Portable and wearable miniaturized spectrometers play a crucial role in various fields. In this paper, we present a method for simultaneously realizing high-accuracy direction measurement and high-resolution computational spectral reconstruction based on the angle sensitivity of conventional photonic crystals (PCs), wherein an optical filter array is composed of multiple one-dimensional PCs. The high-angle sensitivity of PCs results in angle-dependent optical spectra. When these spectra with different angles are used to reconstruct the target spectra in an unknown direction and the interval between adjacent angles is sufficiently small, the accurate direction of the target can be automatically identified. Moreover, the computational spectra still have high resolution over a wide range of incidences. The computational spectra under arbitrary polarizations can also be recognized based on the polarization dependence of the PCs at an oblique incidence. Our research results are significant for engineering a new miniaturized comprehensive computational spectrometer with target-direction perception and omnidirectional spectral reconstruction abilities.