Curvature Minimizing Depth Interpolation for Intuitive and Interactive Space Curve Sketching

Space curve sketching using 2D user interface is a challenging task and forms the foundation for almost all sketch based modeling systems. Since the inverse projection from 2D to 3D is a one to many function, there is no unique solution. In this paper, we propose to interpret the given 2D curve to be the projection of the 3D curve that has minimum curvature among all the candidates in 3D. We present an elegant algorithm to efficiently find a close approximation of this minimum curvature 3D space curve. Fixing the space curve to be the minimum curvature curve does not restrict the user from getting high-curvature space curve, if desired. We analyze the complete behavior of our space curve generation algorithm in order to provide simple sketching rules to achieve the curve that the user wants, even the highcurvature space curve, with no change in our algorithm.