True2Form is a sketch-based modeling system that reconstructs 3D curves from typical design sketches. Our approach to infer 3D form from 2D drawings is a novel mathematical framework of insights derived from perception and design literature. We note that designers favor viewpoints that maximally reveal 3D shape information, and strategically sketch descriptive curves that convey intrinsic shape properties, such as curvature, symmetry, or parallelism. Studies indicate that viewers apply these properties selectively to envision a globally consistent 3D shape. We mimic this selective regularization algorithmically, by progressively detecting and enforcing applicable properties, accounting for their global impact on an evolving 3D curve network. Balancing regularity enforcement against sketch fidelity at each step allows us to correct for inaccuracy inherent in free-hand sketching. We perceptually validate our approach by showing agreement between our algorithm and viewers in selecting applicable regularities. We further evaluate our solution by: reconstructing a range of 3D models from diversely sourced sketches; comparisons to prior art; and visual comparison to both ground-truth and 3D reconstructions by designers.