How the triangulation method works
The rectangle opening is split into four corners and the round into equal stations. Each corner fans to the stations in its quadrant, forming a near-conical corner that is rolled. Between corners, a flat triangle joins each rectangle side to the round. Because the round lies in a plane parallel to the rectangle and each side is aligned with an axis, that triangle touches the round exactly at 0°, 90°, 180° or 270°—even when the round is offset—so those stations are true tangent points. The pattern is laid out triangle by triangle from the true 3D length of every edge, starting and ending at the seam in the middle of a side.
Choosing divisions, seams and pieces
More round divisions shorten each chord: 24 stations leave a curved edge about 0.3% short of the true circumference, 48 about 0.07%. The summary reports the difference so you can fair a smooth curve through the stations. A one-piece pattern is easiest to assemble but needs the largest sheet; two or four pieces fit smaller stock and press brakes, with every seam placed on a flat side where it is easy to join.
Material thickness
Enter whether each opening is an inside, outside or mean dimension. The generator develops the neutral surface by adding or subtracting one thickness to the entered size, which suits thin gauge ductwork and hoppers. Height is applied as entered. For heavy plate, the neutral surface shifts with the forming method, so confirm with your shop’s development rules.
Fabrication boundary
This is an ideal-geometry layout aid, not a certified fabrication drawing. It does not add seam, lap, lock or flange allowances, collars, bend reliefs, kerf or springback compensation, and it does not check minimum bend radius, forming feasibility, pressure rating or code compliance. Patterns are developed on the neutral surface with straight chords along the round edge. Check the exported file in CAD, measure the scale square on printed pages, and make a test piece from scrap before cutting production material.
Frequently asked questions
How is a square-to-round transition developed?
By triangulation. Each rectangle corner fans to a quarter of the round, and a flat triangle joins each rectangle side to the point where it touches the round. The true 3D length of every line is laid out in sequence to produce the flat pattern.
Can the round be off-center?
Yes. Enter X and Y offsets for the round’s center. If the round extends past the rectangle in plan, one side leans outward; the generator still develops it and adds a warning.
Which dimensions should I enter for sheet thickness?
Choose inside, outside or mean for each opening. The neutral (mean) surface is developed by adding or subtracting one thickness.
Will the printed PDF be the right size?
The PDF is drawn at 1:1 in vector form. Print at 100% or actual size, then measure the 50 mm (or 2 in) scale-check square on the final assembly page before cutting.
Technical references
Triangulation of transition pieces is covered in classic sheet-metal pattern-development texts and in the SMACNA duct construction standards that define fittings such as square-to-round transitions. The DXF export uses the Autodesk DXF reference LINE entity on CUT, BEND and FORM layers.
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