HiXDraw: An Improved XDraw Algorithm Free of Chunk Distortion

Abstract

Viewshed analysis is of great interest to location optimization, environmental planning, ecology and tourism. There have been plenty of viewshed analysis methods which are generally time-consuming and among these methods, the XDraw algorithm is one of the fastest algorithms and has been widely adopted in various applications. Unfortunately, XDraw suffers from chunk distortion which greatly lowers the accuracy, which limits the application of XDraw to a certain extent. Previous works failed to remove chunk distortion because they are unaware of the underlying contribution relationship. In this paper, we propose HiXDraw—an improved XDraw algorithm free of chunk distortion. We first uncover the causation of chunk distortion from an innovative contributing perspective. Instead of recording LOS (line-of-sight) height, we use a new auxiliary grid to preserve contributing points. By preventing improper terrain data from contributing to determining the visibility, we significantly improve the accuracy of the outcome viewshed. The experimental results reveal that the error rate largely decreases by 65%. Given the same computing time, HiXDraw is more accurate than previous improvements in XDraw. To validate the removal of chunk distortion, we also present a pillar experiment.

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

“…algorithms, for example as in Zhu et al (2019), this study conducted 6 experiments with each of the three algorithms, on the three DEMs, at heights from 1 m to 5000 m from the ground (in 1 m intervals), with a radius of 10.77 km, at randomly selected locations, totaling 15,000 comparison experiments. We used a concept called time consumption ratio (R), similar to Zhu's approach (Zhu et al 2019), to evaluate the speed difference between PDERL, XDraw, and reference plane. Time consumption of PDERL, XDraw, and reference plane were defined as T PDERL , T XDraw , and T rp , respectively.…”

“…The speed performance of the PDERL algorithm is not very stable, particularly at a low height, but the overall difference in speed is not large, a little faster than half the speed of XDraw, and a little slower than half the speed of reference plane. Although we did not implement the method in Zhu et al (2019) we made a comparison based on their research. Their algorithm is 4.4 times as time-consuming as XDraw with limited accuracy improvement (Zhu et al 2019), while PDERL is at most 2.25 times as time-consuming as XDraw with completely accurate results.…”

“…Zhi et al (2011) proposed that the reference plane algorithm was flawed for topographic calculation in areas such as peaks and valleys, and they proposed a solution to this problem by recording the historic minimum visible elevation of each target point and comparing to the LOS height. Although its accuracy improved by 56.91%, the computation time increased by 9.34 times (Zhu et al 2019). Zhu et al (2019) proposed an algorithm called HiXDraw to limit the chunk distortion of XDraw by finding the most related contributing points of the target.…”

“…Although its accuracy improved by 56.91%, the computation time increased by 9.34 times (Zhu et al 2019). Zhu et al (2019) proposed an algorithm called HiXDraw to limit the chunk distortion of XDraw by finding the most related contributing points of the target. According to their research, this method achieved a 34.96% improvement in accuracy with 4.4 times the computation time, when compared with XDraw.…”

“…The three-dimensional geographic space, in which traditional basic non-parallel algorithms are always derived (e.g. Franklin et al 1994;Izraelevitz 2003;Qiang et al 2019;Wu 2001;Zhi et al 2011;Zhu et al 2019), leads to very concise position descriptions; however, perspective problems like viewshed analysis are complex and therefore the computational load can only be reduced by approximate calculation. If we use a coordinate system suitable for perspective, we can obtain an algorithm with both speed and accuracy.…”