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I understand that a perspective view is essentially a type of projection. Is it possible to create projection definitions for a typical GIS system that will mimic a perspective view from a particular location? If so, how feasible would it be to use common 2D GIS tools to create perspective renderings of data, similar to what can be achieved in 3D tools such as Arc Scene and Google Earth?

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Perspective isn't just a "type" of projection to be "mimiced": it is a projection. E.g., ArcGIS supports it (but note that the illustration on its help page is terrible). So all you have to do is tell your GIS to use an aspect of this projection. ("Aspects" vary by how much of the earth they show, the angle they look at it from, and where the viewpoint is located in 3D.)

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