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The angular resolution limits achievable for perfect ground-based high-altitude gamma-ray air shower detectors are investigated, to serve as benchmarks for the design of real detectors. A ‘perfect’ detector is assumed to accurately measure impact position, time and energy of all electromagnetic shower particles reaching the ground. The shower direction is determined from a likelihood fit to all measured particles, using parametrized likelihood functions. The impact of energy thresholds of the particle detector, of detection efficiency, of finite time and energy resolution and of spatial granularity is discussed.