The curve where two solids or pipes intersect, and the flat "unrolled" pattern a solid's surface develops into — cylinders, prisms, cones and pyramids.
Interpenetration and development aren't just exam topics — they're exactly how sheet-metal ducting, pipework and pressed-steel components are actually manufactured. A flat sheet of metal can only be cut, then bent or rolled; nobody can "cut" a finished 3D pipe directly out of stock. Every curved or angled duct, hopper or pipe fitting starts life as a flat development pattern, cut from sheet metal and then folded or rolled into its final shape.
Whenever two pipes or ducts meet — a T-junction, a Y-branch, an air-conditioning duct joining a main trunk — a fabricator needs the EXACT curve where their surfaces meet, so the branch piece can be cut to fit the main pipe perfectly, with no gaps to seal. That curve is the curve of interpenetration, found using the same 12-point method taught throughout this course.
Once the curve of interpenetration is known, the branch pipe itself still needs to be cut from a FLAT sheet before it's rolled into a cylinder. That means the interpenetration curve itself has to be transferred onto the pipe's OWN development — combining both techniques from this chapter into a single real fabrication drawing.
Each exercise below prints as a full-scale A3 sheet — the same format used in EGD practical assessments. The reference thumbnail shows the completed drawing; redraw it full-size on paper using correct line types and true measurements. Use your printer's "Actual Size" setting (not "Fit to Page").