The semiconductor manufacturing industry has been continuously shrinking the critical dimension of integrated circuits. An important step in manufacturing integrated circuits is transforming the photomasks into constituent shots, a process referred to as fracturing. A major problem with fracturing is the explosion of shots which leads to long mask write times and costly masks. In this paper, we develop fracturing algorithms that are tailored towards curvilinear layouts, such as those optimized by pixel based OPC. Our proposed fracturing algorithms generate the location, size, and dosage of shots given the mask layout and mask manufacturing parameters. We propose two classes of algorithms that both allow for shot overlap. The first manhattanizes a curvilinear mask and applies our previously developed rectilinear fracturing algorithm upon the resulting rectilinear mask. The second one directly generates the shots by matching the boundary of the input polygon with a dictionary of possible shot corners that are associated with a shot dosage. This is followed by the same rectilinear fracturing algorithm to refine the shot edges. An important feature of all our algorithms is that they can readily trade off between mask error and shot count by adjusting input parameters. Compared to a commercially available non- overlapping shot software package, our algorithm results in up to a 50% reduction in shot count with comparable mask error.