We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each of these extra conditions ensure additional geometric properties of a fitted conic, in particular, centre point position at the origin of coordinate system, axial alignment with coordinate axes, or, eventually, combination of both. All derived algorithms are accompanied by a discussion of the underlying algebra and optimisation issues, together with the implementation in MATLAB. Finally, we present examples on a sample dataset and offer possible use of the algorithms.

翻译：我们通过将附加条件纳入优化问题,对几何代数中的二次相近性进行了几处修改,以确保安装的二次曲线的更多几何特性,特别是坐标系统起源处的中心点位置,与坐标轴的轴轴对齐,或最终两者的结合。所有衍生的算法都伴随着对基本代数和优化问题的讨论,以及MATLAB的落实。最后,我们举例说明了一组抽样数据集,并提供了算法的可能用途。