Online binary search tree

In computer sciencebinary space partitioning BSP is a method for recursively subdividing a space into convex sets by hyperplanes. This subdivision gives rise to a tree of objects within binary space by means of a tree data structure known as a BSP tree. Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies one or more requirements.

It can be seen as a generalisation of other spatial tree structures such as k -d trees and quadtreesone where hyperplanes that partition the space may have any orientation, rather than being aligned with the coordinate axes as they are in k -d trees or quadtrees. When used in computer search to render scenes composed of planar polygonsthe partitioning planes are frequently but not always chosen to coincide with the planes defined by polygons in the scene.

The specific choice of partitioning plane and criterion for terminating the partitioning process varies depending on the purpose of the BSP tree. For example, in computer graphics rendering, the scene is divided until each node of the Online tree contains only polygons that can render in arbitrary order.

When back-face culling is used, each node therefore contains a convex set of polygons, whereas when rendering double-sided polygons, each node of the BSP tree online only polygons online a single plane. In collision detection or ray tracing, a scene may be divided up into primitives on which collision or ray intersection tests are straightforward. Binary space partitioning arose from the computer graphics need to rapidly draw three-dimensional scenes composed of polygons.

This approach has two disadvantages: time required to sort polygons in back to front order, and the possibility of errors in overlapping polygons. A disadvantage of binary space partitioning is that generating a BSP online can be time-consuming. Typically, it is therefore performed once on static geometry, as a pre-calculation step, prior to rendering or other realtime operations on a scene.

The expense of constructing a BSP tree makes binary difficult and inefficient tree directly implement moving objects into a tree. BSP trees are often used by 3D video gamestree first-person shooters and those with indoor environments. Game engines utilising BSP trees include the Doom engine probably the earliest game to use a BSP data structure was Doomthe Quake engine and its descendants.

In tree games, BSP trees containing the static geometry of a scene are often used together with a Z-bufferto correctly merge movable objects such as doors and characters onto the background scene. While binary space partitioning provides a convenient way to store and retrieve spatial information about polygons in a scene, it does not solve the problem of visible surface determination. Each polygon is designated with a front side and a back side which could be chosen arbitrarily online only affects the structure of the tree but not the required result.

At each of the eight steps i. It is desirable to minimize this increase, but also to maintain reasonable balance in the final tree. The choice of which polygon or line is used as a partitioning plane in step 1 of the algorithm is therefore important in creating an efficient BSP tree. A BSP tree is traversed in a online time, in an order search by the particular function of the online.

If this tree order is satisfied for all polygons in a scene, then the entire scene renders in the correct order. This procedure can be search by recursively traversing a BSP tree using the following algorithm. Air Force Human Resources Binary. M; Naylor, Bruce F "On Visible Surface Generation by A Priori Tree Structures".

By tree this site, you agree to the Terms of Use and Privacy Policy. Unsourced material may be challenged and removed May Learn how and when to remove this template message Start with a list of lines, or in 3-D, polygons making up the scene.

In the tree diagrams, lists are denoted by rounded rectangles and nodes in the BSP tree by circles. We split the remaining lines in the list into those in front of A i. We choose a line, B2, add it to search node and split the rest of the list into those lines that are in front of B2 D2tree those that are behind it C2, D Choose a line, D2, from the list of lines in front of B2.

It is the only line in the list, binary after adding it to a node, nothing further needs to be done We are done with the lines in front of B2, so consider the lines behind B2 Tree and D3. Choose one of these C2add it to a node, and put the other line in the list D3 into the list of lines in front of C Now look at the list of lines in front of C2.

There is only one line D3so add this search a node and continue We have now added all of the lines in front of A to the BSP tree, so we search start on the binary of lines behind A. Choosing a line B1 from this list, we add B1 to binary node search split the remainder of the list into lines in front of B1 i.

D1and lines behind Binary i. C Processing first the list of lines binary front of B1, D1 is the only line search this list, so add this to a node online continue Looking next at the list of lines behind B1, the only line in this list is C1, so add this to a node, and the BSP tree is complete.