Using an implicit min/max KD-tree for doing efficient terrain line of sight calculations

Abstract

The generation of accurate Line of Sight (LOS) visibility information consumes significant resources in large scale synthetic environments such as many-on-many serious games and battlefield simulators. Due to the importance of optimum utilisation of computing resources, a number of LOS algorithms are reported in the literature to either efficiently compute LOS information or reduce the impact of LOS queries on the run-time performance of synthetic environments. From the literature it is known that a k-dimensional tree (kd-tree) based raytracing approach, to calculating LOS information, is efficient.A new implicit min/max kd-tree algorithm is discussed for evaluating LOS queries on large scale spherical terrain. In particular the value of low resolution boundary information, in quickly evaluating the LOS query, is emphasised. The min/max algorithm is empirically compared to other LOS approaches that have either implicitly or explicitly used kd-trees to optimise LOS query evaluation. The min/max algorithm is shown to have comparable performance to these existing LOS algorithms for flat earth, but improved performance when the application domain is extended to spherical earth. An average of a factor 3.0 performance increase is experienced over that of the existing implicit and explicit max kd-tree algorithms on spherical earth. This is achieved by combining the existing kd-tree algorithm with the classic smooth-earth LOS obscuration test and from there the min in min/max kd-tree.

Reverse Subdivision for Optimizing Visibility Tests

“…Spatial subdivision can be used to produce an asymptotically faster algorithm. (Duvenhage, 2009) uses an implicit min/max k-d tree to quickly cull regions of the terrain that lie completely under or over the sight line to obtain an algorithm that is logarithmic in the number of elevation values that lie along the sight line's path, on average.…”

“…In many computer graphics applications, such as flight simulations and geographic information systems (GIS), a digital representation of a terrain is required. In general, digital terrain models are divided into two types: digital elevations models (DEMs), which are regular grids of elevations values; and triangulated irregular networks (TINs), which are irregular polygonal meshes composed of triangles (Duvenhage, 2009). These terrain models can become very large and detailed, especially for large areas.…”

Faster Parallel Exact Density Peaks Clustering

“…Our first new algorithm for solving Step 2's dependent point finding task utilizes a priority search kd-tree. A priority search kd-tree is an optimization of a max kd-tree [33,21]. The priority search kd-tree can be constructed from a data set of n points similar to a regular kd-tree [68] in O(n log n) work and O(log n log log n) span.…”