The main objective of the ongoing investigation described in this paper is to produce a Corinthian capital through generative modelling and digital prototyping, and according to Leon Battista Alberti's treatise on architecture, De re aedificatoria. This investigation is part of the Digital Alberti research project, which aims to decode Alberti's treatise through the use of new technologies. This treatise can be interpreted as a set of instructions regarding the art of building. Some of these instructions were translated into computational models, capable of generating digital instances of column elements according to the classical canons prescribed in the treatise. These instances were then digitally produced, materializing Alberti's theory. Despite Alberti's thoroughness, some detailing information is missing, namely for the Corinthian capital; observation and computational geometry were important for filling in the gaps. Such investigation allows determining the suitability of different modeling strategies, as well as the potential of different prototyping technologies.