Interpolation Matrix Segmentation for Computational Load Reduction
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Solution Overview
Problem
Existing methods for interpolating data in a grid, such as meteorological data, are computationally intensive due to the need for extensive matrix algebra operations, particularly when using large transformation matrices like the 16×16 matrix, which increases the processing load significantly.
Innovation Solution
The method involves defining a 4×4 data value matrix and a set of 4×4 transformation matrices to calculate a 4×4 coefficient matrix, using x and y vectors based on offsets, and then calculating the interpolated data value efficiently, which can be performed using a GPU with shaders to reduce computational load.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a 16×16 transformation matrix is used for data interpolation, then interpolation accuracy is maintained, but computational load becomes extremely substantial
Solution Approach 1:
The patent segments the single 16×16 matrix operation into multiple smaller 4×4 matrix operations. Specifically, it divides the 16-element vector into four 4-element vectors and performs four separate 4×4 matrix multiplications, which are then combined to produce the final interpolated value. This segmentation reduces the computational complexity from O(16²) to 4×O(4²), significantly lowering the computational load while preserving interpolation accuracy.
2Measurement precision
If matrix algebra operations are performed for every interpolated data point, then accurate interpolation is achieved, but processing time increases substantially
Solution Approach 1:
By segmenting the matrix operations into smaller 4×4 components, the patent enables faster computation for each individual interpolated point. The reduced matrix size allows for quicker multiplication and combination operations, directly decreasing the processing time required per data point while maintaining the same interpolation accuracy through the structured combination of the segmented results.
Data Source
AI summary
A method and apparatus for interpolating data on a data grid having a plurality of data grid points to provide an interpolated data value at an interpolated point offset from a data grid point by offsets x, y, the method comprising the steps of obtaining a data value and a plurality of derivative values for each of a set of data grid points defining a sub-grid, defining a 4×4 data value matrix from the data values and derivative values, defining a plurality of 4×4 transformation matrices, calculating a 4×4 coefficient matrix from the transformation matrices and the data value matrix, defining a x vector based on the offset x and a y vector based on the offset y, and calculating the interpolated data value from the x vector, y vector and coefficient matrix.