Given an n-sided polygon P on the plane with \(n \ge 4\), a quadrangulation of P is a geometric plane graph such that the boundary of the outer face is P and that each finite face is quadrilateral. Clearly, P is quadrangulatable (i.e., admits a quadrangulation) only if n is even, but there is a non-quadrangulatable even-sided polygon. Ramaswami et al. [Comp Geom 9:257–276, (1998)] proved that every n-sided polygon P with \(n \ge 4\) even admits a quadrangulation with at most \(\lfloor \frac{n-2}{4} \rfloor\) Steiner points, where a Steiner point for P is an auxiliary point which can be put in any position in the interior of P. In this paper, introducing the notion of the spirality of P to control a structure of P (independent of n), we estimate the number of Steiner points to quadrangulate P.

给定一个平面上的n边多边形P与\(n \ge 4\)，P的四边形是一个几何平面图，使得外表面的边界是P并且每个有限面都是四边形。显然，只有当n是偶数时，P才是可四边形的（即，允许四边形），但存在不可四边形的偶数边多边形。拉马斯瓦米等人。[Comp Geom 9:257–276, (1998)] 证明了每个具有\(n \ge 4\) 的n边多边形P甚至承认最多为\(\lfloor \frac{n-2}{4 } \rfloor\) Steiner 点，其中 Steiner 点为P是一个辅助点，可以放在P内部的任何位置。在本文中，引入的螺旋形的概念P来控制的结构P（独立Ñ），我们估计的斯坦纳点的数目quadrangulate  P。