A weld joint usually joins two or more parts. In any case we assume that the position of any weld joint in space can be associated with a curve in 3D space. This curve is parameterized by distance and hence has a start and stop point. At each point on this curve, a tangent vector r exists and a normal vector s is specified. In addition a third basis vector t is specified that is orthogonal to r and linearly independent of 5 but need not be orthogonal to s. Hence at each point on the curve the three basis vectors (r, s, t) define a curvilinear coordinate system. The basis vectors (s, t) define a 2D curvilinear coordinate system at each point on the curve in a plane normal to r, i. e., the cross-section to the curve.

The weld procedure can be imagined to slide along this curve so that at any point on the curve, the weld procedure lies in the plane normal to r. Figure 7-1 shows an example of such a curvilinear coordinate system for a weld Tee-joint and Figure 7-2 shows an example of the geometry of a Tee-joint with three weld passes.