Generic programming for mesh algorithms: Implementing universally usable geometric components pdfauthor

Geometric functionality is crucial for a variety of application domains, including computational mechanics. Typically, geometric tasks are embedded into a larger problem frame. Due to the diversity of tasks, geometric tools must often be combined to achieve the desired solution. As implementing geometric algorithms is difficult and time-consuming, reusing them is highly desirable. Unfortunately, traditional implementations are intimately tied to the underlying representations of the geometric data, and hence are not directly usable in a different context. Conventional approaches to implementing geometric tools are thus limited to copying the data via an API (or to a file), and calling an external routine (or application) application implementing the desired functionality or even implementing an ad-hoc solution, and have obvious drawbacks in terms of efficiency, composability, scalability or quality. Here, we present a radically different approach, concentrating on the case of algorithms working on cellular structures, for example meshes (tesselations, grids) of surfaces and solids. Exploiting the common underlying mathematical structure we define an abstract interface capturing this mathematical notion. Algorithms are implemented generically on top of this interface, thus making the implementations independent of any concrete representation issues. Special emphasis is placed on a separation of combinatorial and geometric aspects and on a general framework for associating arbitrary data to mesh entities of any dimension. A wide variety of reusable geometric tools is implemented in the open source C++ library GRAL. They can be combined and nested in very flexible ways to solve geometric task arising in computational mechanics, independently of the underlying data structures. We conclude by discussing some practical issues of the generic approach, including the quite competitive efficiency of generic components.