Current solid freeform fabrication data exchange practice supports only discretized approximations of part geometry. For producing accurate patterns and functional parts, the adequacy of linear approximations is suspect. The most efficient way of minimizing the degradation of geometric entities is to eliminate this intermediate format and directly exchange the source geometry. However, each commercial CAD vendor has its own representation, and choosing a single format has proven somewhat problematic. As an alternative, we have developed a method to approximate a contour from a set of discrete points using high order polynomials and to efficiently generate scan vectors from the high order contour. Our method exploits the so-called algebraic spline (A-spline) curve. Data fitting using A-splines gives a set of implicit curve segments with C3 local continuity, compared to the C0 continuous collection of line segments that is common in SFF practice. The A-spline approximation is capable of representing sliced geometry generated from various types of surfaces, including parametric, implicit, and mixed surface forms. The A-spline approximation method was tested by fabricating a curved object by Selective Laser Sintering. The resulting part showed higher surface quality with none of the tessellation artifacts inherent in part generation from polygonal contours. The run-time efficiency of the method is comparable to that of linear contour processing.