading for each color
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component separately for each surface.
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Given an ambient-light red intensity of IA~red~ and a surface red
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reflectance R~red~, the displayed red ambient shading for that surface,
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as a fraction of the maximum red intensity, is simply min(IA~red~x
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R~red~, 1). The green and blue color components are handled similarly.
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That’s really all there is to ambient shading, although of course we
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must design some way to map displayed color components into the
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available palette of colors; I’ll do that in the next chapter. Ambient
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shading isn’t the whole shading picture, though. In fact, scenes tend to
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look pretty bland without diffuse shading.
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#### Diffuse Shading {#Heading6 align="center"}
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Diffuse shading is more complicated than ambient shading, because the
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effective intensity of directed light falling on a surface depends on
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the angle at which it strikes the surface. According to Lambert’s law,
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the light energy from a directed light source striking a surface is
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proportional to the cosine of the angle at which it strikes the surface,
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with the angle measured relative to a vector perpendicular to the
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polygon (a polygon normal), as shown in Figure 54.1. If the red
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intensity of directed light is ID~red~, the red reflectance of the
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surface is R~red~, and the angle between the incoming directed light and
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the surface’s normal is theta, then the displayed red diffuse shading
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for that surface, as a fraction of the largest possible red intensity,
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is min (ID~red~xR~red~xcos(θ), 1).
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That’s easy enough to calculate—but seemingly slow. Determining the
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cosine of an angle can be sped up with a table lookup, but there’s also
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the task of figuring out the angle, and, all in all, it doesn’t seem
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that diffuse shading is going to be speedy enough for our purposes.
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Consider this, however: According to the properties of the dot product
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(denoted by the operator “•”, as shown in Figure 54.2), cos(q)=(v•w)/
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|v| x |w| ), where v and w are vectors, q is the angle between v and w,
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and |v| is the length of v. Suppose, now, that v and w are unit vectors;
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that is, vectors exactly one unit long. Then the above equation reduces
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to cos(q)=v•w. In other words, we can calculate the cosine between N,
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the unit-normal vector (one-unit-long perpendicular vector) of a
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polygon, and L', the reverse of a unit vector describing the direction
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of a light source, with just three multiplies and two adds. (I’ll
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explain why the light-direction vector must be reversed later.) Once we
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have that, we can easily calculate the red diffuse shading from a
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directed light source as min(ID~red~xR~red~x(L'• N), 1) and likewise for
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the green and blue color components.
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\
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**Figure 54.1** *Illumination by a directed light source*
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\
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**Figure 54.2** *The dot product of two vectors.*
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The overall red shading for each polygon can be calculated by summing
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the ambient-shading red component with the diffuse-shading component
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from each light source, as in min((IA~red~xR~red~) +
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(ID~red0~xR~red~x(L~0~' • N)) + (ID~red1~xR~red~x(L~1~' • N)) +..., 1)
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where ID~red0~ and L~0~' are the red intensity and the reversed
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unit-direction vector, respectively, for spotlight 0. Listing 54.2 shows
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the X-Sharp module DRAWPOBJ.C, which performs ambient and diffuse
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shading. Toward the end, you will find the code that performs shading
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exactly as described by the above equation, first calculating the
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ambient red, green, and blue shadings, then summing that with the
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diffuse red, green, and blue shadings generated by each directed light
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source.
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------------------------ --------------------------------- --------------------
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[Previous](54-02.html) [Table of Contents](index.html) [Next](54-04.html)
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------------------------ --------------------------------- --------------------
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* * * * *
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Graphics Programming Black Book © 2001 Michael Abrash
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