Avoid repeated triangulation in multiple PiecewiseAffineTransform calls

I am trying to make a movie based on PiecewiseAffineTransform, warp for multiple timesteps. Individual frames are constructed as in e.g. as in https://scikit-image.org/docs/dev/auto_examples/transform/plot_piecewise_affine.html
but for example the phase of the sine wave would change between frames.
With the current implementation, it seems the estimate method runs a triangulation each time it is called. As the topology of the points and the source coordinates do not change between frames, is it possible to calculate the triangulation once and store it for re-use.
The reason would be efficiency, but also I imagine that changes in the triangulation pattern from frame to frame could result in flickering