BSP hidden surface removal
From CGAFaq
Probably the most common application of BSP trees is hidden surface removal in three dimensions. BSP trees provide an elegant, efficient method for sorting polygons via a depth first tree walk. This fact can be exploited in a back to front "painter's algorithm" approach to the visible surface problem, or a front to back scanline approach.
BSP trees are well suited to interactive display of static (not moving) geometry because the tree can be constructed as a preprocess. Then the display from any arbitrary viewpoint can be done in linear time. Adding dynamic (moving) objects to the scene is discussed in another section of this document.
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Painter's algorithm
The idea behind the painter's algorithm is to draw polygons far away from the eye first, followed by drawing those that are close to the eye. Hidden surfaces will be written over in the image as the surfaces that obscure them are drawn. One condition for a successful painter's algorithm is that there be a single plane which separates any two objects. This means that it might be necessary to split polygons in certain configurations. For example, this case can not be drawn correctly with a painter's algorithm:
+------+
| |
+---------------| |--+
| | | |
| | | |
| | | |
| +--------| |--+
| | | |
+--| |--------+ |
| | | |
| | | |
| | | |
+--| |---------------+
| |
+------+
One reason that BSP trees are so elegant for the painter's algorithm is that the splitting of difficult polygons is an automatic part of tree construction. Note that only one of these two polygons needs to be split in order to resolve the problem.
To draw the contents of the tree, perform a back to front tree traversal. Begin at the root node and classify the eye point with respect to its partition plane. Draw the subtree at the far child from the eye, then draw the polygons in this node, then draw the near subtree. Repeat this procedure recursively for each subtree.
Scanline hidden surface removal
It is just as easy to traverse the BSP tree in front to back order as it is for back to front. We can use this to our advantage in a scanline method method by using a write mask which will prevent pixels from being written more than once. This will represent significant speedups if a complex lighting model is evaluated for each pixel, because the painter's algorithm will blindly evaluate the same pixel many times.
The trick to making a scanline approach successful is to have an efficient method for masking pixels. One way to do this is to maintain a list of pixel spans which have not yet been written to for each scan line. For each polygon scan converted, only pixels in the available spans are written, and the spans are updated accordingly.
The scan line spans can be represented as binary trees, which are just one dimensional BSP trees. This technique can be expanded to a two dimensional screen coverage algorithm using a two dimensional BSP tree to represent the masked regions. Any convex partitioning scheme, such as a quadtree, can be used with similar effect.
Implementation notes
When building a BSP tree specifically for hidden surface removal, the partition planes are usually chosen from the input polygon set. However, any arbitrary plane can be used if there are no intersecting or concave polygons, as in the example above.
Pseudo C++ code example
Using the BSP_tree structure defined in the section, How do you build a BSP Tree?, here is a simple example of a back to front tree traversal:
void Draw_BSP_Tree (BSP_tree *tree, point eye)
{
real result = tree->partition.Classify_Point (eye);
if (result > 0)
{
Draw_BSP_Tree (tree->back, eye);
tree->polygons.Draw_Polygon_List ();
Draw_BSP_Tree (tree->front, eye);
}
else if (result < 0)
{
Draw_BSP_Tree (tree->front, eye);
tree->polygons.Draw_Polygon_List ();
Draw_BSP_Tree (tree->back, eye);
}
else // result is 0
{
// the eye point is on the partition plane...
Draw_BSP_Tree (tree->front, eye);
Draw_BSP_Tree (tree->back, eye);
}
}
If the eye point is classified as being on the partition plane, the drawing order is unclear. This is not a problem if the Draw_Polygon_List routine is smart enough to not draw polygons that are not within the viewing frustum. The coincident polygon list does not need to be drawn in this case, because those polygons will not be visible to the user.
It is possible to substantially improve the quality of this example by including the viewing direction vector in the computation. You can determine that entire subtrees are behind the viewer by comparing the view vector to the partition plane normal vector. This test can also make a better decision about tree drawing when the eye point lies on the partition plane. It is worth noting that this improvement resembles the method for tracing a ray through a BSP tree, which is discussed in another section of this document.
Front to back tree traversal is accomplished in exactly the same manner, except that the recursive calls to Draw_BSP_Tree occur in reverse order.
Initial content for this page from the BSP tree FAQ, included with permission of its maintainer, Bretton Wade.
