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James Gregory 2013-12-31 07:56:10 +11:00
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@ -18,8 +18,7 @@ valid choice for the initial split; we'll return to the issue of
choosing splitting walls in the next chapter.) This splitting into front
and back is the essential dualism of BSP trees.
![](images/59-03.jpg)\
**Figure 59.3**  *Initial split along the line of wall C.*
![**Figure 59.3**  *Initial split along the line of wall C.*](images/59-03.jpg)
Next, in Figure 59.4, the front subspace of wall C is split by wall D.
This is the only wall in that subspace, so we're done with wall C's
@ -30,13 +29,11 @@ There's a difference here, though: Wall A straddles the splitting line
generated from wall B. Does wall A belong in the front or back subspace
of wall B?
![](images/59-04.jpg)\
**Figure 59.4**  *Split of wall C's front subspace along the line of
wall D.*
![**Figure 59.4**  *Split of wall C's front subspace along the line of
wall D.*](images/59-04.jpg)
![](images/59-05.jpg)\
**Figure 59.5**  *Split of wall C's back subspace along the line of
wall B.*
![**Figure 59.5**  *Split of wall C's back subspace along the line of
wall B.*](images/59-05.jpg)
Both, actually. Wall A gets split into two pieces, which I'll call wall
A and wall E; each piece is assigned to the appropriate subspace and
@ -75,11 +72,9 @@ children is on the far side from the viewpoint, draw the wall, and then
visit the node's nearer child, in that order. Visiting a child is
recursive, involving the same far-near visiting order.
![](images/59-06.jpg)\
**Figure 59.6**  *The final BSP tree.*
![**Figure 59.6**  *The final BSP tree.*](images/59-06.jpg)
![](images/59-07.jpg)\
**Figure 59.7**  *Viewing the BSP tree from an arbitrary angle.*
![**Figure 59.7**  *Viewing the BSP tree from an arbitrary angle.*](images/59-07.jpg)
The key is that each BSP splitting line separates all the walls in the
current subspace into two groups relative to the viewpoint, and every
@ -88,9 +83,8 @@ single member of the nearer. By applying this ordering recursively, the
BSP tree can be traversed to provide back-to-front or front-to-back
ordering, with each node being visited only once.
![](images/59-08.jpg)\
**Figure 59.8**  *Back-to-front traversal of the BSP tree as viewed in
Figure 59.7.*
![**Figure 59.8**  *Back-to-front traversal of the BSP tree as viewed in
Figure 59.7.*](images/59-08.jpg)
The type of tree walk used to produce front-to-back or back-to-front BSP
traversal is known as an *inorder* walk. More on this very shortly;