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For automated spray painting robots, the choice of a start curve from which all subsequent paths will be determined, plays a critical role in ensuring uniform coverage of the target surface. In this paper, we ultimately propose a method to determine the start curve for two different procedures of coverage path construction. For the first procedure, we average the target surface normal to optimize the average error between desired and resultant deposition with the added goal of minimizing cycle time. For the second technique, we make recourse to the Gauss-Bonnet theorem to minimize the non-uniformity of paint deposition and cycle time for the entire coverage path.