Spatial linkages have been used to measure the relative position of anatomical bodies in vivo. If an accurate method is used for mathematically representing the articular surfaces, the relative position of which is measured by a linkage, in vivo areas of contact in anatomical joints can be determined. Articular surfaces can be represented mathematically in a piecewise continuous fashion using parametric surface patches. This paper describes the use of Coons' bicubic surface patches, with null twist vectors, to obtain the piecewise mathematical representation of the articular surfaces of the proximal humerus and scapula from the shoulder of a German Shepherd Dog. The accuracy of the representation is examined qualitatively and quantitatively.