In Virtual Reality, immersive systems such as the CAVE provide an important tool for the collaborative exploration of large 3D data. Unlike head-mounted displays, these systems are often only partially immersive due to space, access, or cost constraints. The resulting loss of visual information becomes a major obstacle for critical tasks that need to utilize the users' entire field of vision. We have developed a conformal visualization technique that establishes a conformal mapping between the full 360° field of view and the display geometry of a given visualization system. The mapping is provably angle-preserving and has the desirable property of preserving shapes locally, which is important for identifying shape-based features in the visual data. We apply the conformal visualization to both forward and backward rendering pipelines in a variety of retargeting scenarios, including CAVEs and angled arrangements of flat panel displays. In contrast to image-based retargeting approaches, our technique constructs accurate stereoscopic images that are free of resampling artifacts. Our user study shows that on the visual polyp detection task in Immersive Virtual Colonoscopy, conformal visualization leads to improved sensitivity at comparable examination times against the traditional rendering approach. We also develop a novel user interface based on the interactive recreation of the conformal mapping and the real-time regeneration of the view direction correspondence.