In proceedings of Mobilware 2009, The Second International ICST Conference on MOBILe Wireless MiddleWARE, Operating Systems, and Applications, April 27-29, 2009, Berlin, Germany.
3D Digital Maps of Earth provide elevation values at specific longitudinal and latitudinal positions.
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DTED maps consist of a square grid structure of cells covering the surface of Earth, with terrain elevation values sampled at the intersection points. There are three distinct detail levels: Level 0, Level 1, and Level 2. DTED Level 0 contains the least amount of detail while requiring the minimum amount of storage space. Higher levels require several gigabytes to represent the whole world, while at most a few hundred MBs will suffice for DTED Level 0 storage, depending on the data types used in the datafiles. |
Top view of a sample DTED level 0 grid of 3D terrain cells. |
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Level 0 maps are algorithmically downsampled and generated from Level 1 source profiles, where the spacing interval between two node points in Level 0 is roughly 1 km.
Each discrete cell in DTED Level 0 packages 7 targeted elevation metrics:
Although the locations of the 4 corner coordinates are mathematically fixed, the other 3 metric attributes (max, min, average) do not carry predefined position values inside the Level 0 cell grid.
In this architecture, the highest and lowest terrain features are localized inside the cell matrix, and the remaining coordinate nodes are smoothed via interpolation relative to the tracking average value across these 6 boundary reference points.
| Planar Surfaces (As-Is) | Smoothed Surface Interpolation |
|---|---|
Sample cell with corner points numbered (1–4) |
Sample smooth interpolation utilizing 4 corner landmarks |
DTED Level 0 cells contain maximum and minimum elevation values extracted from the corresponding source DTED Level 1 cell. Programmatically locating these bounding points significantly improves the surface interpolation model in terms of maintaining consistency with the average overall elevation profile of the original terrain layout.
Figure: Comparison showing interpolation improvement after maximum and minimum points are located according to Singular Positioning.
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DTED Level 0 cells store the absolute maximum and minimum elevation markers of their corresponding Level 1 parent cells. Explicitly defining coordinates for these extremums increases the precision of local terrain mesh generation, pinning down structural variances relative to the broader surface average. |
Locating Segmentation Points (Points Projected on x-y Plane) |
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To calculate the spatial coordinates of a maximum or minimum feature point inside the grid cell boundaries, intermediate segmentation markers are generated based on the direct elevation deltas between corner points and the destination peak or valley target value. As an example execution pathway, target boundaries p5-I and p5-II are localized inside the cell plane and are then bisected an additional time to pinpoint p5 (the designated maximum peak). Similarly, node p6 serves as the computed index representing the localized minimum valley point. Mathematically, the smaller the structural elevation variance a specific corner boundary point maintains relative to the peak or valley threshold, the closer its coordinate position will sit next to that respective maximum or minimum node index. |
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If diagonally opposing matrix corners hold identical altitude values (e.g., the NW point matches the SE point elevation, and the NE point mirrors the SW point elevation), a mathematical conflict occurs: both the singular maximum and minimum calculations resolve onto the exact same coordinate junction—the exact geometric center of the cell space. To resolve this collision scenario, a circular tracking distribution algorithm deploying multiple secondary maximum and minimum node offsets is applied across the active region. |
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Under this approach, the absolute center of the cell layout is assigned the minimum (or maximum) value, while being uniformly ringed by four matching maximum (or minimum) node structures. Additional specialized control point markers are layered along the exterior perimeter circles.
These secondary control points function strictly as tuning elements to lock the aggregate arithmetic mean of the resulting interpolated grid cell surface to match the true baseline parameters supplied by the uncompressed parent DTED Level 1 dataset.
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If the delta between the average and the minimum value (AVG – MIN) tracks smaller than the delta between the maximum and the average value (MAX – AVG), it indicates that the vast majority of the spatial landmass area sits lower than the mean elevation, clustering nearer to the valley floor. Positioning the singular maximum anchor point directly in the center of the cell grid while radiating four matching minimum anchors outward onto an external perimeter circle balances the resulting mesh surface geometry to fit this specific skew profile. |
Condition: MAX – AVG > AVG – MIN
Condition: MAX – AVG < AVG – MIN |
Figure: Central profile cross sections charting the boundary adjustments for both interpolation scenarios. |
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Even though only a marginal fraction of the grid elements within our target study region mathematically encounter the geometric criteria forcing a circular distribution, the technique is systematically applied as a stabilization override whenever maximum and minimum anchors map too closely together. The total volume of explicit control nodes required to resolve circular geometry maps out to exactly three times the density profile of the standard singular approach. Consequently, this method outputs superior fidelity and smoother contour surface maps. However, because the associated programmatic overhead involving matrix inversion and linear transformation steps scales heavily on low-power mobile architectures, the application threshold determining when to tag cells for circular processing must be carefully managed to remain within sensible hardware bounds. |
Digital map visualization of the evaluation area composed of 14,400 active cells. |
Based on the Inverse Distance Weighting (IDW) interpolation analysis, the proposed technique yields significantly better interpolation accuracy compared to baseline models that utilize only the available corner points of grid cells.
| Cell Size (points) | % Of Cells Where Method Finds Better Average | Mean and Std. Deviation of Average Value Difference | |||||
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| IDW | IDW Extra | Equal Distance | Mean (IDW) | Std. Dev. (IDW) | Mean (IDW Extra) | Std. Dev. (IDW Extra) | |
| 6x6 | 3.55% | 93.69% | 2.76% | -57.74m | 45.38m | -40.7m | 39.05m |
| 11x11 | 2.28% | 96.67% | 1.06% | -68.72m | 52.13m | -44.1m | 43.38m |
| 26x26 | 1.82% | 97.63% | 0.56% | -77.39m | 56.58m | -42.4m | 43.76m |
| 51x51 | 1.57% | 97.83% | 0.60% | -81.47m | 58.35m | -39.6m | 42.34m |
| Cell Size (points) | % Of Cells Closer To Real Elevation Values | Mean and Standard Deviation of Elevation Value Difference | |||||
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| IDW | IDW Extra | Equal Distance | Mean (IDW) | Std. Dev. (IDW) | Mean (IDW Extra) | Std. Dev. (IDW Extra) | |
| 6x6 | 17.30% | 46.38% | 36.32% | -57.40m | 68.50m | -40.52m | 63.05m |
| 11x11 | 16.20% | 57.30% | 26.49% | -68.35m | 71.25m | -43.84m | 63.78m |
| 26x26 | 14.10% | 67.84% | 18.06% | -76.99m | 72.91m | -42.18m | 62.03m |
| 51x51 | 13.16% | 73.09% | 13.75% | -81.07m | 73.72m | -39.46m | 60.24m |
| Cell Size | Total Points | IDW 50m | IDW 20m | IDW Extra 50m | IDW Extra 20m |
|---|---|---|---|---|---|
| 6x6 | 518,400 | 58.39% | 33.30% | 66.72% | 42.67% |
| 11x11 | 1,742,400 | 50.46% | 23.68% | 64.03% | 37.39% |
| 26x26 | 9,734,400 | 43.35% | 17.68% | 64.91% | 37.06% |
| 51x51 | 37,454,400 | 39.67% | 15.76% | 66.43% | 37.97% |