Confocal imaging is a well-established method for investigating plant phenotypes on the tissue and organ level. However, many differences are difficult to assess by visual inspection and researchers rely extensively on ad hoc manual quantification techniques and qualitative assessment. Here we present a method for quantitatively phenotyping large samples of plant tissue morphologies using triangulated isosurfaces. We successfully demonstrate the applicability of the approach using confocal imaging of aerial organs in Arabidopsis thaliana. Automatic identification of flower primordia using the surface curvature as an indication of outgrowth allows for high-throughput quantification of divergence angles and further analysis of individual flowers. We demonstrate the throughput of our method by quantifying geometric features of 1065 flower primordia from 172 plants, comparing auxin transport mutants to wild type. Additionally, we find that a paraboloid provides a simple geometric parameterisation of the shoot inflorescence domain with few parameters. We utilise parameterisation methods to provide a computational comparison of the shoot apex defined by a fluorescent reporter of the central zone marker gene CLAVATA3 with the apex defined by the paraboloid. Finally, we analyse the impact of mutations which alter mechanical properties on inflorescence dome curvature and compare the results with auxin transport mutants. Our results suggest that region-specific expression domains of genes regulating cell wall biosynthesis and local auxin transport can be important in maintaining the wildtype tissue shape. Altogether, our results indicate a general approach to parameterise and quantify plant development in 3D, which is applicable also in cases where data resolution is limited, and cell segmentation not possible. This enables researchers to address fundamental questions of plant development by quantitative phenotyping with high throughput, consistency and reproducibility.