Normal quotes

50-02.md

@@ -2,7 +2,7 @@
   [Previous](50-01.html)   [Table of Contents](index.html)   [Next](50-03.html)
   ------------------------ --------------------------------- --------------------
 
-One note: I’ll use a purely *right-handed* convention for coordinate
+One note: I'll use a purely *right-handed* convention for coordinate
 systems. Right-handed means that if you hold your right hand with your
 fingers curled and the thumb sticking out, the thumb points along the Z
 axis and the fingers point in the direction of rotation from the X axis
@@ -29,12 +29,12 @@ Working backward from the final image, we want to take the vertices of a
 polygon, as transformed into view space, and project them to 2-D
 coordinates on the screen, which, for projection purposes, is assumed to
 be centered on and perpendicular to the Z axis in view space, at some
-distance from the screen. We’re after visual realism, so we’ll want to
+distance from the screen. We're after visual realism, so we'll want to
 do a perspective projection, in order that farther objects look smaller
 than nearer objects, and so that the field of view will widen with
 distance. This is done by scaling the X and Y coordinates of each point
 proportionately to the Z distance of the point from the viewer, a simple
-matter of similar triangles, as shown in Figure 50.3. It doesn’t really
+matter of similar triangles, as shown in Figure 50.3. It doesn't really
 matter how far down the Z axis the screen is assumed to be; what matters
 is the ratio of the distance of the screen from the viewpoint to the
 width of the screen. This ratio defines the rate of divergence of the
@@ -60,7 +60,7 @@ the object may be located anywhere.
 #### Rotation {#Heading7}
 
 *Rotation* is the process of circularly moving coordinates around the
-origin. For our present purposes, it’s necessary only to rotate objects
+origin. For our present purposes, it's necessary only to rotate objects
 about their centers in object space, so as to turn them to the desired
 attitude before translating them into world space.
 
@@ -77,8 +77,8 @@ matrix can then be used to perform the rotations more efficiently.
 
 Second, 3x3 rotation matrices can become the upper-left-hand portions of
 4x4 matrices that also perform translation (and scaling as well, but we
-won’t need scaling in the near future), as shown in Figure 50.5. A 4x4
-matrix of this sort utilizes homogeneous coordinates; that’s a topic way
+won't need scaling in the near future), as shown in Figure 50.5. A 4x4
+matrix of this sort utilizes homogeneous coordinates; that's a topic way
 beyond this book, but, basically, homogeneous coordinates allow you to
 handle both rotations and translations with 4x4 matrices, thereby
 allowing the same code to work with either, and making it possible to
@@ -86,9 +86,9 @@ concatenate a long series of rotations and translations into a single
 matrix that performs the same transformation as the sequence of
 rotations and transformations.
 
-There’s much more to be said about transformations and the supporting
+There's much more to be said about transformations and the supporting
 matrix math, but, in the interests of getting to working code in this
-chapter, I’ll leave that to be discussed as the need arises.
+chapter, I'll leave that to be discussed as the need arises.
 
 ### A Simple 3-D Example {#Heading8}
 
@@ -96,8 +96,8 @@ At this point, we know enough to be able to put together a simple
 working 3-D animation example. The example will do nothing more
 complicated than display a single polygon as it sits in 3-D space,
 rotating around the Y axis. To make things a little more interesting,
-we’ll let the user move the polygon around in space with the arrow keys,
-and with the “A” (away), and “T” (toward) keys. The sample program
+we'll let the user move the polygon around in space with the arrow keys,
+and with the "A" (away), and "T" (toward) keys. The sample program
 requires two sorts of functionality: The ability to transform and
 project the polygon from object space onto the screen (3-D
 functionality), and the ability to draw the projected polygon (complete
@@ -109,13 +109,13 @@ functionality).
 
 Happily (and not coincidentally), we put together a nice 2-D animation
 framework back in Chapters 47, 48, and 49, during our exploratory
-discussion of Mode X, so we don’t have much to worry about in terms of
-non-3-D details. Basically, we’ll use Mode X (320x240, 256 colors), and
-we’ll flip between two display pages, drawing to one while the other is
+discussion of Mode X, so we don't have much to worry about in terms of
+non-3-D details. Basically, we'll use Mode X (320x240, 256 colors), and
+we'll flip between two display pages, drawing to one while the other is
 displayed. One new 2-D element that we need is the ability to clip
 polygons; while we could avoid this for the moment by restricting the
 range of motion of the polygon so that it stays fully on the screen,
-certainly in the long run we’ll want to be able to handle partially or
+certainly in the long run we'll want to be able to handle partially or
 fully clipped polygons. Listing 50.1 is the low-level code for a Mode X
 polygon filler that supports clipping. (The high-level polygon fill code
 is mode independent, and is the same as that presented in Chapters 38,
@@ -124,7 +124,7 @@ level, by trimming the Y extent of the scan line list up front, then
 clipping the X coordinates of each scan line in turn. This is not a
 particularly fast approach to clipping—ideally, the polygon would be
 clipped before it was scanned into a line list, avoiding potentially
-wasted scanning and eliminating the line-by-line X clipping—but it’s
+wasted scanning and eliminating the line-by-line X clipping—but it's
 much simpler, and, as we shall see, polygon filling performance is the
 least of our worries at the moment.