Bilinear Interpolation Calculator
Interpolate a value from four corners of an axis-aligned rectangle. Use matching coordinate units.
Formula
u=(x−x₀)/(x₁−x₀), v=(y−y₀)/(y₁−y₀); z=z₀₀(1−u)(1−v)+z₁₀u(1−v)+z₀₁(1−u)v+z₁₁uv.
Interpolated z ≈ (0)×(1-(0.5))×(1-(0.5))+(4)×(0.5)×(1-(0.5))+(2)×(1-(0.5))×(0.5)+(1)×(0.5)×(0.5)
How to use
- Enter two distinct coordinates on each axis.
- Enter the four corner values and target point.
- Read the interpolated value.
Examples
- At the center, corners 0, 4, 2, 1 give 1.75.
Frequently asked questions
Which corner is z₁₀?
The value at (x₁,y₀); z₀₁ is at (x₀,y₁).
What if the point is outside?
The same formula extrapolates; it may exceed the corner values.
May a side have zero length?
No. Equal coordinates on either axis make the calculation undefined.
Sources
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