在本論文中,我們考慮以其頂點角度之序列,來重建最小面積直角多邊形的問題。我們提出以下兩個結果: 1. 研究n 點的最小面積直角多邊形的性質,並以此性質將之分為四類,以及算出其中三類多邊形的個數。 2. 給定一直角凸多邊形之角度序列S,我們提出一計算其最小面積之公式。;In this thesis, we consider the problem of reconstructing rectilinear polygons with minimum area, from a sequence of angles of vertices. We provide two results:
1. Studying properties of n-vertex rectilinear polygons with minimum area, classifying those polygons into four types by these properties, and computing the number of polygons in each of three of them.
2. Given a sequence S of angles of a monotone rectilinear polygon, we propose a formula to compute the minimum of area of monotone rectilinear polygons with turn sequence S.