Remove heading ids, let pandoc generate them
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@ -11,9 +11,9 @@ pages: 1095-1114
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---
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## Chapter 59\
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The Idea of BSP Trees {#Heading1}
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The Idea of BSP Trees
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### What BSP Trees Are and How to Walk Them {#Heading2}
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### What BSP Trees Are and How to Walk Them
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The answer is: Wendy Tucker.
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@ -94,7 +94,7 @@ the most from them.
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Before we begin, I'd like to thank John Carmack, the technical wizard
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behind DOOM, for generously sharing his knowledge of BSP trees with me.
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### BSP Trees {#Heading3}
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### BSP Trees
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A BSP tree is, at heart, nothing more than a tree that subdivides space
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in order to isolate features of interest. Each node of a BSP tree splits
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@ -117,7 +117,7 @@ powerful way to implement Constructive Solid Geometry (CSG). BSP trees
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can also be used for hit testing, line-of-sight determination, and
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collision detection.
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#### Visibility Determination {#Heading4}
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#### Visibility Determination
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For the time being, I'm going to discuss only one of the many uses of
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BSP trees: The ability of a BSP tree to allow you to traverse a set of
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@ -158,7 +158,7 @@ trees.
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#### Limitations of BSP Trees {#Heading5}
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#### Limitations of BSP Trees
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Powerful as they are, BSP trees aren't perfect. By far the greatest
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limitation of BSP trees is that they're time-consuming to build, enough
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@ -207,7 +207,7 @@ I'll present in the next chapter, which visually depicts the process of
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spatial subdivision as a BSP tree is constructed, help a great deal with
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BSP debugging.
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### Building a BSP Tree {#Heading6}
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### Building a BSP Tree
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Now that we know a good bit about what a BSP tree is, how it helps in
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visible surface determination, and what its strengths and weaknesses
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@ -280,7 +280,7 @@ treated as a separate wall. As shown in Figure 59.6, each of the split
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pieces then has a subspace to itself, and each becomes a leaf of the
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tree. The BSP tree is now complete.
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#### Visibility Ordering {#Heading7}
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#### Visibility Ordering
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Now that we've successfully built a BSP tree, you might justifiably be a
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little puzzled as to how any of this helps with visibility ordering. The
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@ -379,7 +379,7 @@ void WalkBSPTree(NODE *pNode)
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> partition space identically and can't occlude one another, so it
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> suffices to generate one splitting node for each collinear set.
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### Inorder Walks of BSP Trees {#Heading8}
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### Inorder Walks of BSP Trees
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It was implementing BSP trees that got me to thinking about inorder tree
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traversal. In inorder traversal, the left subtree of each node gets
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@ -472,7 +472,7 @@ fully functional model to follow, with all the problems solved, but they
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can't make the connection between that model and the code they're trying
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to implement. Why is this?
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#### Know It *Cold* {#Heading9}
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#### Know It *Cold*
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The problem is that these people don't understand inorder walking
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through and through. They understand the concepts of visiting left and
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@ -604,7 +604,7 @@ pants.
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> the model down cold, you can always tell if the implementation is
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> correct by comparing it with the model.
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#### Measure and Learn {#Heading10}
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#### Measure and Learn
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How much difference does all this fuss make, anyway? Listing 59.5 is a
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sample program that builds a tree, then calls `WalkTree` () to walk it
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@ -749,7 +749,7 @@ run fast enough to keep up if you just keep at it.
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Depths within depths indeed!
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### Surfing Amidst the Trees {#Heading11}
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### Surfing Amidst the Trees
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In the next chapter, we'll build a BSP-tree compiler, and after that,
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we'll put together a rendering system built around the BSP trees the
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@ -761,7 +761,7 @@ must investigate at
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up in the familiar Internet Frequently Asked Questions (FAQ) style, and
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is very good stuff.
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#### Related Reading {#Heading12}
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#### Related Reading
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Foley, J., A. van Dam, S. Feiner, and J. Hughes, *Computer Graphics:
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Principles and Practice (Second Edition)*, Addison Wesley, 1990, pp.
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