We propose here a quasiperiodic structure whose reciprocal space is tailored to achieve wavelength and direction selective scattering and corresponding trapping. Reciprocal space of such structures contains belts of Bragg peaks which would allow us to fully scatter the normally incident light into directions which are trapped by total internal reflection inside the slab. We could verify the expected direction of scattered waves and trapping of the quasiperiodic structure using CST studio suite. We used planewave incidence vertically on the scattering volume with open boundaries on at the top and bottom and mirror boundaries on other sides. This allows to represent a continuous film of such material. We showed nearly 85% trapping of incident light power in numerical simulation at designed wavelength for the refractive index contrast of 1.58/1.48. The approach can be utilized to make transparent detectors and displays.