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Calculadora de dupla interpolação

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A Double Interpolation Calculator helps estimate unknown values within a two-dimensional grid using bilinear interpolation. This method applies a weighted average of the four closest known data points to determine an intermediate value. It is widely used in engineering, meteorology, and computer graphics for approximating values between tabulated data points.

Formula of Double Interpolation Calculator

f(x,y) = f(x₁,y₁) × (x₂-x)(y₂-y)/[(x₂-x₁)(y₂-y₁)] + 
f(x₂,y₁) × (x-x₁)(y₂-y)/[(x₂-x₁)(y₂-y₁)] + 
f(x₁,y₂) × (x₂-x)(y-y₁)/[(x₂-x₁)(y₂-y₁)] + 
f(x₂,y₂) × (x-x₁)(y-y₁)/[(x₂-x₁)(y₂-y₁)]

Onde:

  • f(x,y) is the interpolated value at point (x,y).
  • (x₁,y₁), (x₂,y₁), (x₁,y₂), (x₂,y₂) are the four corners of the rectangular grid containing (x,y).
  • f(x₁,y₁), f(x₂,y₁), f(x₁,y₂), f(x₂,y₂) are the known function values at these points.
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This formula provides an accurate approximation for missing values by considering the influence of adjacent data points.

Termos Comuns e Tabela de Conversão

INVERNODefinição
InterpolaçãoThe process of estimating unknown values between known data points
Interpolação BilinearA method of interpolation in two dimensions using linear interpolations along both axes
Pontos de GradeThe known data points that surround the target point
Média ponderadaA method of computing an intermediate value by assigning different weights to different values
Known PointsValor estimado
(2,3), (5,3), (2,7), (5,7)Interpolated Value
(10,15), (20,15), (10,25), (20,25)Interpolated Value

Example of Double Interpolation Calculator

Suppose you have four known values at the corners of a rectangular grid:

  • f (2,3) = 10, f (5,3) = 14
  • f (2,7) = 18, f (5,7) = 22
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You want to determine the value at (3,5).

Using the bilinear interpolation formula:

f(3,5) = 10 × (5-3)(7-5)/[(5-2)(7-3)] + 
14 × (3-2)(7-5)/[(5-2)(7-3)] + 
18 × (5-3)(5-3)/[(5-2)(7-3)] + 
22 × (3-2)(5-3)/[(5-2)(7-3)]

After solving, the interpolated value at (3,5) is 16.

Perguntas frequentes mais comuns

1. What is double interpolation used for?

Double interpolation is commonly used in numerical analysis, physics, engineering, and meteorology to estimate values in datasets where direct medições estão indisponíveis.

3. Can this calculator be used for temperature or pressure data?

Yes, double interpolation is frequently used to estimate temperature, pressure, and other environmental parameters in weather forecasting and engineering applications.

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