The development of novel trapping potentials for degenerate quantum gases has been an important factor driving experimental progress in the field. The introduction of spatial light modulators (SLMs) into quantum gas laboratories means that a range of configurable geometries are now possible. Here we demonstrate the production of arbitrary and dynamic high-resolution traps for Bose-Einstein condensates (BECs) using a (1200 x 1920) pixel digital-micromirror device (DMD) and commercially available microscope objectives. Direct imaging of the DMD provides significant advantages over phase-based SLMs, while still providing high resolution projected patterns. We find that atoms confined in a hybrid optical/magnetic or all-optical potential can be patterned using repulsive blue- detuned (532 nm) light with 630(10) nm full-width at half-maximum (FWHM) resolution, while imaging at 780 nm similarly achieves 960(80) nm resolution FWHM, within 5% and 8% of the diffraction limit respectively. This performance is > 7 times improved over previously reported DMD trapping. The result is near arbitrary control of the atomic distribution over the spatial extent of the BEC trapping volume. Furthermore, we produce time-averaged potentials with the DMD, demonstrating the ability to produce multiple grayscale levels with minimal heating of the atomic cloud. These techniques, along with the high level of dynamic control afforded by DMDs, will enable the realization and control of diverse optical potentials for superfluid dynamics and atomtronics applications with quantum gases.