Normal quotes

54-03.md

@@ -8,14 +8,14 @@ So far, the polygons out of which our animated objects have been built
 have had colors of fixed intensities. For example, a face of a cube
 might be blue, or green, or white, but whatever color it is, that color
 never brightens or dims. Fixed colors are easy to implement, but they
-don’t make for very realistic animation. In the real world, the
+don't make for very realistic animation. In the real world, the
 intensity of the color of a surface varies depending on how brightly it
 is illuminated. The ability to simulate the illumination of a surface,
-or shading, is the next feature we’ll add to X-Sharp.
+or shading, is the next feature we'll add to X-Sharp.
 
 The overall shading of an object is the sum of several types of shading
 components. *Ambient shading* is illumination by what you might think of
-as background light, light that’s coming from all directions; all
+as background light, light that's coming from all directions; all
 surfaces are equally illuminated by ambient light, regardless of their
 orientation. *Directed lighting*, producing diffuse shading, is
 illumination from one or more specific light sources. Directed light has
@@ -24,7 +24,7 @@ determines how brightly it lights that surface. *Specular reflection* is
 the tendency of a surface to reflect light in a mirrorlike fashion.
 There are other sorts of shading components, including transparency and
 atmospheric effects, but the ambient and diffuse-shading components are
-all we’re going to deal with in X-Sharp.
+all we're going to deal with in X-Sharp.
 
 #### Ambient Shading {#Heading5 align="center"}
 
@@ -43,40 +43,40 @@ Given an ambient-light red intensity of IA~red~ and a surface red
 reflectance R~red~, the displayed red ambient shading for that surface,
 as a fraction of the maximum red intensity, is simply min(IA~red~x
 R~red~, 1). The green and blue color components are handled similarly.
-That’s really all there is to ambient shading, although of course we
+That's really all there is to ambient shading, although of course we
 must design some way to map displayed color components into the
-available palette of colors; I’ll do that in the next chapter. Ambient
-shading isn’t the whole shading picture, though. In fact, scenes tend to
+available palette of colors; I'll do that in the next chapter. Ambient
+shading isn't the whole shading picture, though. In fact, scenes tend to
 look pretty bland without diffuse shading.
 
 #### Diffuse Shading {#Heading6 align="center"}
 
 Diffuse shading is more complicated than ambient shading, because the
 effective intensity of directed light falling on a surface depends on
-the angle at which it strikes the surface. According to Lambert’s law,
+the angle at which it strikes the surface. According to Lambert's law,
 the light energy from a directed light source striking a surface is
 proportional to the cosine of the angle at which it strikes the surface,
 with the angle measured relative to a vector perpendicular to the
 polygon (a polygon normal), as shown in Figure 54.1. If the red
 intensity of directed light is ID~red~, the red reflectance of the
 surface is R~red~, and the angle between the incoming directed light and
-the surface’s normal is theta, then the displayed red diffuse shading
+the surface's normal is theta, then the displayed red diffuse shading
 for that surface, as a fraction of the largest possible red intensity,
 is min (ID~red~xR~red~xcos(θ), 1).
 
-That’s easy enough to calculate—but seemingly slow. Determining the
-cosine of an angle can be sped up with a table lookup, but there’s also
-the task of figuring out the angle, and, all in all, it doesn’t seem
+That's easy enough to calculate—but seemingly slow. Determining the
+cosine of an angle can be sped up with a table lookup, but there's also
+the task of figuring out the angle, and, all in all, it doesn't seem
 that diffuse shading is going to be speedy enough for our purposes.
 Consider this, however: According to the properties of the dot product
-(denoted by the operator “•”, as shown in Figure 54.2), cos(q)=(v•w)/
+(denoted by the operator "•", as shown in Figure 54.2), cos(q)=(v•w)/
 |v| x |w| ), where v and w are vectors, q is the angle between v and w,
 and |v| is the length of v. Suppose, now, that v and w are unit vectors;
 that is, vectors exactly one unit long. Then the above equation reduces
 to cos(q)=v•w. In other words, we can calculate the cosine between N,
 the unit-normal vector (one-unit-long perpendicular vector) of a
 polygon, and L', the reverse of a unit vector describing the direction
-of a light source, with just three multiplies and two adds. (I’ll
+of a light source, with just three multiplies and two adds. (I'll
 explain why the light-direction vector must be reversed later.) Once we
 have that, we can easily calculate the red diffuse shading from a
 directed light source as min(ID~red~xR~red~x(L'• N), 1) and likewise for