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 computational optimisation issues. Finally, we present examples of use on a sample dataset and offer possible applications of the algorithms.

中文翻译：

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论圆锥曲线几何代数中的多条件圆锥拟合

我们通过将附加条件合并到优化问题中，对二次曲线的几何代数中的二次曲线拟合进行了几种修改。这些额外条件中的每一个都确保了拟合圆锥的额外几何特性，特别是坐标系原点的中心点位置、与坐标轴的轴向对齐，或者最终是两者的组合。所有派生算法都伴随着对基础代数和计算优化问题的讨论。最后，我们展示了在样本数据集上的使用示例，并提供了算法的可能应用。