Applying quantitative spatial phenotypes analysis to the investigation of peltate glandular trichomes development pattern in Perilla frutescens

Table 1 The calculated formula of spatial phenotypic parameters

No	Name	Abbreviation	Calculated formula
1	Primary growth distance	L₀	\({\mathrm{L}}_{0}=\sqrt{{({x}_{s}-{x}_{p})}^{2}+{({y}_{s}-{y}_{p})}^{2}}\times \rho \)
2	Secondary growth distance	L₁	\({\mathrm{L}}_{1}=\sqrt{{({x}_{g}-{x}_{s})}^{2}+{({y}_{g}-{y}_{s})}^{2}}\times \rho \)
3	Sum of growth distance	L_sum	\({L}_{Sum}={L}_{0}+{L}_{1}\)
4	Growth angle	θ	\( \theta = {\text{arctan}}\left( {\left\| {\frac{{\frac{{(y_{g} - y_{s} )}}{{(x_{g} - x_{s} )}} - \frac{{(y_{t} - y_{s} )}}{{(x_{t} - x_{s} )}}}}{{1 - \frac{{(y_{g} - y_{s} )}}{{(x_{g} - x_{s} )}}*\frac{{(y_{t} - y_{s} )}}{{(x_{t} - x_{s} )}}}}} \right\|} \right) \times \frac{\pi }{2} \times 90^{^\circ } \)
5	Vertical growth distance	h	\(h=\mathrm{cos}(\uptheta )\times {L}_{1}\)
6	Edge distance	e	/
7	Nearest distance	d	/

\(\uprho \) is the actual distance represented by the unit coordinate value, which was 0.538414 mm; L₀ is the primary growth distance, which is the distance between the PGT and SGP; L₁ is the secondary growth distance, which is the distance between SGP and PGT; θ is the growth angle, which is the angle between the line from SGP to PGT and the mid-vein; h is the vertical growth distance, which is the vertical distance between PGT and the mid-vein; e is the edge distance, which is the nearest distance between PGT and the leaf margin; d is the adjacent distance, which is the average distance between the target PGT and its three adjacent PGTs; L_sum is the comprehensive growth distance, which is the sum of primary growth distance and secondary growth distance (Fig. 2)

ISSN: 1746-4811