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Although this improvement increases the approximation order from two to three without any extra cost, the continuity order remains C<jats:sup><jats:italic>0<\/jats:italic><\/jats:sup>. In this paper, we go one step further showing that a C<jats:sup><jats:italic>1<\/jats:italic><\/jats:sup>continuous triquadratic B\u2010spline reconstruction and its analytic partial derivatives can be evaluated by taking only one more trilinear sample into account. Thus, our method is the first volume\u2010resampling technique that is nearly as fast as trilinear interpolation combined with on\u2010the\u2010fly central differencing, but provides a higher\u2010quality reconstruction together with a consistent analytic gradient calculation. 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