PCHIP - piecewise cubic Hermite interpolating polynomial - is the shape-preserving interpolation used to fit each encoder's rate-quality points so the gap between two curves can be integrated for BD-rate. Bjontegaard's original 2001 method fit a single cubic polynomial through four points, but later work, including the metric author's own follow-up and the Bjontegaard Bible analysis, showed that a plain cubic can overshoot - wiggle above or below the real data between points, the Runge phenomenon - and invent quality that was never measured, distorting the result. PCHIP is a monotone piecewise cubic that cannot overshoot its data points, and the closely related Akima spline does the same job; current practice uses one of them. The integration is also done in the log-bitrate domain so the high-bitrate end does not dominate, and only over the overlapping quality range. The catch is honesty of reporting: which interpolation was used should be stated, because the method choice can shift the BD-rate by a meaningful amount.
