1) hyperbolic circumscribed polygon
双曲线外切多边形
1.
Using the fixed value method of directed areas, we research the relationship between two kinds of triangles in hyperbolic circumscribed polygons thoroughly.
利用有向面积定值法,对双曲线外切多边形中对角线三角形和切点线三角形之间的关系进行研究。
2) second-order curves circumscribed polygons with 2n-sides
二次曲线外切2n边形
1.
We obtain some fixed value theorems for directed areas in second-order curves circumscribed polygons with 2n-sides,and thus deduce some concurrent results,including the famous Brianchon theorems for second-order curves circumscribed hexagons and quadrilaterals easily.
利用有向面积方法,对二次曲线外切2n边形(n≥2)进行研究,得到二次曲线外切2n边形(n≥2)中有向面积的几个定值定理及其推论,从而把射影几何中著名的Brianchon定理推广到二次曲线外切2n边形的情形。
4) parabolic circumscribed polygon
抛物线外切多边形
1.
Using fixed value method of directed areas,we research the relationship between two kinds of triangles in parabolic circumscribed polygons thoroughly.
利用有向面积定值法,对抛物线外切多边形中的对角线三角形和切点三角形之间的关系进行研究,得到抛物类二次曲线外切n边形(n≥4)中有向面积的一个定值定理,并据此推出抛物线外切多边形中三线共点的点多达n(n-3)个,以及射影几何中著名的Brianchon定理等结论。
5) tangent polygon
切线多边形
1.
G~2-continuous cubic algebraic curve with the given tangent polygon;
与给定切线多边形相切的G~2连续的三次代数曲线
2.
Cubic Bézier spline curve with given tangent polygon;
与给定切线多边形相切的3次Bézier样条曲线
3.
Trigonometric spline curve with given tangent polygon;
与给定切线多边形相切的三角样条曲线
6) polygonal curves
多边形曲线
1.
The algorithm consists of the following parts: Firstly,the contour points of polygonal curves are extracted by an edge tracking technique,then an affine-invariant descriptor is computed from the extracted contour points by the ICA.
首先采用边缘跟踪算法获取矢量图形的轮廓曲线坐标;然后对坐标数据进行独立元分析处理,以获取仿射不变描述子,根据提取的仿射不变描述子生成与之正交的水印,并将水印加性嵌入到不变描述子中;最后通过上述过程的逆过程恢复出嵌有水印的多边形曲线。
补充资料:凹多边形
Image:11534686683212413.jpg
把一个各边不自交的多边形任意一边向两方无限延长成为一直线,如果多边形的其他各边不在此直线的同旁,那么这个多边形就叫做凹多边形。
凹多边形的内角和的解,其实我们可以通过(n-2)·180来计算。实际上是把大于平角的角划分为两个角(如图)
说明:补充资料仅用于学习参考,请勿用于其它任何用途。