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We present ILoveSketch, a 3D curve sketching system that captures some of the affordances of pen and paper for professional designers, allowing them to iterate directly on concept 3D curve models. The system coherently integrates existing techniques of sketch-based interaction with a number of novel and enhanced features. Novel contributions of the system include automatic view rotation to improve curve sketchability, an axis widget for sketch surface selection, and implicitly inferred changes between sketching techniques. We also improve on a number of existing ideas such as a virtual sketchbook, simplified 2D and 3D view navigation, multi-stroke NURBS curve creation, and a cohesive gesture vocabulary. An evaluation by a professional designer shows the potential of our system for deployment within a real design process.