Laplacian-based Design: Sketching 3D Shapes

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.

Sketching in early conceptual phases
of product design: guidelines and tools