Normal quotes

40-01.md

@@ -8,28 +8,28 @@ Chapter 40\
 
 ### Dealing with Irregular Polygonal Areas {#Heading2}
 
-Every so often, my daughter asks me to sing her to sleep. (If you’ve
+Every so often, my daughter asks me to sing her to sleep. (If you've
 ever heard me sing, this may cause you concern about either her hearing
 or her judgement, but love knows no bounds.) As any parent is well
 aware, singing a young child to sleep can easily take several hours, or
 until sunrise, whichever comes last. One night, running low on
-children’s songs, I switched to a Beatles medley, and at long last her
-breathing became slow and regular. At the end, I softly sang “A Hard
-Day’s Night,” then quietly stood up to leave. As I tiptoed out, she
-said, in a voice not even faintly tinged with sleep, “Dad, what do they
-mean, ‘working like a dog’? Chasing a stick? That doesn’t make sense;
-people don’t chase sticks.”
+children's songs, I switched to a Beatles medley, and at long last her
+breathing became slow and regular. At the end, I softly sang "A Hard
+Day's Night," then quietly stood up to leave. As I tiptoed out, she
+said, in a voice not even faintly tinged with sleep, "Dad, what do they
+mean, ‘working like a dog'? Chasing a stick? That doesn't make sense;
+people don't chase sticks."
 
 That led us into a discussion of idioms, which made about as much sense
 to her as an explanation of quantum mechanics. Finally, I fell back on
 my standard explanation of the Universe, which is that a lot of the time
-it simply doesn’t make sense.
+it simply doesn't make sense.
 
 As a general principle, that explanation holds up remarkably well. (In
 fact, having just done my taxes, I think Earth is actually run by
 blob-creatures from the planet Mrxx, who are helplessly doubled over
-with laughter at the ridiculous things they can make us do. “Let’s make
-them get Social Security numbers for their pets next year!” they’re
+with laughter at the ridiculous things they can make us do. "Let's make
+them get Social Security numbers for their pets next year!" they're
 saying right now, gasping for breath.) Occasionally, however, one has
 the rare pleasure of finding a corner of the Universe that makes sense,
 where everything fits together as if preordained.
@@ -42,12 +42,12 @@ In Chapter 38, I described three types of polygons: convex, nonconvex,
 and complex. *The RenderMan Companion*, a terrific book by Steve Upstill
 (Addison-Wesley, 1990) has an intuitive definition of *convex*: If a
 rubber band stretched around a polygon touches all vertices in the order
-they’re defined, then the polygon is convex. If a polygon has
-intersecting edges, it’s complex. If a polygon doesn’t have intersecting
-edges but isn’t convex, it’s nonconvex. Nonconvex is a special case of
-complex, and convex is a special case of nonconvex. (Which, I’m well
+they're defined, then the polygon is convex. If a polygon has
+intersecting edges, it's complex. If a polygon doesn't have intersecting
+edges but isn't convex, it's nonconvex. Nonconvex is a special case of
+complex, and convex is a special case of nonconvex. (Which, I'm well
 aware, makes nonconvex a lousy name—noncomplex would have been
-better—but I’m following X Window System nomenclature here.)
+better—but I'm following X Window System nomenclature here.)
 
 The reason for distinguishing between these three types of polygons is
 that the more specialized types can be filled with markedly faster
@@ -57,24 +57,24 @@ require less sorting, because edges never cross. Convex polygons can be
 filled fastest of all by simply scanning the two sides of the polygon,
 as we saw in Chapter 39.
 
-Before we dive into complex polygon filling, I’d like to point out that
-the code in this chapter, like all polygon filling code I’ve ever seen,
+Before we dive into complex polygon filling, I'd like to point out that
+the code in this chapter, like all polygon filling code I've ever seen,
 requires that the caller describe the type of the polygon to be filled.
-Often, however, the caller doesn’t know what type of polygon it’s
+Often, however, the caller doesn't know what type of polygon it's
 passing, or specifies complex for simplicity, because that will work for
 all polygons; in such a case, the polygon filler will use the slow
 complex-fill code even if the polygon is, in fact, a convex polygon. In
-Chapter 41, I’ll discuss one way to improve this situation.
+Chapter 41, I'll discuss one way to improve this situation.
 
 #### Active Edges {#Heading4}
 
 The basic premise of filling a complex polygon is that for a given scan
-line, we determine all intersections between the polygon’s edges and
+line, we determine all intersections between the polygon's edges and
 that scan line and then fill the spans between the intersections, as
-shown in Figure 40.1. (Section 3.6 of Foley and van Dam’s *Computer
+shown in Figure 40.1. (Section 3.6 of Foley and van Dam's *Computer
 Graphics*, Second Edition provides an overview of this and other aspects
 of polygon filling.) There are several rules that might be used to
-determine which spans are drawn and which aren’t; we’ll use the odd/even
+determine which spans are drawn and which aren't; we'll use the odd/even
 rule, which specifies that drawing turns on after odd-numbered
 intersections (first, third, and so on) and off after even-numbered
 intersections.
@@ -83,9 +83,9 @@ The question then becomes how can we most efficiently determine which
 edges cross each scan line and where? As it happens, there is a great
 deal of coherence from one scan line to the next in a polygon edge list,
 because each edge starts at a given Y coordinate and continues unbroken
-until it ends. In other words, edges don’t leap about and stop and start
+until it ends. In other words, edges don't leap about and stop and start
 randomly; the X coordinate of an edge at one scan line is a consistent
-delta from that edge’s X coordinate at the last scan line, and that is
+delta from that edge's X coordinate at the last scan line, and that is
 consistent for the length of the line.
 
 ![](images/40-01.jpg)\
@@ -95,7 +95,7 @@ This allows us to reduce the number of edges that must be checked for
 intersection; on any given scan line, we only need to check for
 intersections with the currently active edges—edges that start on that
 scan line, plus all edges that start on earlier (above) scan lines and
-haven’t ended yet—as shown in Figure 40.2. This suggests that we can
+haven't ended yet—as shown in Figure 40.2. This suggests that we can
 proceed from the top scan line of the polygon to the bottom, keeping a
 running list of currently active edges—called the *active edge table*
 (AET)—with the edges sorted in order of ascending X coordinate of
@@ -110,7 +110,7 @@ First, we must add to the AET any edges that start on the current scan
 line, making sure to keep the AET X-sorted for efficient odd/even
 scanning. Second, we must remove edges that end on the current scan
 line. Third, we must advance the X coordinates of active edges with the
-same sort of error term-based, Bresenham’s-like approach we used for
+same sort of error term-based, Bresenham's-like approach we used for
 convex polygons, again ensuring that the AET is X-sorted after advancing
 the edges.