| 1. | The convex decomposition of arbitrary planar polygon
任意平面多边形的凸分解。 |
| 2. | 3 ) locally modifiable morph of planar polygons : this paper presents a method for morphing planar polygons via discrete curvature interpolation
3 )可局部修改的平面多边形的变形：提出了平面多边形的离散曲率插值变形方法。 |
| 3. | A new algorithm is presented for recognizing planar objects from a line drawing under axonometric and perspective projections based on principle of homograph
基于类似形的定义给出了在透视投影下平面多边形为类似形的识别算法。 |
| 4. | 2 ) intersection - free morph of planar polygons : this paper presents a shape feature based and triangulations embedded method for morphing planar polygons
2 )可避免自交的平面多边形的变形：提出了基于形状特征的嵌入网格的平面多边形变形方法。 |
| 5. | As to simple concave polygons or complicated planar polygons with holes , they must be decomposed to the collection of triangular facets or arbitrary convex polygons to satisfy the requirement of succeeding graphic operations
对于简单凹多边形或有内孔的复杂平面多边形，需要将它们剖分成三角面片的集合或任意凸多边形的集合。 |
| 6. | The polygon morphing was investigated , and a morphing method was proposed , in which the polygon is deformed by interpolating the rotation angles and rotation matrices of their corresponding edge vectors
摘要研究平面多边形的变形问题，提出了一种通过插值边向量间旋转角度及旋转矩阵的变形方法，较好地克服了顶点线性插值法引起的多边形边长变化不均匀的萎缩现象。 |
| 7. | Once a region of the line drawing and a surface of the planar object are homographs , the adjacent surfaces are following to be analyzed . repeat this processing until all surfaces of the planar object have been examined
任何平面立体都是若干个平面多边形围成的，平面多边形的特性能惟一确定平面立体的特性，通过对平面多边形的识别可以达到对整个平面立体的识别。 |
| 8. | Then , studies and improves some basic algorithms , including determining orientation of planar polygon , determining point inclusion of polygon , determining relationship of location between contours in the same plane , extracting skeleton of contour , reducing the data for contours
研究并改进了一些轮廓线相关的基础算法，包括平面多边形的方向判别、点在多边形内外位置关系判别、同平面内两个多边形间的相互位置关系判别、轮廓多边形的特征骨架计算、轮廓线数据的精简。 |
| 9. | We introduce five topological characteristics and geometry characteristics that are invariant under projective transformation specially perspective projection . the definition of homograph is given by means of these characteristics , and then the recognizing method of the homograph is proposed according to the definition of homograph
接着，根据透视投影不变性提出了5个用来描述多边形形状的拓扑特征和几何特征，这些特征在透视投影下是不变的，以这些特征给出了在透视投影下平面多边形为类似形的定义。 |
| 10. | After deeply studying current relative algorithms , and adopting the ideas of advanced decomposition algorithms , a convex decomposition algorithm for arbitrary planar polygons is put forward in the dissertation , which is based on the algorithm of nearest bridging and the ideas of second bridging and loop division
本文通过对国内外相关算法的深入研究，借鉴先进剖分算法的思想，提出了基于环分割的任意平面多边形的凸分解算法，包括最近搭桥算法、二次搭桥思想和环分割思想。 |
