Generalized cylinders are objects defined by sweeping an arbitrary 2D closed contour along an arbitrary 3D trajectory while simultaneously scaling the contour in two perpendicular directions. A display algorithm for generalized cylinders is presented that is based on generating successive points on contours positioned at successive points on the trajectory. This surface-scanning algorithm requires that the contours as well as the points on a contour are taken close enough to guarantee that no gaps occur in the projected surface of the generalized cylinder. On the other hand, for the sake of efficiency, care has to be taken to restrict the number of super-fluous points. The paper describes solutions for these problems and shows that a surface-scanning algorithm is an elegant and efficient display algorithm for parametrically defined generalized cylinders.