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In the real world, there are many places there it is not differentiable, from table edges to hairs. How will computer graphics handle that?


Does the gradient remain consistent when we change the coordinate system or reproject to different bases?


Is it possible to approximate functions that are not differentiable to handle the problem?


How are gradients and directional derivatives calculated in coordinate systems that are not orthonormal?


Given that many functions have points or lines that are not differentiable, how do we deal with that in functions and algorithms? Is there any way, or do we simply restrict the domain?


When trying to model an edge, would computer graphics just make a curve as small as possible? In that case, it would still be differentiable right?


If there is a not differentiable component in computer graphics, can we replace it with a differentiable component