Despite its widespread use, bilinear interpolation is frequently misapplied or misunderstood, leading to incorrect results and poor performance in practical applications. Understanding these common pitfalls is essential for proper implementation.
Misconception 1: Arbitrary Grid Orientation
Many users incorrectly assume that coordinate orientation doesn't matter or use inconsistent coordinate systems, leading to calculation errors.
Correct Method: Always establish a clear, consistent coordinate system. Define (x₁,y₁) as one corner and (x₂,y₂) as the diagonally opposite corner, ensuring proper grid orientation.
Misconception 2: Extrapolation Beyond Grid Bounds
Some applications attempt to use bilinear interpolation for points outside the defined grid, which can produce unreliable and physically meaningless results.
Correct Method: Restrict bilinear interpolation to points strictly within the rectangular grid bounds. For external points, consider appropriate extrapolation methods or grid extension techniques.
Misconception 3: Assuming Perfect Linearity
Users sometimes expect bilinear interpolation to accurately capture complex nonlinear relationships that require higher-order interpolation methods.
Correct Method: Recognize that bilinear interpolation assumes approximately linear variation in both directions. For highly nonlinear data, consider bicubic interpolation, spline methods, or higher-order polynomial techniques.
Misconception 4: Inadequate Grid Resolution
Applications sometimes use bilinear interpolation on grids that are too coarse to capture important variations or features in the underlying data.
Correct Method: Ensure grid resolution is sufficient to represent the underlying data characteristics. Consider adaptive mesh refinement or higher-density sampling for complex datasets.