The eccentric pie chart, a generalization of the traditional pie chart is introduced. An arbitrary point is fixed within the circle, and rays are drawn from it. A sector is bounded by a pair of neighboring rays and the arc between them. Eccentric pie charts have the potential of visualizing multiple sets of data, especially for small numbers of items/features. The calculations of the area-proportional diagram are based on well-known equations in coordinate geometry. The resulting system of polynomial and trigonometric equations can be approximated by a fully polynomial system, once the non-polynomial functions are approximated by their Taylor series written up to the first few terms. The roots of the polynomial system have been found by the homotopy continuation method, then used as starting points of a Newton iteration for the original (non-polynomial) system. The method is illustrated on a special pie-cutting problem.

中文翻译：

---

古怪的饼图和不寻常的饼图

偏心饼图是对传统饼图的概括介绍。任意点固定在圆内，并从中绘制射线。一个扇区以一对相邻的射线和它们之间的弧为界。偏心饼图具有可视化多组数据的潜力，特别是对于少量项目/特征。面积比例图的计算基于坐标几何中众所周知的方程。一旦非多项式函数通过它们的泰勒级数来近似，那么生成的多项式和三角方程系统就可以通过一个完全多项式系统来近似。多项式系统的根已经通过同伦延拓法找到，然后用作原始（非多项式）系统的牛顿迭代的起点。该方法在一个特殊的切饼问题上进行了说明。