Oblique orthographic projection: terrain without perspective

When we look at a map, we usually take it for granted that "it just looks like that". But behind every cartographic representation there is always a choice: the projection.

What is a map projection?

In simple terms, a map projection is the way we transfer the curved surface of the Earth onto a flat plane. The Earth, or any other spherical or ellipsoidal surface, cannot be represented on a flat surface without introducing some type of distortion. These distortions affect shape, area, distance, and direction: each projection chooses what to preserve and what to sacrifice.

Once we have built our map — meaning we have chosen a projection and drawn the shapes on a plane — we can think of it as a two-dimensional drawing, as if it were printed on a virtual drawing sheet.

From flat map to 3D model

When I create one of my 3D maps, I start exactly from this sheet: the flat map. If I want to give relief to the terrain, I extrude the various elements based on digital elevation data. This means that I assign an elevation to each point on the map and raise it along a direction perpendicular to the drawing plane. It's as if a small "pillar" rises upwards from every point on the map.

At this stage, I have a three-dimensional representation of the terrain: mountains, valleys, and plains emerge from the surface.

Now: from where do we observe?

This is where the question of orthographic projection comes into play.

Imagine observing this 3D model from very, very far away. So far that the viewing rays are practically parallel to each other: it would be like looking at the Earth from the Moon or from a distant spacecraft. There is no perspective: objects do not appear smaller if they are far, nor larger if they are close. This produces what is called a vertical orthographic projection (top-down view).

If instead we tilt the model plane — that is, we tilt the map while keeping the viewing rays parallel — we obtain an oblique orthographic projection: a "tilted top-down" view that allows us to simultaneously visualize both the horizontal distribution and the elevation of the terrain, without introducing perspective deformations. This is a particularly effective solution for representing terrain in a readable and geometrically consistent way.

To achieve a view closer to how we naturally perceive the landscape, during rendering I use a virtual camera set with a focal length equivalent to 50 mm, which approximately simulates the human eye's field of view. In this case, we enter the realm of perspective views: nearby objects appear larger, parallel lines converge toward vanishing points, and depth is perceived naturally, resulting in a more immersive and "photographic" effect.

The advantages of oblique orthographic projection

This type of view has very specific characteristics:

• Proportions are preserved: nearby and distant mountains appear at their correct size.
• No perspective distortion: a tall mountain in the distance does not appear "small" just because it is far away.
• Shapes remain accurate: mountain profiles, valleys, and ridges retain their true geometries.

For cartography — especially for artistic cartography and panoramic models — this projection allows for very clear and accurate representations of terrain, avoiding the "dramatic" effects that can often distort the perception of distances and elevations.

But it’s not a natural view

There is, of course, a trade-off: oblique orthographic projection doesn’t correspond to how we perceive the landscape in real life.

Our eyes observe the world in perspective: distance makes objects appear smaller, parallel lines converge toward the horizon, and distant reliefs visually compress. All these visual cues help our brain build the perception of depth and distance.

Oblique orthographic projection omits this perspective component, favoring instead a geometrically rigorous representation where sizes and shapes remain constant regardless of their position in the field of view.

The diagram below illustrates the difference between perspective projection (left) and orthographic projection (right). In perspective view, the viewing rays start from a finite observation point and diverge, causing scale distortions as objects move farther away. In orthographic projection, instead, the rays are parallel: object sizes remain constant, regardless of distance.

However, when looking at the sample images I generated and included in this article, I must admit I am still somewhat torn about which approach to favor in my future work. The choice largely depends on the scale and subject of the map: for wide-scale representations, such as the Dolomites map, oblique orthographic projection allows consistent proportions and shapes across the entire map, avoiding typical perspective deformations. Conversely, for more focused subjects concentrated on a single mountain group — such as the Bernese Alps, which I am currently working on and which are shown in the images in this article — using a perspective view can produce a more natural, immersive, and, in some ways, more “photographic” effect.

In conclusion

Oblique orthographic projection is an extremely effective tool for anyone working with relief, aiming to produce clear, legible, and faithful representations of terrain morphology.

Perspective views, on the other hand, while introducing unavoidable geometric distortions, offer a visual result much closer to our natural perception and may be particularly suitable in certain contexts — especially when emphasizing the volume and depth of a single mountain group.

In the end, there is no absolute choice: every cartographic project may require a different approach, and I will likely continue to alternate between both solutions depending on the type of map I am creating.