Digital geometry processing is an important research field which has been extensively developed for more than forty years. It deals with the definition and implementations of models and operations for describing and handling geometrical objects. Computers have become increasingly powerful and are now capable of handling detailed representations of complex objects. In addition, powerful tools have recently been developed that are able to scan real objects in order to reconstruct the corresponding electronic descriptions. For these reasons, real objects can now be described in computers with a very high level of precision, and we can use these precise descriptions to perform analysis and processing tasks on the corresponding objects.
One main challenge for digital geometry processing is the elaboration of geometrical models to describe digital objects and to propose algorithms that use these models to compute information and to handle the objects represented.
Due to the considerable diversity of all the different domains of application, the needs are very varied as each application has its own specificity:
- specific dimension: 2D models in image analysis/processing. 3D models in medical imagery, CAD, geology, etc; 4D for example to describe a 3D animated object, the additional dimension being time, or higher dimensional objects by adding some feature spaces, for example in geographic information systems;
- specific objects to represent: regular when all the cells have the same type versus non-regular; manifold (when each point has a neighborhood equivalent to a ball) versus non-manifold;
- specific relations between objects: two objects can touch several times (multi-incidence) or not; two objects can be adjacent only along one of their faces (quasi-manifold) or along any cell in their boundary.
In this framework, our overall research goal in this project is to design the next generation technologies for modeling the full complexity of living and designed structures. In order to do this, we plan to define a generic purpose representation for geometric structures of arbitrary topology and different high level powerful operations capable of building and modifying this representation. In addition, we want to develop libraries and software implementing our solutions to serve as a basis for future software development in computer graphics.
In the NGTMod proposal, we said “The results of the NGTMod project will improve existing solutions by allowing handling of very big objects in any dimension thanks to compact and streamable representation and powerful operations”. The two first goals were reached thanks to our compact definition of 2D, 3D and nD representations based on unit elements. Indeed, our solution allows compact encoding, by using only symbols to encode our words. It is thus possible to represent very big objects that can not fit in memory when using a classical datastructure for combinatorial maps. Moreover, our solution is local which thus provides directly streaming operations. Our second main contribution, the distributed combinatorial maps, is another possible solution to the problem of very big object representation. For this second contribution, we also show that it simplifies the definition of parallel algorithm and thus it is possible to define powerful operations. Our main goal following the NGTMod project is to use our solutions in many different domains of application and to share models and techniques across domains thanks to a universal representation. This goal is not yet reached since it was not planed in the NGTMod proposal, but this is an important part of the work in order to convince users of the interest of our solutions. We plan to work on this topic after the end of the NGTMod project.
