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Coming back to this slide after the lecture, perhaps a "good" mesh is not only approximating the shape well but also providing some desired features for certain tasks (i.e. isotropic mesh). In that case, can you give us more instances in which we want the meshes to have extra features in addition to approximating well?


@hanliny Yes. This paper is a terrific place to start: What is a Good Linear Element?


Two slides after this, it is mentioned that long and skinny triangles are generally considered to be bad. In the mesh on this slide, are the long and skinny triangles good enough, or would regular and small triangles work even better here? Is there a situation where the long and skinny triangles are ever strictly better to use?


@ericchan It's a trade off: do you want to use a small number of triangles to get good approximation of shape, but not necessarily get elements with good angles (i.e., close to 60 degrees)? Or do you want to have better angles but at the cost of more triangles? Can't have both!


@ericchan Also, if you want a deeper discussion of this issue, see What is a Good Linear Element?