abzubilden

Abzubilden is the infinitive with zu of the German verb abbilden. The core meaning is to depict, illustrate, reproduce, or map something in a representation. The prefix ab- conveys the idea of producing a representation from a source, while bilden means to form or shape. In usage, abzubilden appears in contexts ranging from visual illustration to data modeling and mathematical mapping.

In everyday and formal German, abzubilden is used after verbs that require an infinitive with zu, for example: Ich hoffe, das Diagramm abzubilden. The simple form abbildern is used in finite clauses, as in Das Diagramm bildet die Verteilung der Werte ab. The noun Abbildung refers to the representation itself, such as eine Abbildung einer Szene, eine Abbildung von Daten oder eine Abbildung einer Funktion in der Mathematik.

Applications and nuances:

- Visual depiction: to render a scene, object, or concept in an image or graphic form, e.g., Die Grafik bildet die Struktur des Objekts ab.

- Data and modeling: to map or transform information from one form to another, e.g., Die Daten müssen in das Zielmodell abgebildet werden.

- Mathematics and computer science: Abbildung is a formal term for a function or mapping between sets; eine Abbildung ordnet jedes Element des Definitionsbereichs einem Element des Wertebereichs zu. In this sense can be described as abbilden.

Related terms include Abbildung (noun, the depiction or mapping), Abbild (a physical copy or image), and darstellen (to present or portray, with a broader or different nuance). Overall, abzubilden denotes producing a faithful or structured representation of something across visual, informational, and formal contexts.