Let \(A\) and \(B\) be smooth surfaces of the real Euclidean 3-space and let \(n_A\) resp. \(n_B\) be their normal vector fields. The convolution surface of \(A\) and \(B\) is the point set \(\{a+b\mid a\in A\), \(b\in B\wedge n_A(a)\parallel n_B(b)\}=:A+B\) where \(n_A(a)\) and \(n_B(b)\) are the surface normal vectors at \(a\) and \(b\), respectively. Offset surfaces can be treated within the mentioned concept.
Assuming that \(A\) is a paraboloid and \(B\) a parametrizeable surface the authors give an explicit parametrization of \(A+B\) and apply this to the cases with \(B\) being (1) a quadric, (2) a surface of rotation, (3). a skew or developable ruled surface and (4) a translational surface. If \(B\) is a rational surface, then \(A+B\) is rational too. Convolution surfaces and convolution curves are illustrated in 7 excellent figures.