This paper presents a generic method for eager interpretation of online hand-drawn sketches. This work takes place within the ACTIF project, with the objective of designing an e-learning system for geometry lessons in middle-schools. The goal is to analyze on the fly the child's inputs (using a pen-based interaction on tablet), and to give real-time feedback (visual, corrective, or guidance ones). We are therefore faced with the constraint of real-time strokes interpretation. We propose to use an incremental analysis process enabling to decrease the search space size. Nevertheless, we encounter combinatorial problems given the application field is complex. For example, create subfigures from an existing one means the parser has to consider all possible combinations of connected segments that are contained in the original shape. To tackle this issue, we extend the definition and the parsing of bi-dimensional grammars by formalizing a hierarchy between production rules. Therefore, we propose alternative exploration strategies and reduce the search space of applicable production rules at any given level of the analysis. Thus, the parser is able to dynamically switch between the exploration strategies in the analysis process. The system has been tested with different drawing scenarios of geometric figures sketching. It reached interesting real-time performance, without loosing the generic aspect of the approach.