4.8.30. Orthogonal projection

Maps are based on orthogonal (parallel) projections where the projecting rays are perpendicular to the line on the ground.

Orthogonal projection refers to a method used in creating maps where the lines or rays representing the objects on the ground are drawn at right angles (90 degrees) to the surface of the Earth. This technique allows for a flat representation of the surface, making it easier to measure distances and areas on the map. Unlike perspective projections, which can distort the image based on viewing angle, orthogonal projections provide a uniform scale throughout the map.

Imagine standing directly above a square piece of paper and looking straight down at it. All the lines you draw from your eyes straight down to the paper form right angles with the surface of the paper. This is similar to how orthogonal projections work, ensuring that the distances on the paper accurately represent the distances on the ground.

The advantage of this projection is that the distances, angles or areas on the plane are independent of the elevation differences of the objects, and these measurements compare well with the actual ground.

One of the significant benefits of orthogonal projection is that it eliminates the distortions caused by changes in height or elevation of objects. When creating a map in this way, measurements for distances, angles, and areas remain consistent regardless of how tall or short the objects are. This feature is crucial for accurate mapping as it allows the information on the map to correlate closely with real-world measurements.

Think of a flat drawing of a city skyline made from above. While high-rise buildings and trees have different heights, the map doesn’t show those elevations but instead provides an accurate layout of where each building is positioned, just like an orthogonal projection ensures everything is in the right place without the influence of height.

In contrast to perspective projections, where objects appear smaller at greater distances, orthogonal projections maintain the same scale for all objects, preventing distortion.

Unlike perspective projections, which can make objects appear smaller as they are further away from the viewer, orthogonal projections maintain a consistent size for all objects regardless of their position relative to the viewer. This lack of distortion is particularly important for tasks that require precise measurements such as construction planning and land surveys.

Imagine looking at a photograph of a street taken with a regular camera; objects further away from the camera appear smaller compared to those up close. In contrast, if you laid out a diagram of that street where every object is marked without changing the size based on distance, you've created something akin to an orthogonal projection. Everything looks accurate and proportionate irrespective of how far away they are from the ‘camera’ or drawing perspective.

Since the orthogonal projection produces a uniform scale, it can be effectively used as an alternate to a map.

Due to its ability to create consistent scale without distortion, orthogonal projection maps serve as reliable substitutes for traditional maps. These projections are essential in fields such as urban planning, architecture, and engineering, where precise measurements are critical and can lead to informed decision-making and effective design.

Consider an architect who relies on blueprints to design a building. These blueprints are typically orthogonal projections, ensuring that all dimensions are accurate and can be translated into real-life measurements without confusion. Just like how blueprints guide the construction process, orthogonal projections enable accurate mapping of land and features.

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