We analyze loci of triangles centers over variants of two-well known triangle porisms: the bicentric family and the confocal family. Specifically, we evoke a more general version of Poncelet's closure theorem whereby individual sides can be made tangent to separate caustics. We show that despite a more complicated dynamic geometry, the locus of certain triangle centers and associated points remain conics and/or circles.

翻译：我们分析三角形中心的位置,而不是已知的双形三角形圆柱形的变体:双心家庭和组合家庭。具体地说,我们引用了更笼统的庞斯莱封闭理论版本,通过该理论,可以使个别方面切换为分开的苛刻。我们显示,尽管存在更复杂的动态几何,但某些三角形中心和相关点的位置仍然是锥形和/或圆形。