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 formula:

Where:

• \( a \) — Constant term
• \( b \) — Coefficient for x
• \( c \) — Coefficient for y
• \( d \) — Coefficient for xy term
• \( x \) — First input value
• \( y \) — Second input value

Explanation: The formula calculates a weighted average of the four nearest grid points to approximate values between them.

3. Applications of Bilinear Interpolation

Details: Commonly used in computer vision, image processing, texture mapping, and geographic information systems (GIS) for resampling raster data.

4. Using the Calculator

Tips: Enter all coefficients (a, b, c, d) and input values (x, y). The calculator will compute the interpolated value at point (x,y).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between linear and bilinear interpolation?
A: Linear interpolation works in one dimension, while bilinear interpolation extends this to two dimensions.

Q2: When should I use bilinear interpolation?
A: When you need to estimate values between known data points in a 2D grid, like resizing images or estimating elevation between survey points.

Q3: Are there higher-order interpolation methods?
A: Yes, bicubic interpolation uses 16 neighboring points for smoother results but is more computationally intensive.

Q4: What are the limitations of bilinear interpolation?
A: It can produce artifacts when interpolating discontinuous data and isn't suitable for non-grid data.

Q5: How does this relate to Desmos?
A: Desmos can visualize bilinear interpolation surfaces when you input this formula into their graphing calculator.