A method for generating 3D printing points may include obtaining a Steiner patch that is part of a tessellation approximation of the 3D object, determining a parametric curve of a slicing plane and the Steiner patch, determining a classification of the parametric curve, sampling, based upon the classification, first and second points spaced by a parametric spacing along the parametric curve, determining a Euclidean spacing of the first and second points, and comparing the Euclidean spacing to a predefined spacing threshold. In response to the Euclidean spacing failing to satisfy the predefined threshold, sampling a third point along the parametric curve between the first and second points, generating 3D printing points in Euclidean space for the object based upon the first point, second point and third point sampled along the parametric curve.