In this paper, noniterative interface reconstruction algorithms for volume of fluid (VOF) method are presented. Analytical expressions are derived to determine the coefficients of the curve to achieve a noniterative reconstruction procedure. Static interface reconstruction tests of standard geometries like circle and ellipse are performed. The noniterative algorithm based on Piecewise Linear Interface Calculation from an earlier work is found to reconstruct the VOF value within machine tolerance. Two piecewise continuous algorithms are also proposed in this work, which ensures C0 continuity. The first algorithm, namely, Piecewise Continuous Linear Interface Calculation (PCLIC), uses piecewise continuous linear segments to approximate the interface. The second algorithm uses piecewise continuous quadratic curve and is named as Piecewise Continuous Quadratic Interface Calculation. PCLIC is seen to achieve machine tolerance in reconstructing the VOF value. Piecewise Continuous Quadratic Interface Calculation is found to give a more accurate estimate of the length of the interface than Piecewise Linear Interface Calculation and PCLIC. © 2013 John Wiley & Sons, Ltd.