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The statement: transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.
What is 3D to 2D projection?
A three-dimensional (3D) object is displayed on a two-dimensional (2D) surface using a 3D projection, also known as a graphic projection. In order to project a complex object for viewing capability on a simpler plane, these projections rely on visual perspective and aspect analysis.
The fundamental method is: u = x / z; v = y / z; if you're converting from world-space (x, y, z) coordinates to screen-space (u, v) coordinates. Before applying the projection matrix, transform (x, y, z) by the view matrix if the camera is not positioned at the origin.
Hence, the statement transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.
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