Dot planimeter

In some variations, dots that land on or near the boundary of the shape are counted as half of a unit.

[3][4][5] In forestry, cartography, and geography, the dot planimeter has been applied to maps to estimate the area of parcels of land.

[1][4][5][6] In botany and horticulture, it has been applied directly to sampled leaves to estimate the average leaf area.

[3] The method using a finer grid tends to have better statistical efficiency than repeated measurement with random placements.

[5] The Steinhaus longimeter is a similar transparency-based device for estimating the length of curves by counting crossings.

A radius-5 circle overlaid with a grid of dots in the pattern of a dot planimeter. When counting dots near the boundary of the shape as 1/2, there are 69 interior dots and 20 boundary dots for an estimated area of 79, close to the actual area of 25 π ≈ 78.54.