The geometry processing pipeline covers applications from modeling 3D digital objects, also aided by sketch-based techniques, to meshing 3D digital objects for simulations, where research is increasingly enhancing the 3D models with semantics.
In the context of geometry processing, we work with techniques such as:
- Meshing and remeshing
- Surface reconstruction from point clouds
- Discrete differential geometry
- Analysis of 3D objects
- Modeling of 3D objects
Meshing is a set of methods used in computer graphics for discretizing a continuous 3D object. For example, simple flat elements with straight edges such as triangles are concatenated to each other along their edges to generate a piecewise linear surface that approximates the continuous surface and thus forming a discretized representation of the surface. The finer the mesh is (i.e. the smaller its flat elements are), the greater the accuracy of the approximation is. Remeshing enables the refinement of part of a mesh, using smaller elements to locally improve the accuracy of the approximation. The ability to inspect such 3D surfaces or their meshes often depends on the available computer power. Meshes can have different resolutions (Multiresolution Mesh) depending on the application, in order to improve the exploration and handling experience. Discrete Differential Geometry studies meshes as a whole rather than its individual geometric parts. An example of this is curvature analysis, which allows for recognizing the shape of a 3D object by means of analyzing the type of curvature and therefore understanding the arrangement between curved and planar surfaces. We offer efficient interactive surface reconstruction based on this approach. When modeling 3D objects , we work with the Generative Modeling Language (GML). This is a programming language for describing three dimensional objects with structures and parameters. GML describes 3D objects by using functions rather than collections of geometric elements (triangles, points, NURBS patches).