As an addition to proper points of the real plane, we introduce a representation of improper points, i.e. points at infinity, in terms of Geometric Algebra for Conics (GAC) and offer possible use of both types of points. More precisely, we present two algorithms fitting a conic to a dataset with a certain number of points lying on the conic precisely, referred to as the waypoints. Furthermore, we consider inclusion of one or two improper waypoints, which leads to the asymptotic directions of the fitted conic. The number of used waypoints may be up to four and we classify all the cases.

中文翻译：

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二次曲线几何代数中给定正确和错误路点的二次曲线拟合算法

作为真实平面的适当点的补充，我们引入了不适当点的表示，即无穷远点，根据圆锥曲线几何代数（GAC），并提供了两种类型点的可能使用。更准确地说，我们提出了两种将圆锥曲线拟合到数据集的算法，其中一定数量的点精确地位于圆锥曲线上，称为路径点。此外，我们考虑包含一两个不正确的航路点，这会导致拟合二次曲线的渐近方向。使用的航点数量最多可达四个，我们对所有情况进行分类。