Abstract:With a support function as a tool, the estimations and representations of pointwise convex modulus in two-dimensional and three-dimensional Euclidean spaces are discussed, and the calculations of the pointwise convex modulus in the surface of ellipse and ellipsoid surface are carried out. It is shown that the smaller this spot, the stronger its convexity degree. The convex modulus describes an overall degree of convexity of the unit sphere in the space, which is very different from the degree of convexity at each point and which may have very great influence on the whole feature of the space. Therefore, the study of pointwise properties is very important. The pointwise constant geometry of the space can enhance the understanding of the nature of the space.