By utilizing geometric and astronomical knowledge, a model for the length of a solar shadow in relation to its geographical location and object height is established. The variations of shadow length concerning various parameters are analyzed. The model incorporates geographical latitude, longitude, day of the year, time, etc., to calculate the solar altitude angle and, in conjunction with object height, establishes a model for calculating object projection length. Finally, using the provided data in the appendix, the curve of solar shadow length variation at a given time is obtained.
It has a direct application for three-variable rational interpolation in geometrical modeling, image processing and CAGD, etc. In this paper, We try to put the interpolation points in the space and corresponding function values as a ternary complex, then by using the formula of one-variable Thiele interpolation and the recursive algorithms of continued fractions to derive a new method for computing three-variable rational interpolation, An illustrative example can prove that the method has better practicability and maneuverability.
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