We introduce a flexible projection framework that is capable of modeling a wide variety of linear, nonlinear, and hand-tailored artistic projections with a single camera. This framework introduces a unified geometry for all of these types of projections using the concept of a flexible viewing volume. With a parametric representation of the viewing volume, we obtain the ability to create curvy volumes, curvy near and far clipping surfaces, and curvy projectors. Through a description of the framework's geometry, we illustrate its capabilities to recreate existing projections and reveal new projection variations. Further, we apply two techniques for rendering the framework's projections: ray casting, and a limited GPU based scanline algorithm that achieves real-time results.