Surgical jigs for guiding bone resectioning in knee replacement surgery, one for the femur and another for the tibia, contain both the various bone-jig contact surfaces and the cutting guide as a single unitary piece. The contact surfaces are curvilinear surfaces formed into ends of planar fins that project from the jig base or substrate. Each jig has three (3) pairs of contact surfaces selected to abut low-wear, lateral and medial, articular surface features, such that the jig has one and only one possible self-locking position against the bone (or cartilage) and so the jig's integral cutting guide will define one and only one cut plane for the bone resectioning. The presence of osteophytes generally does not adversely impact the proper fit of the jigs. An improved rotational transformation method for converting the scan views into the desired proper axes is based not only on planar rotations, but also on a projection of the rotated coordinates onto the plane of rotation and produces parameters that correspond much more closely to the joint surfaces in the desired jig coordinates.
