Performance assessment of three simplified Gielis equations in quantifying the geometries of lanceolate bamboo leaves.

Accurate quantification of bamboo leaf morphology is essential for understanding plant morphogenesis and development. However, most bamboo leaves exhibit long lanceolate shape characteristic, posing challenges in finding suitable mathematical models for accurate shape description. Previous studies indicated that the simplified versions of Gielis equation, a nonlinear polar coordinate system derived from the superellipse equation, have shown promise in describing bamboo leaf geometries. Nevertheless, selecting an optimal nonlinear equation that precisely fits empirical bamboo leaf data remains a formidable challenge in morphological studies. This persistent limitation underscores the critical need for developing systematic evaluation methods to assess the performance of such nonlinear models. In the present study, three distinct versions of simplified Gielis equation, i.e., four-parameter version (referred to as SGE-1), three-parameter version (referred to as SGE-2), and two-parameter version (referred to as SGE-3), were used to fit the two-dimensional contours of bamboo leaves with a long lanceolate shape across two species (