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this slide could be made more clearer to show that the origin maps back to origin is a important premise for a linear map.

I overlooked it easily


What are some use cases for nonlinear maps in computer graphics? Are we going to use them in this course? If so, what for?


Is there a term for a map that satisfies the conditions of a linear map, but does not keep the origin fixed? If so, are they used for anything?


Since linear maps are themselves functions, can we treat any of them as vectors, and if so, are there any useful insights to be gained from this?


If the origin is fixed, how can a linear map represent a translation?


What exactly are the lines being preserved? In this case it seems like it would be the edge of the pentagon, but what if we were mapping a plane without defined edges?


What are the constraints from linear translation if the origin will be fixed?


Are nonlinear maps ever used in computer graphics applications and if so, what are the specific scenarios in which it would be advantageous to using those over linear maps?


where and when would nonlinear mappings be useful?


So visually, as it indicates in the diagram, would that indicate that linear maps really only rotate the figure or project it onto a plane?