Hermite Interpolation Algorithm For Constructing Reasonable Analytic Curves Through Discrete Data Points

Hermite Interpolation Algorithm for Constructing Reasonable Analytic Curves Through Discrete Data Points

Research was conducted using winds and temperatures measured on a 1500-ft tower at a few irregularly spaced levels. The research methodology required the construction of reasonable analytic curves of wind and temperature vs height. The curves were to be capable of integration and differentiation and were to be generated and plotted by computer without human intervention. Reasonable was subjectively defined as the curve that an individual would most probably draw by hand through the same data points. Of the several techniques tried, only an algorithm consisting of Hermite interpolation between every two successive points with artificial construction of required derivatives generated reasonable curves. Derivatives are artificially constructed by a subroutine which duplicates the constraints that an individual subconsciously employs when drawing a curve through discrete data points. The report discusses the techniques investigated, graphically demonstrates the advantages and reasonableness of this algorithm, and describes it in detail. This algorithm should be applicable for fitting a continuous curve to discrete data of any sort. (Author).

Hermite Interpolation Algorithm for Constructing Reasonable Analytic Curves Through Discrete Data Points

Research was conducted using winds and temperatures measured on a 1500-ft tower at a few irregularly spaced levels. The research methodology required the construction of reasonable analytic curves of wind and temperature vs height. The curves were to be capable of integration and differentiation and were to be generated and plotted by computer without human intervention. Reasonable was subjectively defined as the curve that an individual would most probably draw by hand through the same data points. Of the several techniques tried, only an algorithm consisting of Hermite interpolation between every two successive points with artificial construction of required derivatives generated reasonable curves. Derivatives are artificially constructed by a subroutine which duplicates the constraints that an individual subconsciously employs when drawing a curve through discrete data points. The report discusses the techniques investigated, graphically demonstrates the advantages and reasonableness of this algorithm, and describes it in detail. This algorithm should be applicable for fitting a continuous curve to discrete data of any sort. (Author).

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