This paper is concerned with free-form surface constructions using implicit quadrics. More specifically, we are interested in the following problem: given a polyhedron with triangular facets and tangent planes prescribed at its vertices, fit a smooth (tangent-plane continuous), implicit, and piecewise quadric surface through the vertices of the polyhedron so that the surface is tangent to the prescribed tangent plane at each vertex. We show that in order to solve this problem without splitting the facets of the polyhedron, the prescribed tangent planes must satisfy a condition, and under this condition we give a local scheme for constructing the smooth piecewise quadric surface. Using this scheme, we can represent arbitrary shapes by quadric primitives. The implementation results are reported.