Recovery of 3D shapes from 2D sketches

The objective of this research is to recover 3D freeform surfaces depicted in a single line drawing, with the aim of taking conceptual design sketches and converting them into 3D models. This work is a continuation of the project “3D Surface Reconstruction from a 2D Line Drawing” (SRLD) done at Nanyang Technological University. SRLD is a system to reconstruct planar objects. The work in this thesis extends the capability of SRLD by recovering freeform shapes. In this thesis, a novel method of reconstructing freeform surface patches from 2D line drawings is introduced. The study focuses on drawings containing four edges that form the boundary of surface patches. The four edges form two pairs of opposite edges which are used as the basis of interpolation to create two sets of backbone curves. After recovering all the 3D curves of one set of backbones, a freeform surface is fitted over them. Controls are provided within the system to adjust the shape of a surface; this is a useful tool given the non-unique nature of the result. An optimization-based method for reconstructing surface patches, cylinder-like shapes and their combination with polyhedron from its projection on a drawing plane is also presented. The rough drawing is first transformed into a straight line drawing. Then, a polyhedron is rebuilt from the straight line drawing. Finally, planar objects are converted back to freeform shapes. Our implementation of the method produces results that are consistent with human perception of the curves as surfaces. Due to the inherent inaccuracies in the input, the models reconstructed are likely to be aesthetically unpleasing. A post-processing is necessary to improve these curved models aesthetically. Our work focuses on improving objects with symmetrical curved boundaries. Symmetrical curved boundaries are detected and fitted to two exactly symmetrical curves on the drawing plane. And then a planar object is reconstructed and beautified from its converted straight line drawing. Finally, curved surfaces are recovered. Experiments show that our method is able to improve shapes with planar and curved surfaces reconstructed from its projection on a drawing plane well.Doctor of Philosophy (MAE