This paper presents DEDALE, a spatial database system which provides an abstract and non-specialized data model and query language for representating and manipulating geometric data in arbitrary dimension. DEDALE relies on a logical model based on linear constraints. The main features of the constraint model are (1) a uniform representation of all sorts of data, including geometric, spatio-temporal or elevation data, (2) an algebraic query language whose formal foundations constitute a basis for practical query optimization. We show the practical relevance of the approach by describing an implementation which builds on standard technology for data storage, database indexing and on the parsing and optimization of SQL. DEDALE validates the linear constraint model over various applications, proposes a user query language based on SQL which allows to query the database in a purely declarative way, and gives some first steps towards query optimization. We believe that this experience is a fruitful step toward sound and consistent database models which hide the complexity of arbitrary geometric data, while keeping manipulation languages intuitive and efficient.