General remarks
An unfolding is an equal-area projection of a 3D-surface to a plane. This transformation is necessary, because the source material for lots of workpieces like tubes, funnels nozzles, transition fits are based on planar sheets, boards or panels of synthetics. Metal sheet constructors , plumbers, shipbuilders, roofers, carpenters, model constructors are daily confronted with the problem to unfold difficult bodies. Whereas it is relative easy to unfold cylindric and prismatic bodies, it is very difficult to unfold rotation-surfaces, screwing-surfaces and surface-penetrations.  Free-Form-Surfaces. e.g. spanned synthetics, boat-frames etc.,  are a particular challenge for every engineer. Using classic drawing tools either it's not possible to unfold them or only by making huge time and constructive efforts.
Before using the computer as a consequence thereof the CAD-Technic, but also still today, the scriber supplies the basis of any unfolding. His spatial imaginative power, accurate working and not at all his many years of experience are necessary to generate the unfolding basing on the ready workpiece and to draw the 2D-cutting-sheets.
After cutting the material the required parts can be produced by bending, soldering, welding and adherence. Considering the workflow from all aspects the 2D-cutting sheet is one of the most important. An incorrect cutting-sheet requires always a costly reworking. According to the "try and error"-principle at this point isn't effective. Before the cutting can start an accurate drawing must be there.
In industry and crafts precise unfolding is the key-competence to meet the requirements of modern production. Getting the 2D-cuttings-sheets fast and correct is crucial factor for production.

In mathematics you can find methods for some special cases (like pipe-bends, T-pieces, Y-branch pipes etc.) to find templates for the cutting. These methods are often implemented in CAD-programs. But if in praxis constructions differ from this methods (e.g. free-form-surfaces, transition-fits, pipe-penetrations, letters, geographical reliefs ) you really need innovative solutions. Unfolding such things is only possible by dismantling in triangles. The surfaces to unfold is divided in lathy triangles, which will be laid together in the x-y-plane. Using this "triangulation" you can unfold most complexe bodies and surfaces. But in practise this method is only suitable to a limited extend without an computer because you can only get a limited numbers of triangles using the manual method and complex 3D-curves (splines) are hardly controllable.

Innovative Solution BLACK CAD V.6
Excatly for this "triangulation-method" we compiled a program running under AutoCADŽ / BricscadŽ.  The only conditions is that the surface to unfold got an upper and lower edge, which are linear-conform and the position of a welding seam is defined in the 3D-model. So you can get 2D-cutting-sheets for very complex bodies, created by transition-fits with the volume-modelling in  AutoCADŽ / BricscadŽ .