Formula
R₁ = Q₁₁ + (x − x₁)(Q₂₁ − Q₁₁)/(x₂ − x₁)
R₂ = Q₁₂ + (x − x₁)(Q₂₂ − Q₁₂)/(x₂ − x₁)
f = R₁ + (y − y₁)(R₂ − R₁)/(y₂ − y₁)
Interpolate along x on the bottom and top edges, then interpolate between those two results along y.
Example
Corners: 100, 140 (at y = 10) and 120, 180 (at y = 20). Find f at x = 1.5, y = 14.
R₁ = 120, R₂ = 150, f = 120 + 0.4 × 30 = 132
Using it with a steam table
- Find the two pressures and two temperatures that bracket your state.
- Read the property (e.g. specific volume) at the four combinations.
- Enter pressures as x₁/x₂, temperatures as y₁/y₂, and the four values as Q.
- Enter your actual pressure and temperature as x and y.
FAQ
Is double interpolation the same as bilinear?
Yes. Engineering courses call interpolation in a two-input table (e.g. a superheated steam table) double interpolation.
Does it matter whether I go along x or y first?
No. Both orders give the same result.
Where is it used?
Steam and property tables, image resizing, terrain height maps and 2D lookup tables.