Mercator: Extreme pushes the boundaries of the web Mercator projection by visualizing the entire world map at incredibly high zoom levels, far beyond traditional map applications. It demonstrates the inherent distortion of Mercator as landmasses become increasingly stretched and warped, especially near the poles. The project uses custom tiling and rendering techniques to handle the immense detail required for such extreme zoom levels and allows users to interactively explore this unusual cartographic perspective.
The blog post entitled "Mercator: Extreme" by MrGris details an extended exploration and visualization of the Mercator projection, a cylindrical map projection method renowned for preserving angles and shapes, making it particularly suitable for navigation. The author meticulously demonstrates the inherent distortion of area that increases drastically with latitude as a consequence of this projection. While conventional Mercator maps typically truncate at latitudes around 85° North and South to mitigate the visual exaggeration of polar regions, MrGris pushes the boundaries of this representation by computationally extending the projection far beyond these conventional limits.
The post presents a series of images showcasing the ever-increasing distortion, depicting Greenland ballooning to improbable sizes, ultimately exceeding the apparent size of Jupiter in the projection. This visually striking exaggeration serves to highlight the mathematical nature of the projection and the exponential growth in apparent area as one approaches the poles. The author explicitly notes the theoretical limit of the Mercator projection existing at infinity, as complete representation of the poles is mathematically impossible within this projection system. The visualizations are accompanied by brief explanations of the underlying principles that cause this distortion, emphasizing the trade-off between preserving shapes and accurately representing areas. The project serves as a thought-provoking demonstration of the limitations inherent in any two-dimensional representation of a three-dimensional sphere and the specific distortions characteristic of the Mercator projection. The extreme visualizations, culminating in Greenland dwarfing Jupiter, offer a compelling and memorable illustration of the mathematical realities of mapping the Earth.
Summary of Comments ( 19 )
https://news.ycombinator.com/item?id=42783948
Hacker News users discuss the extreme Mercator projection, mostly focusing on its comedic distortion of landmasses at higher latitudes. Some commenters appreciate the project as a clear demonstration of how Mercator's cylindrical projection stretches areas away from the equator. Others highlight the educational value, contrasting it with the common misconception of Greenland's size relative to Africa. A few users suggest alternative visualizations, such as a globe or comparing the distorted areas to their true size on a map using different projections. One commenter notes the inherent difficulty in accurately representing a sphere on a flat surface, while another points out the project creator's other interesting work. There's also brief discussion of the historical context and usage of Mercator projections, including its suitability for navigation.
The Hacker News post "Mercator: Extreme" has generated a moderate amount of discussion, with several commenters focusing on the novelty and potential applications of the extreme Mercator projection demonstrated in the linked project.
One commenter expresses fascination with the projection, stating that they could "stare at this all day," and highlighting the surprising nature of how Greenland's shape changes as it approaches the edge of the projection. They then make a humorous connection to the game "Where in the World Is Carmen Sandiego?".
Another commenter discusses the usefulness of such projections for visualizing large datasets, particularly mentioning flight paths. They note that while standard Mercator heavily distorts areas at high latitudes, this extreme version provides a different perspective that could be valuable in specific contexts.
The creator of the project also participates in the discussion, responding to a question about the antimeridian cut. They clarify that the code handles the cut "implicitly" due to the mathematical nature of the projection and the use of complex numbers. They also explain how shapes that cross the antimeridian are handled seamlessly in their implementation. They further elaborate on the underlying mathematics, explaining how they achieved the smooth wrapping effect.
One commenter mentions a historical context, recalling a map they saw as a child that showed Alaska elongated in a similar fashion. This suggests the idea, though visually striking in its extreme form, isn't entirely new.
Another commenter points out a detail in the animation, noting how the distortion affects the apparent motion of a simulated plane as it crosses higher latitudes. This illustrates the impact of the projection on perceived movement and distance.
A discussion arises around the mathematical concept of infinity and its representation in the projection. One commenter humorously remarks about the "infinite Greenland" depicted, prompting another to explain how this visual infinity relates to the mathematics behind the projection.
Finally, there's a comment comparing this project to a previous project on Hacker News that explored similar concepts. This highlights the recurring interest in non-standard map projections and their visual and mathematical properties within the Hacker News community.
In summary, the comments section explores the novelty of the extreme Mercator projection, discusses its potential applications for visualization, clarifies some technical aspects of its implementation, and connects it to broader mathematical and historical contexts. The overall tone is one of curiosity and appreciation for the project.