The nearly continuous timewise coverage of recent photometric surveys is free of the large gaps that compromise attempts to follow starspot growth and decay as well as motions, thereby giving incentive to improve computational precision for modeled spots. Due to the wide variety of star systems in the surveys, such improvement should apply to light/velocity curve models that accurately include all the main phenomena of close binaries and rotating single stars. The vector fractional area (VFA) algorithm that is introduced here represents surface elements by small sets of position vectors so as to allow accurate computation of circle-triangle overlap by spherical geometry. When computed by VFA, spots introduce essentially no noticeable scatter in light curves at the level of one part in 10,000. VFA has been put into the Wilson-Devinney light/velocity curve program and all logic and mathematics are given so as to facilitate entry into other such programs. Advantages of precise spot computation include improved statistics of spot motions and aging, reduced computation time (intrinsic precision relaxes needs for grid fineness), noise-free illustration of spot effects in figures, and help in guarding against false positives in exoplanet searches, where spots could approximately mimic transiting planets in unusual circumstances. A simple spot growth and decay template quantifies time profiles, and specifics of its utilization in differential corrections solutions are given. Computational strategies are discussed, the overall process is tested in simulations via solutions of synthetic light curve data, and essential simulation results are described. An efficient time smearing facility by Gaussian quadrature can deal with Kepler mission data that are in 30minute time bins.
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