A canal surface is the envelope of a family of spheres, whose centers move on a curve while their radii vary. By means of a stereographic mapping, a sphere corresponds to a point in 4-space. The canal surface then corresponds to a curve in 4-space. The paper gives insights into this mapping and presents a construction of an osculating Dupin cyclide, which provides the principal curvatures for each generating circle of a curvature continuous canal surface.