This paper presents a new framework to measure farm-level heterogeneity, and productivity change, and to study the rate and direction of technical change within an agricultural sector. Building on the seminal works of Hildenbrand (1981) and Dosi et al. (2016), we show how, while relaxing most of the standard assumptions from production theory, discrete geometry is an effective tool for productivity analysis and technical change in agricultural economics. We apply the framework to a rich panel data from maize farmers in Tanzania to investigate the dynamics of technical heterogeneity and agricultural productivity growth.