Ball与Sphere有什么区别

简而言之：ball 指球体，sphere专指球面。

定义：

A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. A sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball

A ball is the space inside a sphere.

sphere 定义为3维空间中到某一点距离相同的点的集合。

ball 要包含sphere内部的3维空间。如果同时包含sphere就称为closed ball，不包含则称为open ball.

sphere 可求面积

ball 既可求面积也可体积

在数学软件Mathematica中，称ball为实心球，称sphere为球壳。可以求sphere的面积，也可求ball的体积，但如果求sphere的体积会得到0，而求ball的面积会得到无穷大：