Creating a Tissot’s Indicatrix in QGIS

The task of projecting, or unfolding the spherical Earth onto a flat map, is an age old problem in cartography. Projection almost always introduces distortion, most projections cannot preserve angles, areas and distances at the same time, they may be conformal (angle-preserving), equal-area (area-preserving) or equidistant (distance preserving) but not all at once. The only exception is a Globe, which preserves angles, areas and distances perfectly. Thus a projection is a compromise.

The choice of projection depends on a map’s use, scale and audience. Conformal projections, for example, are preferred for nautical charts or small scale maps because they locally preserve angles necessary for navigation and survey drawings. Equal-area projections are best suited for maps of broad continental region as they preserve the relative sizes of countries, seas and oceans and allow comparison between regions. Finally, there are hybrid projections that minimise the distortion by merging conformal and equal-area projections, these can be used to create visually pleasing maps of the entire Earth (for a guide to selecting a map projection see Fig. 9 in Jenny (2011), link below).

But how does one measure the degree and type of distortion in a map projection?

One elegant method was developed in the 1880s century by the French cartographer Monsieur Nicolas Auguste Tissot, the Tissot’s Indicatrix (or Tissot’s Ellipse). This mathematical contrivance consists of a grid of infinitely small circles that measures the degree and type of distortion caused by projection. While Monsieur Tissot’s approach is mathematical, involving infinity small circles, his technique can be approximated overlaying a regular grid of large circles and crosses to a map.

The Indicatrix Mapper plugin for QGIS by Ervin Wirth and Peter Kun creates a Tissot’s Indicatrix by adding a vector layer of circles and crosses in a gridded pattern on a map. The degree and type of distortion of the Tissot’s Indicatrix reveals the class of map projection as follows: –

  • If a projection is conformal, the area of circles and sizes of the crosses will change while the shapes of circles remain the same and intersection angle of the crosses will always meet at 90 degrees e.g. Mercator projection
  • If a projection is equal-area, the area of the circles will remain the same while the shape of the circles change and intersection angle of the crosses will not always meet at 90 degrees e.g. Mollweide projection or Hammer projection
  • If a projection preserves neither property, the area of the circles and their shape will change, and the intersection angle of the crosses will not always meet at 90 degrees e.g. Robinson

After adding the Indicatrix Mapper plugin to QGIS (menu Plugins – Manage and Install Plugins) first add a basemap using the OpenLayers plugin e.g. Bing Aerial layer, then click the Indicatrix Mapper icon and run the plugin using default settings. You can then select different projections (lower right in world icon QGIS) to see the effects of various protections on the Tissot Indicatrix. If the circles appear as squares after selecting a different projection, right click the Circles layer in the layers panel, then select the Rendering tab and deselect the Simplify geometry check box. Also, turn off the basemap layer when using different projections, unfortunately the OpenLayers plugin only supports Google Mercator projection (EPSG 3857). To create the basemap below, that can be displayed using different projections, I styled vector data downloaded from Natural Earth and OpenStreetMap.

Mercator

Mercator Projection – the area of the circles and size of the crosses increase towards the poles but their shape remains the same.

Mollweide

Mollweide Projection – the area of the circles remain the same but their shapes are distorted, the crosses do not always intersect at 90 degrees.

Robinson

Robinson Projection – both the area of the circles and intersection angle of the crosses circles vary.

It is important to note that a Tissot’s Indicatrix generated in QGIS is an approximation of mathematical ideal, we are not no longer dealing with infinity small circles. As a result, here will be some minor distortion visible towards the edge of a map independent of the projection used; notice that the circles in the Mercator projection nearest the poles are not quite symmetrical or the circles at the edge of the Mollweide projection do not appear to preserve area as they should. This anomalous distortion can be minimised by reducing the size and spacing of the circles and crosses created by the Indicatrix Mapper plugin. However, despite these limitations a Tissot’s Indicatrix elegantly reveals the distortion present. This is something to important to understand when when choosing a map projection.

References:

Jenny, B., 2012. Adaptive composite map projections [PDF]. Visualization and Computer Graphics, IEEE Transactions on, 18, 2575–2582.

