Piecewise rational quadratic curves are frequently used in many fields of computer science to represent curved shapes. For a large number of applications of computer aided design, the representation of data with a piecewise parametric curve that lies close to the data is an important consideration. This paper presents a geometric solution to the problem of automatically generating piecewise parametric rational quadratic polynomial approximations to shapes from sampled data. The algorithm takes a set of sample points, automatically generates tangents at some points and derives a piecewise rational quadratic curve that lies close to the data points. Combining this algorithm with the biquadratic search to subdivide the data if it cannot be represented with a single arc, we have a very stable algorithm that gives good results over a range of shapes and applications.