The signed Chi-square measure for mapping

When interest extends beyond purely univariate considerations there is no fixed rule governing the ordering of spatial samples for mapping and statistical analysis. Ratios and numerical differences have conventionally been the basis for comparing samples. As both these are known to be influenced by variations in sample size, they are unsuitable for the comparison of demographic samples which vary greatly in size. Where necessary, the effect of sample size can be accommodated by a modified form of the X2 test statistic which is described in this paper

Testing implementations of Visvalingam's algorithm for line generalisation

There are a growing number of open source and commercial implementations of the Visvalingam algorithm for line generalisation. The algorithm provides scope for implementation-specific interpretations, with different outcomes. This is inevitable and sometimes necessary and, they do not necessarily imply that an implementation is flawed. The only restriction is that the output must not be so inconsistent with the intent of the algorithm that it becomes unusable. This paper provides some ideas, data and sample output to help users compare the output from their implementations with those produced by Visvalingam. This may help them ascertain whether some problems they may encounter appear to be specific to their implementation or whether they are a general feature of the algorithm. This paper assesses the utility and limitations of the Mapshaper options for Visvalingam’s algorithm. Similar, but not identical, depictions of coastlines are produced by Visvalingam’s implementation and by Mapshaper. However, the programs produce very dissimilar output for the rectangular Koch island, also known as the quadratic Koch island - Mapshaper’s output is unbalanced for both its Visvalingam and Douglas-Peucker options. This suggests that the problem, which is not immediately obvious, is in some function inherited by both options. Both programs produce near identical output when Mapshaper’s Visvalingam/weighted area option was compared using coastlines. This suggests that the problem arises from Mapshaper’s treatment of equal-valued metrics; this can be changed. Implementers and users may wish to use the data and methods given in this paper to test their own implementations if and when necessary

Sources of variability in cartographers' deconstruction of fractals : paper presented at the 18 November 1998 meeting of the British Cartographic Society's Design Group at the University of Glasgow

CISRG discussion paper ; 1

Bloch's function D for weighted effective areas : impact of tuning parameters

Abstract When Visvalingam’s algorithm was first presented, it was noted that it could be driven with any metric to suit different purposes, types of features and degrees of generalisation. It was illustrated with the concept of the effective area (EA). The intelligent application of metrics with and without weighting requires the prior segmentation of polylines with heterogeneous shapes into geometrically similar sections. Automatic line segmentation remains a research challenge. Meanwhile, different weighting functions have been used with different types of lines as noted in this paper. EA has a tendency to output spiky lines. Attempts have been made to give less weight to acute angles and favour obtuse angles. This yields visually more pleasing lines but has a tendency to chop elongated features, such as streams. Bloch’s function D (which implements the Visvalingam/ weighted area option in recent versions of Mapshaper) was chosen to investigate whether the parameter values could be tuned to improve the output. The tweaking of parameter values can give unexpected and unpredictable results. The results from a systematic approach to tweaking the parameters are presented here. These suggest that the chopping effect may be exacerbated by the use of inappropriate parameter values. By fine tuning Bloch’s function D, it was possible to derive pleasing smaller scale representations of convoluted coastlines with a complex network of creeks using under 5 percent of the original points. Although the output is not identical to manual generalisations of the same coastline, they may be acceptable (at this stage of research) for this type of coastline. Function D is not useful for generalising unsegmented coastlines, such as the 1: 50000 coastline of Humberside

Trends and concerns in digital cartography

CISRG discussion paper ;

Approximation, generalisation and deconstruction of planar curves

CISRG discussion paper ; 1

Cartography, geographical information systems and maps in perspective

CISRG discussion paper ;

Geometric data for testing implementations of point reduction algorithms : case study using Mapshaper v 0.2.28 and previous versions

There are several open source and commercial implementations of the Visvalingam algorithm for line generalisation. The algorithm provides scope for implementation-specific interpretations, with different outcomes. This is inevitable and sometimes necessary and, they do not imply that an implementation is flawed. The only restriction is that the output must not be so inconsistent with the intent of the algorithm that it becomes inappropriate. The aim of this paper is to place the algorithm within the literature, and demonstrate the value of the teragon-test for evaluating the appropriateness of implementations; Mapshaper v 0.2.28 and earlier versions are used for illustrative purposes. Data pertaining to natural features, such as coastlines, are insufficient for establishing whether deviations in output are significant. The teragon-test produced an unexpected loss of symmetry from both the Visvalingam and Douglas-Peucker options, making the tested versions unsuitable for some applications outside of cartography. This paper describes the causes, and discusses their implications. Mapshaper 0.3.17 passes the teragon test. Other developers and users should check their implementations using contrived geometric data, such as the teragon data provided in this paper, especially when the source code is not available. The teragon-test is also useful for evaluating other point reduction algorithms

Standardising basic spatial units : problems and prospects

CISRG discussion papers ;

Visualisation, VISC and scientific insight

CISRG discussion paper ;