Kirigami can be used to create objects with a nonzero Gaussian curvature. A mathematical method is presented that can be applied to join a single continuous and smooth cut of a kirigami sheet. This is realized by constraining additional discretized strips with origami. The mathematical model evaluates how the strips from both sides of the cut can be constrained. The mathematical model is validated with an experiment, which confirmed the direction of the constraints. However, due to physical elements which are not part of the presented mathematical model, the relative proportion between the constraints did not fully represent reality. Finally, this treatise shows the optimization of a crease pattern, by using this model, resulting in a joined kirigami object.