On spun-normal and twisted squares surfaces

Given a 3 manifold $M$ with torus boundary and an ideal triangulation, Yoshida and Tillmann give different methods to construct surfaces embedded in $M$ from ideal points of the deformation variety. Yoshida builds a surface from twisted squares, whereas Tillmann produces a spun-normal surface. We investigate the relation between the generated surfaces and extend a result of Tillmann's (that if the ideal point of the deformation variety corresponds to an ideal point of the character variety, then the generated spun-normal surface is detected by the character variety) to the generated twisted squares surfaces.