Curves are the basis for product modeling and most product design starts with curve design. As curves are the low-level tools for product modeling, the quality of the curve generated has a decisive effect on the quality of the final product model. It has strong impact on the success rate and efficiency of product design.

Major curve generation methods include interpolation and approximation. We have done comprehensive research on both of these two methods and our work is related but not limited to interpolation of point array, energy minimization based curve approximation and curve fairing.

There are two other important curve construction schemes in product design: the generation of boundary curves and section curves. Boundary curves can be used to create trimmed curves while section curves are used to create lofted surface. These are popular modeling methods in CAD systems.

Boundary Curves of a Mesh	Section Curves from a Mesh

Image silhouette curve extraction:Engineering silhouette graph may include large amount of quadric curves and it is necessary to detect these quadric curves (especially lines and arcs) contained in the sketch silhouette. For most product design, structural features of models are mainly based on sketches, and by modifying feature parameters of sketch (like dimension or geometry constraints), model structures can be changed accordingly to realize design intent. Some systems directly utilize 2D silhouette curves for rapid design of 3D products.

We also developed a freehand sketch tool to let the users sketching their curves freely on a tablet, and our tool can recognize quadratic sketch segments as well as creating freeform spline curves by fitting. This method let the users forget about the precision and constraints, and it's very suitable for conceptual design.