ArcGIS REST API Connector Plugin for QGIS

ArcGIS REST Connector Plugin

Last year we described a command line method that adds ESRI REST layers in QGIS. Well, a team at the Geometa Lab in the University of Applied Sciences Rapperswil (HSR) Switzerland, have released a plugin for QGIS that adds ESRI REST layers via a GUI (Github page). The plugin is experimental so you will need to tick the box “Show also experimental plugins” in the settings panel of the “Plugins – Manage and Install Plugins” dialogue in order to add the plugin to QGIS. The following URLs lists numerous REST layers in the plugin’s GUI:

http://services.arcgisonline.com/arcgis/rest/services

http://basemap.nationalmap.gov/arcgis/rest/services

http://services.nationalmap.gov/arcgis/rest/services

Reference:

REST API Connector Plug-in Wiki Page

Create great looking hillshaded maps in QGIS

Wicklow-Topo-original

In this tutorial I will show you how to create a Hillshaded topographic map in QGIS. We will be using Shuttle Radar Topography Mission (SRTM) data, a near global Digital Elevation Model (DEM) collected in February 2000 aboard NASA’s Space Shuttle Endeavour (mission STS-99). The mission used a X-Band mapping radar to measure the Earth’s topography, built in collaboration with the U.S. Jet Propulsion Laboratory, the U.S. National Imagery and Mapping Agency (now the National Geospatial-Intelligence Agency), and the German and Italian space agencies.

The raw radar data has been continuously processed and improved since it was first collected. Countless artefacts have been painstakingly removed and areas of missing data have been filled using alternate data sources. The version we will be using is the 1 Arc-Second Global SRTM dataset, an enhanced 30 meter resolution DEM that was released last year. It is a substantial improvement over the 3 Arc-Second / 90 meter SRTM data previously available for Ireland. SRTM elevation data can be downloaded from the United States Geological Survey’s EarthExplorer website.

When first loaded into QGIS (via Add Raster Layer), the DEM is displayed as a rather uninformative black and white image.

Wicklow-Topo-blackwhite

It is therefore necessary to apply a suitable colour ramp that accentuates topography. While it is possible to create your own colour ramp, or use one of the colour ramps provided by QGIS, superior colour ramps can be downloaded using Etienne Tourigny’s Color Ramp Manager (Plugins – Manage and Install Plugins). After the plugin is added to QGIS, go to the Plugins menu again and choose the Colour Ramp Manager.

In the window that pops up, choose the full opt-city package and click check for update. The plugin will then download the cpt-city library, a collection of over a hundred cartographic gradients (version 2.15). After the package downloads, quit the dialogue.

Back in QGIS, right click the DEM layer to bring up the Layer Properties dialogue. In the Style tab, change the render type from single band grey to single band pseudocolor. Then click new color ramp and new color ramp again, choose the cpt-city color ramp to bring up the cpt-city dialogue. Click topography and choose the sd-a colour ramp. While this is an excellent colour ramp, I find its colours are a bit too strong for my liking.

Still in the Layer Properties dialogue, change the min and max values to match your DEM’s lowest and highest elevations values and click classify, this applies the new colour ramp. Next, change the brightness to 30 and lower the contrast and saturation to -20. Click OK to apply the new style and quit the Layer Properties dialogue.

Wicklow-Topo-noShade

Next we need to create a Hillshade layer from the DEM, a 3D like visual representation of topographic relief. This is achieved via the menu Raster – Analysis – DEM (Terrain models). There is one small catch, the hillshading algorithm assumes the DEM’s horizontal units are in meters (they are decimal degrees). We need to enter a scale correction factor of 111120 (in the Scale ratio vert. units to horiz. box). Once that is all done, select an output path to save the generated hillshade and click OK. Generating a hillshade may take up to a minute depending on the size of your DEM.

Wicklow-Topo-hillshade

After the hillshade is created, open its Layer properties dialogue. Change the min and max values to 125 and 255, increase its brightness to 45 and contrast to 20. Finally, switch the blending mode from normal to multiply. This allows the DEM beneath the hillshade to show though. Click OK to apply the new style.

If you followed these steps correctly you will have created a fine looking topographic map similar to the one below. It’s also possible to create contours but that’s a tutorial for another day.

Wicklow-Topo

Technical note:

There are two hillshading algorithms available in QGIS, one by Horne (1981) and another by Zevenbergen and Thorne (1987). Jones (1998) examined the quality of hillshading algorithms, he found the algorithm of Fleming and Ho€er (1979) is slightly superior to Horne’s (1981) algorithm. Zevenbergen and Thorne’s (1987) algorithm is a derivation of Fleming and Ho€er’s (1979) formula. QGIS uses Horne’s (1981) algorithm by default.

