Interpolation Method
Mathematical surface construction using third degree polynomials provides a smooth transition between discrete data points arranged on a regular grid. The bicubic spline ensures that both the first and second derivatives remain continuous across the entire calculated area, preventing sharp breaks or sudden changes in slope. This continuity is essential for mapping sensor responses over a two dimensional range where linear approximations would yield artifacts.
The process requires sixteen adjacent data points to determine the coefficients for a single grid square.
Surface Smoothness
Curvature characteristics resulting from this technique produce a more realistic representation of physical phenomena compared to simpler bilinear methods. Such smoothness eliminates the jagged edges often found in low resolution sensor arrays by calculating intermediate values based on the trend of surrounding cells. This approach produces a differentiable surface that is useful for gradient analysis.
Computational Cost
Execution time for these calculations is notably higher than that of linear alternatives due to the number of floating point operations required per pixel. Sixteen coefficients must be stored and processed for each output value, placing a higher load on the digital signal processor. Memory bandwidth constraints often dictate the maximum grid size that a real time system can handle.
Optimized algorithms use precomputed lookup tables to reduce the latency of these operations in embedded environments.
Boundary Condition
Accuracy at the edges of the data set depends on the choice of constraints applied to the outer points. Without additional information, the algorithm must assume specific values for the derivatives at the periphery, which can lead to oscillations known as Runge phenomena. Setting these boundaries to zero or matching the slope of the nearest neighbor prevents such instability.
The interpolation remains valid only within the convex hull of the original measurement points.
