EverybodyLovesSketch, a gesture-based 3D curve sketching system for rapid ideation and visualization of 3D forms, aimed at a broad audience. We first analyze traditional perspective drawing in professional practice. We then design a system built upon the paradigm of ILoveSketch, a 3D curve drawing system for design professionals. The new system incorporates many interaction aspects of perspective drawing with judicious automation to enable novices with no perspective training to proficiently create 3D curve sketches. EverybodyLovesSketch supports a number of novel interactions: tick-based sketch plane selection, single view definition of arbitrary extrusion vectors, multiple extruded surface sketching, copy-and-project of 3D curves, freeform surface sketching, and an interactive perspective grid. Finally, we present a study involving 49 high school students (with no formal artistic training) who each learned and used the system over 11 days, which provides detailed insights into the popularity, power and usability of the various techniques, and shows our system to be easily learnt and effectively used, with broad appeal.