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Mesh Reconstruction assignment for Geometry Processing course

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I'm trying to understand the section in the handout called "Gradients on a regular grid". Suppose we have a $4\times4$ matrix. $D^x$ will have a size of $12 \times 16$....

![image](https://user-images.githubusercontent.com/35909284/94304141-dcb4dc00-ff23-11ea-9aeb-6abd4460b0bf.png) Does anybody know what x refers to in the first question? Thanks!