1. What is Bilinear Interpolation?

Bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables on a regular grid. It performs linear interpolation first in one direction, and then again in the other direction.

2. How Does the Calculator Work?

The calculator uses the bilinear interpolation equation:

Where:

• \( a, b, c, d \) — Coefficients derived from grid values (unitless)
• \( x, y \) — Position coordinates between grid points (unitless)

Explanation: The equation combines linear interpolation in both x and y directions to estimate values between known grid points.

3. Applications of Bilinear Interpolation

Details: Commonly used in image processing, computer graphics, geographic information systems (GIS), and numerical analysis for estimating values between discrete data points.

4. Using the Calculator

Tips: Enter the four coefficients (a, b, c, d) derived from your grid values and the position (x, y) where you want to estimate the value. All values are unitless.

5. Frequently Asked Questions (FAQ)

Q1: How are the coefficients a, b, c, d determined?
A: They are calculated from the four known grid points surrounding your target (x,y) position.

Q2: What's the difference between bilinear and bicubic interpolation?
A: Bicubic uses more neighboring points (16 vs 4) and provides smoother results but is more computationally intensive.

Q3: When should I use bilinear interpolation?
A: When you need a good balance between accuracy and computational simplicity for 2D data.

Q4: What are the limitations of bilinear interpolation?
A: It assumes linearity between points and can produce artifacts when the underlying function has high curvature.

Q5: Can this be extended to 3D?
A: Yes, trilinear interpolation extends this concept to three dimensions.