References:

Horn, B.K., 1981. Hill shading and the reflectance map. Proceedings of the IEEE, 69, 14–47.

Jones, K.H., 1998. A comparison of algorithms used to compute hill slope as a property of the DEM [PDF]. Computers & Geosciences, 24, 315–323.

Zevenbergen, L.W. & Thorne, C.R., 1987. Quantitative analysis of land surface topography. Earth surface processes and landforms, 12, 47–56.

Go2streetview plugin for QGIS

A very handy plugin for QGIS I use day to day is go2streetview by Enrico Ferreguti. The plugin adds an icon to the tool bar in QGIS and when selected I can click a road or street on a base map and a window will open that displays the Google Street or a Bing Maps Bird’s Eye view of the location. The camera’s direction and location is highlighted by a blue marker. I use the plugin when tracing boundaries of parks, open spaces and foot paths from aerial imagery. If the imagery is blurred or the view is obscured by trees, I click a point on a nearby street to see the location up close. The plugin works wherever Google Street view and Bing Birds Eye has coverage.

For example, in the screen-shot below notice there is a footpath leading to a bus shelter that’s not mapped by OpenStreetMap. I know where it is now, I will add it to my map.

Street View

Plugin: go2streetview

Google Map Style with “Shape Burst” effect in QGIS 2.3

Here’s a nice looking map I created using QGIS 2.3, the testing version of QGIS. I downloaded free OpenStreetMap data and I styled it to look just like Google Maps, as per instructions published by Anita Graser. I also outlined county boundaries using the new “Shape Burst” effect, which creates a pleasing graduated colour pattern that faithfully follows polygon outlines (it’s also applied to the Sea, though it’s quite subtle). I used Data Defined Properties to restrict the effect to all counties except Dublin City, this also created a Mask.

Lastly, there’s also a subtle “Coastal Vignette” effect, these are fine lines that trace the coastline and were typical of old style hand drawn maps. Must have taken a tremendous amount of patience. I developed a simple method of reproducing the effect and I’ll let you know how I did it in my next blog post. Oh and by the way, the scale relates to a map printed at A3 size.

 

New Online Beginners Course in QGIS 2.2

A US government funded education institution, the National Information Security and Geospatial Technologies Consortium (NISGTC), is offering a free online beginners course to QGIS 2.2 (GST 101 QGIS 2.2). The seven module course is based on the Introduction to GIS course run by Rick Smith with new course material and tutorials specific to QGIS added by Kurt Menke. The course is in beta form at this time with an official launch planed for August 2014 on GitHub, enrolment is open to all.

Here is the course introduction:

Welcome to the QGIS introductory GIS course.  Please note that this course shell is in beta.  We appreciate your willingness to evaluate our course material in preparation for publication in August 2014.  We are very excited that this new series of five complete GIS courses, all based on Open Source Software, will provide educators the curriculum and tools they need to adopt open source GIS software into their GIS programs.

We ask that you follow the sequence of modules presented in the Modules and complete the lab assignments one at a time.  You are welcome to make remarks on either in the discussion area for each module.  Please note that this is a self-paced, open enrollment, course without instructor support or presence.  We make this material available to the public for their own use.  We will publish the course officially on Github in August 2014.  Anyone is welcome to reuse any of the material at that time for their own courses, with attribution under Creative Commons BY license.

NISGTC: GST 101 QGIS 2.2. Course Enrolment Page

10 years of QGIS on Google Trends

Here is a graph showing how often people entered the search term “QGIS” into Google over the last 10 years. It was generated using Google Trends, a Google utility that displays trend graphs and basic regional statistics of search terms entered into the world’s most popular search engine.

QGIS on Google Trends

It’s also possible to compare search terms e.g. QGIS v’s MapInfo, QGIS v’s Microstation, QGIS v’s Geomedia and finally QGIS v’s ArcGIS.

The frequency of most GIS related search terms entered into Google, except “ArcGIS” and “QGIS”, have decreased considerably over the last 10 years. Only ArcGIS is entered into Google more often than QGIS nowadays, indeed ArcGIS has likely attained a monopoly market position. However, it is likely that QGIS will continue to gain ground on ArcGIS and desktop GIS may become a dichotomy of commercial and opensource software, a reaction to one companies’ market dominance.