Estimating a volume by linearly spaced areas. a) The green dots illustrate known, linearly spaced, areas from an unknown volume. The Y-axis gives the size of these areas and the X-axis at which depth, in the unknown volume, they were measured. b) By multiplying each known area by the linear spacing, the lost areas are approximated (black border), a piecewise constant interpolation is made. The area under the curve is the estimate of the unknown volume. c) The lost areas approximated by two piecewise polynomial interpolations, a piecewise linear interpolation (purple graph) and a cubic spline interpolation (blue graph).