Normal quotes

35-02.md

@@ -2,13 +2,13 @@
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-Let’s examine the case of drawing a line where the horizontal, or X
+Let's examine the case of drawing a line where the horizontal, or X
 length of the line is greater than the vertical, or Y length, and both
 lengths are greater than 0. For example, suppose we are drawing a line
 from (0,0) to (5,2), as shown in Figure 35.2. Note that Figure 35.2
 shows the upper-left-hand corner of the screen as (0,0), rather than
 placing (0,0) at its more traditional lower-left-hand corner location.
-Due to the way in which the PC’s graphics are mapped to memory, it is
+Due to the way in which the PC's graphics are mapped to memory, it is
 simpler to work within this framework, although a translation of Y from
 increasing downward to increasing upward could be effected easily enough
 by simply subtracting the Y coordinate from the screen height minus 1;
@@ -19,7 +19,7 @@ In Figure 35.2, the endpoints of the line fall exactly on displayed
 pixels. However, no other part of the line squarely intersects the
 center of a pixel, meaning that all other pixels will have to be plotted
 as approximations of the line. The approach to approximation that
-Bresenham’s algorithm takes is to move exactly 1 pixel along the major
+Bresenham's algorithm takes is to move exactly 1 pixel along the major
 dimension of the line each time a new pixel is drawn, while moving 1
 pixel along the minor dimension each time the line moves more than
 halfway between pixels along the minor dimension.
@@ -32,9 +32,9 @@ accompany those X coordinates.
 ![](images/35-02.jpg)\
  **Figure 35.2**  *Drawing between two pixel endpoints.*
 
-It’s easy enough to select the Y coordinates by eye in Figure 35.2. The
+It's easy enough to select the Y coordinates by eye in Figure 35.2. The
 appropriate Y coordinates are 0, 0, 1, 1, 2, 2, based on the Y
-coordinate closest to the line for each X coordinate. Bresenham’s
+coordinate closest to the line for each X coordinate. Bresenham's
 algorithm makes the same selections, based on the same criterion. The
 manner in which it does this is by keeping a running record of the error
 of the line—that is, how far from the true line the current Y coordinate
@@ -44,7 +44,7 @@ true line to the extent that the adjacent Y coordinate would be closer
 to the line, then the current Y coordinate is changed to that adjacent Y
 coordinate.
 
-Let’s take a moment to follow the steps Bresenham’s algorithm would go
+Let's take a moment to follow the steps Bresenham's algorithm would go
 through in drawing the line in Figure 35.3. The initial pixel is drawn
 at (0,0), the starting point of the line. At this point the error of the
 line is 0.
@@ -66,11 +66,11 @@ adjustment of one pixel in the current Y coordinate. The running error
 of the pixel actually drawn at this point is C minus D.
 
 ![](images/35-03.jpg)\
- **Figure 35.3**  *The error term in Bresenham’s algorithm.*
+ **Figure 35.3**  *The error term in Bresenham's algorithm.*
 
 The fourth pixel has an X coordinate of 3. The running error at this
 point is E minus D; since this is less than 1/2, the current Y
-coordinate doesn’t change. The fourth pixel is drawn at (3,1).
+coordinate doesn't change. The fourth pixel is drawn at (3,1).
 
 The fifth pixel has an X coordinate of 4. The running error at this
 point is F minus D; since this is greater than 1/2, the current Y
@@ -81,11 +81,11 @@ point is G minus F.
 Finally, the sixth pixel is the end point of the line. This pixel has an
 X coordinate of 5. The running error at this point is G minus G, or 0,
 indicating that this point is squarely on the true line, as of course it
-should be given that it’s the end point, so the current Y coordinate
+should be given that it's the end point, so the current Y coordinate
 remains the same. The end point of the line is drawn at (5,2), and the
 line is complete.
 
-That’s really all there is to Bresenham’s algorithm. The algorithm is a
+That's really all there is to Bresenham's algorithm. The algorithm is a
 process of drawing a pixel at each possible coordinate along the major
 dimension of the line, each with the closest possible coordinate along
 the minor dimension. The running error is used to keep track of when the
@@ -97,10 +97,10 @@ octants in which lines could be drawn, as we will see in the C
 implementation.
 
 The above discussion summarizes the nature rather than the exact
-mechanism of Bresenham’s line-drawing algorithm. I’ll provide a brief
+mechanism of Bresenham's line-drawing algorithm. I'll provide a brief
 seat-of-the-pants discussion of the algorithm in action when we get to
 the C implementation of the algorithm; for a full mathematical
-treatment, I refer you to pages 433-436 of Foley and Van Dam’s
+treatment, I refer you to pages 433-436 of Foley and Van Dam's
 *Fundamentals of Interactive Computer Graphics* (Addison-Wesley, 1982),
 or pages 72-78 of the second edition of that book, which was published
 under the name *Computer Graphics: Principles and Practice*
@@ -110,26 +110,26 @@ code for drawing lines in one of the eight possible octants.
 
 #### Strengths and Weaknesses {#Heading5}
 
-The overwhelming strength of Bresenham’s line-drawing algorithm is
+The overwhelming strength of Bresenham's line-drawing algorithm is
 speed. With no divides, no floating-point operations, and no need for
-variables that won’t fit in 16 bits, it is perfectly suited for PCs.
+variables that won't fit in 16 bits, it is perfectly suited for PCs.
 
-The weakness of Bresenham’s algorithm is that it produces relatively
+The weakness of Bresenham's algorithm is that it produces relatively
 low-quality lines by comparison with most other line-drawing algorithms.
-In particular, lines generated with Bresenham’s algorithm can tend to
+In particular, lines generated with Bresenham's algorithm can tend to
 look a little jagged. On the PC, however, jagged lines are an inevitable
 consequence of relatively low resolution and a small color set, so lines
-drawn with Bresenham’s algorithm don’t look all that much different from
+drawn with Bresenham's algorithm don't look all that much different from
 lines drawn in other ways. Besides, in most applications, users are far
 more interested in the overall picture than in the primitive elements
 from which that picture is built. As a general rule, any collection of
 pixels that trend from point A to point B in a straight fashion is
-accepted by the eye as a line. Bresenham’s algorithm is successfully
+accepted by the eye as a line. Bresenham's algorithm is successfully
 used by many current PC programs, and by the standard of this wide
 acceptance the algorithm is certainly good enough.
 
 Then, too, users hate waiting for their computer to finish drawing. By
-any standard of drawing performance, Bresenham’s algorithm excels.
+any standard of drawing performance, Bresenham's algorithm excels.
 
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