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# BSP Tree Question

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### #1Gammastrahler  Members   -  Reputation: 150

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Posted 13 July 2014 - 04:33 AM

Hi,

i want to use a BSP tree for processing boolean operations on solids (CSG).

In theory, i have understood the algorithm, but what actually confuses me is the step when selecting the splitting polygons for the BSP construction process. For example, if i have a cube, do i need a split plane / left and right nodes for each side of the cube?

Any help would be appreciated.

Regards

Gammastrahler

### #2Ohforf sake  Members   -  Reputation: 2048

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Posted 13 July 2014 - 05:48 AM

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Long answer: Consider a rectangle in 2D (works the same, but has less sides).

Every node splits the space into two halves. Leaf nodes labels it's space as empty or solid.

So for a rectangle
   +-------+
|       |
|       |
|       |
+-------+

you could start by choosing the left side as the first splitting plane (in 2D a splitting line):
  A | B
|
|
+-------+
|       |
|       |
|       |
+-------+
|
|

So your root node now has a splitting plane and two children A and B. A will remain a leaf node and label the left hand side as empty.
B we could now split further by, for example, the top edge:
  A |
|
| [B] C
+-------+------------
|       | [B] D
|       |
|       |
+-------+
|
|

so the node B now has two children C and D. C again labeling it's space as empty. Now after splitting D for example by the right hand side we get:
   A |
|
| [B] C
+-------+------------
|       |
|       |
|       |
+-------+
|       |
|       |
|       |
|[B,D] F|[B,D] E

and there you have it: one splitting plane on the left, and further down the tree one on the right. E, which is a child node of D, which again is a child node of B, denotes the right hand side as empty. Now we can finish things up by splitting F
   A |
|
| [b] C
+-------+------------
|       |
|       |
|B,D,F]H|
+-------+
|B,D,F]G|
|       |
|       |
|       |[B,D] E

and labeling G as empty and H as solid.

And there you have it, a BSP tree with a total of 4 splits, one for each side.

### #3Gammastrahler  Members   -  Reputation: 150

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Posted 13 July 2014 - 06:01 AM

Thank you for the detailed description

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