Sketch-Based Mesh Quadrangulation

In the area of industrial design and industrial manufacture, it is desirable to digitize the product and build its mathematical model: first a large amount of data could be obtained from scanners, and then the designers can build the surface model from these data. This process is well known as Reverse Engineering. The NURBS has become a de facto standard for the representation of curves and surfaces in CAD. But it is not sufficient to represent the model using only one piece of surface, so it is very important to segment the model into several pieces of patches.Partitioning a surface into quadrilateral region is a common requirement in reverse engineering. It is to partition the mesh model into quad region, and then fit B-spline surface for each patch satisfying geometric continually condition between patches. Recently, a large number of algorithms have been presented for the generation of quad elements. They could be classified into two classes: automatic quad domain extraction; interactive quad generation. The former method need less user interaction, but they allow no control over design and leave little control over the local alignment of the mesh elements, resulting in singularities at conspicuous places and elements of arbitrary shapes. The latter is not flexible and need more work. It is difficult to extract the quad domain for the complex model.It shows that it is worthwhile to study a high interactive and high effectively controllable system which generates quadrangles. We propose quadrangles generator system based on manual sketch. During the process of the system, the first step is to automatically extract the main feature lines of entity model by feature extracting algorithm, delete some abundant feature lines, merge the feature lines and extend some feature lines to stroke the model's main structure. Then, the users use the tools provided by our system to conveniently edit these feature lines and add feature lines through indicating manner. According to the cases, the system would extend the feature lines to obtain the desirable lines which the users need and ultimately we canget a singularity graph on the surface of entity model. At the same time, the user can indicate which singularity lines should precisely walk along the boundary of quadrangle and which lines only represent a direction of region's interior. Finally, we obtain a global parameterization by solving the discrete Laplacian equation and automatically obtain the result of the quad extraction of the entity model. The experimental results demonstrate that the main advantage of our approach is automatically extracting the main feature structure of the model and need less times of users' interaction by providing a series of interactive tool which make the user control much easy and convenient. Our approach could obtain global controllable and local controllable effects by sketch to make the quad extraction along the main structure of the model.