Hybrid systems are used to model embedded computing systems interacting with their physical environment. There is a conceptual mismatch between high-level hybrid system languages like Simulink, which are used for simulation, and hybrid automata, the most suitable representation for safety verification. Indeed, in simulation languages the interaction between discrete and continuous execution steps is specified using the concept of zero-crossings, whereas hybrid automata exploit the notion of staying conditions. We describe a translation from a hybrid data-flow language to logico-numerical hybrid automata that treats this issue in detail. We examine various zero-crossing semantics, propose a sound translation, and discuss to which extent the original semantics is preserved.