We present a new approach to derive efficient and precise algorithms of interest to computer graphics. This is illustrated here by the case of the circle. It also yields algorithms for straight lines and more infrequent curves, such as segments of exponentials. The method is, in essence, the numerical integration of vector fields using only integers.
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which could be used to take into account the uncertainties of the quantities to be homogeneously transformed.
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