Abstract: Conic curves and quadric surfaces are widely used in CAD/CAM applications. Two parts paper present a way to represent these items using quadratic aonuniform rational B-splines (NU RB). In the first part, we prove the identity between quadratic non-uniform rational B-splines and co nic curves and shov how to determine a specified NURB representation as well as its weighting fac tors hi by detailed examples.