首先我们必须弄懂几个基本的概念：
singularity: In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points.
A scalar field is a continuous function 
, where 
is a connected domain in 
, 
. The image of 
embedded in 
space, i.e.
is called a hypersurface. When k = 2, 
is called a height field. A common example of a height field is a terrain surface, where the domain is 
and is specified by elevation values at discrete sample points.
A manifold surface with boundary 
is a subset of Euclidean space , for some 
, such that the neighbourhood of each point of is homeomorphic to either the open disc, or to the half-disc (which is obtained by intersecting the open disc with the closed half-plane of the positive x coordinates
simplicial meshes : apart from the wavelet-based methods, can be represented as simplicial meshes, i.e. meshes of triangles or tetrahedra
critical points: points at which the topology of the level sets changes
写着写着，发现自己对critical point还是没有理解，看看再写了