Many materials, including biological tissue, attenuate light mostly by scattering. Because the scattered field is exquisitely sensitive to perturbations, control over the distribution of light after strong scattering is challenging. Though wavefront-shaping techniques enable arbitrary generation of light distributions within strongly scattering or turbid media in principle, the input wavefront necessary for the chosen light distribution is generally unknown. Using two different computational models, we demonstrate a technique called virtual aperture culling of the eigenmodes of a resonator (VACER), which uses weak spatial filtering mechanisms for noninvasive light focusing at arbitrary positions within turbid media. Compatibility with weak spatial filtering mechanisms is critical to innocuously focusing light within turbid media. One model represents an ideal system and could be physically implemented in some scenarios with digital optical phase conjugation, while the other model simulates phase conjugation via gain saturation, and its physical realization would operate fast enough to avoid the effects of speckle decorrelation in biological tissue. Modeling results establish that sound physical principles underlie VACER.