Remove heading ids, let pandoc generate them
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@ -11,9 +11,9 @@ pages: 931-949
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## Chapter 50\
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Adding a Dimension {#Heading1}
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Adding a Dimension
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### 3-D Animation Using Mode X {#Heading2}
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### 3-D Animation Using Mode X
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When I first started programming micros, more than 11 years ago now,
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there wasn't much money in it, or visibility, or anything you could call
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@ -84,7 +84,7 @@ In a sense, I've saved the best for last, because, to my mind, real-time
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be done with a computer—and because, with today's hardware, it can in
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fact be done. Nay, it can be done amazingly well.
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### References on 3-D Drawing {#Heading3}
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### References on 3-D Drawing
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There are several good sources for information about 3-D graphics. Foley
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and van Dam's *Computer Graphics: Principles and Practice* (Second
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@ -113,7 +113,7 @@ you're just starting out, you might want to look at one and see if it
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helps you bridge the gap between the theory and implementation of 3-D
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graphics.
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### The 3-D Drawing Pipeline {#Heading4}
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### The 3-D Drawing Pipeline
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Each 3-D object that we'll handle will be built out of polygons that
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represent the surface of the object. Figure 50.1 shows the stages a
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@ -160,7 +160,7 @@ twice as far away as a coordinate of (0,0,-500).
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#### Projection {#Heading5}
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#### Projection
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Working backward from the final image, we want to take the vertices of a
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polygon, as transformed into view space, and project them to 2-D
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@ -182,7 +182,7 @@ projected X and Y coordinates to integers, appropriately clipped and
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adjusted as necessary to center the origin on the screen or otherwise
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map the image into a window, if desired.
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#### Translation {#Heading6}
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#### Translation
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*Translation* means adding X, Y, and Z offsets to a coordinate to move
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it linearly through space. Translation is as simple as it seems; it
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@ -193,7 +193,7 @@ the object may be located anywhere.
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#### Rotation {#Heading7}
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#### Rotation
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*Rotation* is the process of circularly moving coordinates around the
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origin. For our present purposes, it's necessary only to rotate objects
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@ -225,7 +225,7 @@ There's much more to be said about transformations and the supporting
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matrix math, but, in the interests of getting to working code in this
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chapter, I'll leave that to be discussed as the need arises.
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### A Simple 3-D Example {#Heading8}
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### A Simple 3-D Example
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At this point, we know enough to be able to put together a simple
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working 3-D animation example. The example will do nothing more
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@ -755,7 +755,7 @@ void main() {
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}
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```
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#### Notes on the 3-D Animation Example {#Heading9}
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#### Notes on the 3-D Animation Example
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The sample program transforms the polygon's vertices from object space
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to world space to view space to the screen, as described earlier. In
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@ -812,7 +812,7 @@ it rotates. This is temporal aliasing at its finest! We won't address
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antialiasing further, realtime antialiasing being decidedly nontrivial,
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but this should give you an idea of why antialiasing is so desirable.
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### An Ongoing Journey {#Heading10}
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### An Ongoing Journey
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In the next chapter, we'll assign fronts and backs to polygons, and
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start drawing only those that are facing the viewer. That will enable us
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