Geared to complement UML and to the specification of large software systems by non-mathematicians, constraint diagrams are a visual language that generalizes the popular and intuitive Venn diagrams and Euler circles, and adds facilities for quantifying over elements and navigating relations. The language design emphasizes scalability and expressiveness while retaining intuitiveness. Spider diagrams form a subset of the notation, leaving out universal quantification and the ability to navigate relations. Spider diagrams have been given a formal definition. This paper extends that definition to encompass the constraint diagram notation. The formalization of constraint diagrams is non-trivial: it exposes subtleties concerned with the implicit ordering of symbols in the visual language, which were not evident before a formal definition of the language was attempted. This has led to an improved design of the language.