We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse direction and tricircular moves in 2D and 3D, to explore complex visualisations of extraplanetary movements. These moves are studied in a plane setting. Then, adding increasing complexity, we explore them in a non planar setting (which is a closer model of the real situation). The exploration is followed by using these approaches for creating mathematical art in 2D and 3D printed objects, providing new ways of mathematical representations. Students' activities are organized around this exploration.

翻译：我们提出了二维和三维空间中轨迹的简单模型。初始示例模拟同向双圆周运动，其对应经典曲线（如外摆线等）。随后，我们探索反向双圆周运动以及二维与三维空间中的三圆周运动，以此研究行星外运动的复杂可视化方式。这些运动首先在平面场景中加以分析。进而，通过增加复杂度，我们将其拓展至非平面场景（更贴近真实情况的模型）。基于上述探索，我们利用这些方法开展二维与三维打印物体的数学艺术创作，提供了数学表达的新途径。围绕这一探索过程，我们设计了相关的学生实践活动。