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implicit kd tree
An implicit ''k''-d tree is a ''k''-d tree defined implicitly above a rectilinear grid. Its split planes' positions and orientations are not given explicitly but implicitly by some recursive splitting-function defined on the hyperrectangles belonging to the tree's nodes. Each inner node's split plane is positioned on a grid plane of the underlying grid, partitioning the node's grid into two subgrids.
==Nomenclature and references==
The terms "min/max ''k''-d tree" and "implicit ''k''-d tree" are sometimes mixed up. This is because the first publication using the term "implicit ''k''-d tree" 〔Ingo Wald, Heiko Friedrich, Gerd Marmitt, Philipp Slusallek and Hans-Peter Seidel "Faster Isosurface Ray Tracing using Implicit KD-Trees" IEEE Transactions on Visualization and Computer Graphics (2005)〕 did actually use explicit min/max ''k''-d trees but referred to them as "implicit ''k''-d trees" to indicate that they may be used to ray trace implicitly given iso surfaces. Nevertheless, this publication used also slim ''k''-d trees which are a subset of the implicit ''k''-d trees with the restriction that they can only be built over integer hyperrectangles with sidelengths that are powers of two. Implicit ''k''-d trees as defined here have recently been introduced, with applications in computer graphics.〔Matthias Groß, Carsten Lojewski, Martin Bertram and Hans Hagen "Fast Implicit ''k''-d Trees: Accelerated Isosurface Ray Tracing and Maximum Intensity Projection for Large Scalar Fields" CGIM07: Proceedings of Computer Graphics and Imaging (2007) 67-74〕〔Matthias Groß (PhD, 2009) (Towards Scientific Applications for Interactive Ray Casting )〕 As it is possible to assign attributes to implicit ''k''-d tree nodes, one may refer to an implicit ''k''-d tree which has min/max values assigned to its nodes as an "implicit min/max ''k''-d tree".
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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