We present a theory which predicts when the locus of a triangle center is an ellipse over a Poncelet family of triangles: this happens if the triangle center is a fixed affine combination of barycenter, circumcenter, and a third center which remains stationary over the family. We verify the theory works for the confocal and "with incircle" Poncelet families. For the confocal case, we also derive conditions under which a locus degenerates to a segment or is a circle. We show a locus turning number is either plus or minus 3 and predict its movement monotonicity with respect to vertices of the family.

翻译：我们提出一个理论来预测三角中心的中心是庞塞莱三角族的椭圆时:如果三角中心是一个固定的金方、环中和第三个中心组合,而第三个中心对家庭来说仍然是固定的。我们验证了该理论对于圆和“与无环”庞塞莱家庭的作用。对于这一组合,我们也得出一个圆点变成一个段或圆形的条件。我们显示一个圆点转数是加或减3,并预测其运动对于家庭脊椎的单一性。