Sketch-based free-form shape modelling with a fast and stable numerical engine

In this paper, we present a feature-based free-form shape modelling technique based on solving a fundamental problem of reconstructing the depth information from 2D sketch planes. First, to mathematically define the problem with the human perception, the proposed technique (1) formulates the 2D shaded regions on sketches by a hybrid thin plate surface model that can exhibit controlled continuity over the recovered 3D surface and (2) formulates the ID salient open free-form curves and salient corners as linear sketch constraints. The 3D free-form shape from sketch planes is then achieved by solving a linearly constrained quadratic optimization problem which unifies both 2D region-based and ID contour-based shape information over 2D sketches. Secondly, to solve the formulated optimization problem with an interactive-rate performance, a fast and stable numerical engine is proposed with a rigorous proof that for our specially formulated problem, system decomposition with reduced computational cost is always possible. Stability, accuracy and efficiency are studied in depth for the proposed numerical engine. Finally a prototype system utilizing the proposed technique is presented with two applications that demonstrate the usefulness and effectiveness of the proposed technique. (c) 2005 Elsevier Ltd. All rights reserved