Читать книгу Computer Aided Design and Manufacturing - Zhuming Bi - Страница 60

Objects in the physical world are solid. A solid object consists of solid elements and the process of adding, merging, uniting, or deleting solid elements in a solid object is commonly called Euler operation. To sustain a valid solid object, the second condition in the Euler–Poincare Law, which is usually called the Euler formula (F − E + V = 2), must be satisfied. This leads to the following features of a solid object:

1 Each vertex must have at least three edges to meet together

2 Each edge must be shared by two and only two faces.

3 Any face must be homomorphic to a disk with no holes; it is simply connected and bounded by a single ring of edges.

4 A solid must be simply connected with no through hole.