PDERL: an accurate and fast algorithm with a novel perspective on solving the old viewshed analysis problem

Abstract

Viewshed analysis based on the regular grid digital elevation model (DEM) is one of the basic functions of geographic information systems. Traditional viewshed analysis algorithms are mainly carried out in a geospatial coordinate system, that create complexities when it is necessary to accurately express a perspective relationship. Moreover, it can only reduce the amount of calculation by using approximation methods, which result in decreased accuracy. We found that the error ratio of approximation algorithms is low but uneven and thereby highly likely to result in continuous area visibility errors. Despite the quality of DEM data having improved significantly in the last decade, traditional approximation algorithms have been unable to take full advantage of the improved data. Finding a fast and accurate algorithm has therefore become an urgent task. This study takes a new perspective to solve this problem by establishing a ‘proximity-direction-elevation’ (PDE) coordinate system and proposing a PDE spatial reference line (PDERL) algorithm within it. Many experiments prove that the accuracy of PDERL is the same as the R3 algorithm and its speed is about half that of the XDraw and reference plane algorithms, but much faster than R3. Due to the speed of PDERL, it is now possible and practical to do an accurate large-area DEM-based viewshed analysis.

HiPDERL: An Improved Implementation of the PDERL Viewshed Algorithm and Accuracy Analysis

“…Their transformation relationships with XYZ coordinate system are shown in Equations ( 1)-( 3), adapted from Ref. [19]. The algorithm computes the viewshed based on the PDE coordinate system.…”

“…Although the horizontal coordinate D corresponds to uneven actual distance, the original literature on the PDERL algorithm has proved that in the D-E coordinate system, the e value between every two points on each polyline still changes linearly as the horizontal coordinate D changes [19]. column) into the D-E coordinate system and computes the visibility of each target point on the C2 column with the help of the reference polyline.…”

“…The first part is to calculate the In the D-E coordinate system, for any given direction D, if there are corresponding points on L R and L C , whose e values are assumed to be e R and e C, respectively, the difference value ∆E is calculated as shown in Equation ( 5), adapted from Ref. [19]. Let the visibility of the terrain corresponding to the point on current polyline L C be r C , the value of r C is shown in Equation ( 6), where zero means invisible and one means visible in the corresponding region.…”

“…In the implementation of the PDERL algorithm, let the horizontal coordinate D at the end of the subsection be d i and the ∆E value be ∆E i , the horizontal coordinate D at the beginning of the subsection be d i−1 and the ∆E value be ∆E i−1 , the slopes of L R and L C within the subsection be a i R and a i C , respectively, (obtained by referring to the reference polyline and the DEM, respectively), then the value of ∆E i is shown in Equation (7), adapted from Ref. [19]. The ∆E i value calculated in this way depends on the value of ∆E i−1 .…”

“…This paper deeply studies another algorithm proposed by Wu et al [19], based on a 'proximity-direction-elevation' (PDE) coordinate system and named the PDE spatial reference line (PDERL) algorithm. The PDERL algorithm stores some computational results in a data structure named the reference line, in order to present the exact elevation values of different positions with the greatest capability to block the LOS in all directions by accurate interpolation computation rather than an approximation to near grid point.…”