Normal quotes

65-04.md

@@ -11,13 +11,13 @@ regarding range and precision. Floating-point is much easier—and, with
 the Pentium generation of processors, is generally comparable in speed.
 In fact, for some operations, such as multiplication in general and
 division when the floating-point unit is in single-precision mode,
-floating-point is much faster. Check out Chris Hecker’s column in the
+floating-point is much faster. Check out Chris Hecker's column in the
 February 1996 *Game Developer* for an interesting discussion along these
 lines.
 
 Second, the planes that form the frustum are shifted ever so slightly
 inward from their proper positions at the edge of the field of view.
-This guarantees that it’s never possible to generate a visible vertex
+This guarantees that it's never possible to generate a visible vertex
 exactly at the eyepoint, averting the divide-by-zero error that such a
 vertex would cause when projected and at no performance cost.
 
@@ -40,12 +40,12 @@ objects began to warp visibly after many rotations.
 
 Fourth, Listing 65.3 processes each input polygon into a clipped
 polygon, one line segment at a time. It would be more efficient to
-process all the vertices, categorizing whether and how they’re clipped,
+process all the vertices, categorizing whether and how they're clipped,
 and then perform a test such as the Cohen-Sutherland outcode test to
 detect trivial acceptance (the polygon is entirely inside) and sometimes
 trivial rejection (the polygon is fully outside) without ever dealing
 with the edges, and to identify which planes actually need to be clipped
-against, as discussed in “Line-Segment Clipping Revisited,” *Dr. Dobb’s
+against, as discussed in "Line-Segment Clipping Revisited," *Dr. Dobb's
 Journal*, January 1996. Some clipping approaches also minimize the
 number of intersection calculations when a segment is clipped by
 multiple planes. Further, Listing 65.3 clips a polygon against each
@@ -88,7 +88,7 @@ For a game, 90 degrees is a pretty good field of view, but can we get
 the same sort of efficient clipping if we need some other field of view?
 Sure. All we have to do is scale the x and y results of the
 world-to-view transformation to account for the field of view, so that
-the coordinates lie in a viewspace that’s normalized such that the
+the coordinates lie in a viewspace that's normalized such that the
 frustum planes extend along lines of x==z and y==z. The resulting
 visible projected points span the range -1 to 1 (before scaling up to
 get pixel coordinates), just as with a 90-degree field of view, so the
@@ -96,27 +96,27 @@ rest of the drawing pipeline remains unchanged. Better yet, there is no
 cost in performance because the adjustment can be added to the
 transformation matrix.
 
-I didn’t implement normalized clipping in Listing 65.3 because I wanted
+I didn't implement normalized clipping in Listing 65.3 because I wanted
 to illustrate the general 3-D clipping mechanism without additional
 complications, and because for many applications the dot product (which,
 after all, takes only 10-20 cycles on a Pentium) is sufficient. However,
-the more frustum clipping you’re doing, especially if most of the
+the more frustum clipping you're doing, especially if most of the
 polygons are trivially visible, the more attractive the performance
 advantages of normalized clipping become.
 
 ### Further Reading {#Heading9}
 
 You now have the basics of 3-D clipping, but because fast clipping is
-central to high-performance 3-D, there’s a lot more to be learned. One
+central to high-performance 3-D, there's a lot more to be learned. One
 good place for further reading is Foley and van Dam; another is
 *Procedural Elements of Computer Graphics*, by David F. Rogers. Read and
-understand either of these books, and you’ll know everything you need
+understand either of these books, and you'll know everything you need
 for world-class clipping.
 
 And, as you read, you might take a moment to consider how wonderful it
-is that anyone who’s interested can tap into so much expert knowledge
+is that anyone who's interested can tap into so much expert knowledge
 for the price of a book—or, on the Internet, for free—with no strings
-attached. Our part of the world is a pretty good place right now, isn’t
+attached. Our part of the world is a pretty good place right now, isn't
 it?
 
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