Swept triangle wireframe

This problem started out with the question: How can you sweep a triangle through a circular path such that the point of the triangle points "out" at the top and sides but "in" at the bottom?

This requires us to select a function that gives the angle of the triangle relative to the angular position within the circle. The requirements give four fixed points which the function must hit but otherwise leaves it open. This particular model uses a linear piecewise connection between these points. Although the simplest possible solution to these conditions, it also seems to give the most aesthetic final product.

Two different wireframe spacings are provided.