We introduce Skippy, a novel algorithm for 3D interactive curve modeling from a single view. While positing curves in space can be a tedious task, our rapid sketching algorithm allows users to draw curves in and around existing geometry in a controllable manner. The key insight behind our system is to automatically infer the 3D curve coordinates by enumerating a large set of potential curve trajectories. More specifically, we partition 2D strokes into continuous segments that land both on and off the geometry, duplicating segments that could be placed in front or behind, to form a directed graph. We use distance fields to estimate 3D coordinates for our curve segments and solve for an optimally smooth path that follows the curvature of the scene geometry while avoiding intersections. Using our curve design framework we present a collection of novel editing operations allowing artists to rapidly explore and refine the combinatorial space of solutions. Furthermore, we include the quick placement of transient geometry to aid in guiding the 3D curve. Finally we demonstrate our interactive design curve system on a variety of applications including geometric modeling, and camera motion path planning.