volzo

Christopher Getschmann

mostly CC BY

Hatching, Hachures, and Contour Lines - Shaded Reliefs for Pen Plotter Maps

25 Apr 2025

In mapmaking, one of the oldest problems is finding a visually pleasing way to represent elevation using just two dimensions (or as Edward Tufte would call it: trying to escape flatland).

Websites like shadedrelief.com, shadedreliefarchive.com, and reliefshading.com list map examples for good terrain and bathymetry (ocean depth) representations, but (almost all) of the modern techniques are designed for pixel-based printing techniques1.

Historically it was necessary to engrave or etch dots and lines in a metal plate for printing. When working with pen plotters, lines are the geometry of choice so it makes sense to spend some time with the historical methods:

Contour Lines

Contour lines (lines representing an elevation slice, crossing the slope direction at a 90-degree angle) are probably the most common method of representing terrain on maps.

Hoover Dam plan. 1930

The closer to each other the contour lines run, the darker the map appears. Thus, any dark areas indicate the steep slopes, not a shadow which should create some perception of depth. To convey some sense of shading, hatching or hachure lines are used on top of contour lines, as in this tourist map of San Francisco:

The Chevalier Map of San Francisco

However, there is a notable improvement on the classic contour lines called illuminated contours or Tanaka contours2. Creating the visual effect of a relief by using a lighter color for raised line segments perpendicular to the direction of a simulated sun.

Source: Tweet by Daniel P. Huffmann

This can be combined with variations in line thickness and other tricks (papers linked below).

The illuminated contours effect works best with rather large geographical features, I had some issues with small and detailed segments:

Links:

Hachures

Hachures on hachure maps are hatching-like lines along the elevation direction first standardized in 1799. The most prominent example are the Swiss topographic maps, also called Dufour Maps:

Dufour Map, Sheet XVII

These hachures can be visually pleasing, as seen in this crop from the Admiralty Chart No 1854 Azores San Miguel, Published 1849: Admiralty Chart No 1854 Azores San Miguel, Published 1849

For complicated geographies, the hachures act like a grayscale dithering filter:

Admiralty Chart No 1870c Tenerife, Published 1848 Admiralty Chart No 1870c Tenerife, Published 1848

There are some proposals on how to automate these hand-drawn/carved hachure lines from historical copperplate prints for modern computer-generated maps:

Hatching & Other Techniques

Regular Hatching

Parallel lines in a fixed angle with varying distances. That’s what I used for my giant wall map: Sometimes historical maps do not use parallel lines but make use of shrinking outlines, especially for coastlines:

Combinations

Hatching lines in combination with contour lines may make sense as well, as presented by Marjan Sikora:

Streamline-based hatchings

Using a Digital Elevation Model the angle and magnitude of elevation changes (basically the steepness of a slope and its direction) can be treated like a vector flow field. This allows to orient free-flowing hatching lines to align with the shape of the surface. The example above has been generated with my implementation of the algorithm in the paper Creating Evenly-Spaced Streamlines of Arbitrary Density by Bruno Jobard and Wilfrid Lefer.

Very similar results have been achieved by Daniel Huffmann in his projects.

In addition to that, there is a large body of work from the computer graphics community regarding hatching techniques and pen-drawing styles for 3d objects, but this would be out of scope for a short overview.

Resources, Links, Recommendations

  1. The simplest way is just to load a Digital Elevation Model in a 3d modeling software such as Blender and render the scene to capture highlights and shadows. Example tutorial ↩

  2. Also called Kitiro-Tanaka method ↩