The P39 Demos illustrate the reciprocal relationship between a physical tangent basis and its corresponding dual basis, which serves as a specialized set of measuring sticks for extracting vector data. While the tangent basis is used for vector construction—physically assembling a vector by stepping along its grid lines—the dual basis functions as a measurement sieve designed to probe and isolate specific values. These dual vectors are strategically oriented to be perpendicular to the grid lines they are not intended to measure, a configuration that allows them to filter out interference from other directions. This geometric arrangement is crucial because it maintains orthogonality even in systems where the physical frame is distorted or nearly parallel, ensuring that the isolated measurements remain accurate and free from cross-contamination.
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