Physical sketching: Reconstruction and analysis of 3D objects from freehand sketches

When designing a 3D object, designers, engineers and teachers often begin investigating potential design tradeoffs by creating informal sketches. Ideally, these sketches–in combination with a variety of engineering analysis tools–would allow prediction of the object’s physical properties, especially those that affect the critical early design process. We introduce a pen-based system that reconstructs 3D spatial geometry from a single 2D freehand-sketch consisting of straight and curved lines in interactive time. Several optimization-based approaches to this problem have been proposed, but these generally have difficulty converging to an acceptable solution because the dimensionality of the search space is large. The primary contribution of this paper is a new reconstruction algorithm for orthographic projections of 3D wireframes. The algorithm reconstructs the depths of each vertex by exploiting geometric regularities among the graph lines in a reduced solution space, then optimizes a cost function over this space to recover the vertex depths. A second optimization algorithm is used to infer the 3D geometry of curved strokes once the vertex depths have been recovered. The proposed approach can recover the geometry of several objects with approximately 50 curved strokes in near interactive time. We also present an iterative, Tablet-PC-based design system that uses the proposed reconstruction algorithm to recover 3D objects from 2D orthographic sketches. The system allows the reconstructed objects to be subjected to two types of physical analysis, the results of which are superimposed directly on the sketch: a fast, kinematic simulation, and a complete finite-element-based static analysis. The object can quickly be modified in place using the pen-based interface according to the results of the analysis to allow for iterative design work. We demonstrate the system in action on a variety of early-stage design analyses.