Abstract
The sketch-based shape modeling is one of the most challenging and active problems in computer graphics. In this paper, we present an interactive modeling system for generating free-form surfaces using a 2D sketch interface. Since inferring 3D shape from 2D sketches is an one to many function with no unique solution, 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. In this way, firstly, we present an algorithm to efficiently find a close approximation of this minimum curvature 3D space curve. In the second step, our system could identify the 3D surfaces automatically, and then we apply Delaunay triangulation on these surfaces. Finally, the shape of the triangular surface mesh that follows the 3D profile curves is computed using harmonic interpolation by solving Laplacian equations. We present experimental results on various kinds of drawings by the interactive modeler
Highlights
Nowadays, most designers still prefer to express their creative design idea through 2D sketches
We propose that the 3D curve corresponding to the given 2D curve is the one that minimizes the maximum normal curvature in 3D
There are four main contributions in this paper as follows: 1) We prove the existence of the projection from 2D curves to 3D curves using curvature minimizing, and developed the technique to account for a profile curve to infer a 3D curve
Summary
Most designers still prefer to express their creative design idea through 2D sketches. Most of the sketch-based modeling tools try to avoid addressing this fundamental problem directly due to its complexity. These systems provide a fixed canvas to the user to draw the 2D curve, fixing the 3D curve to be on the canvas. We attempt to provide a physically sound and mathematically elegant method of 3D space curve determination from a 2D curve. We propose an FEM-based sketch modeling method for general unstructured free-form hand-drawings. 3) Given the articulated sketches, we present an effective algorithm to generated shape of the surface mesh using a finite element method (FEM).
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