FabLayout

Eccentric square to round calculator

For a square to round whose round end is off centre but still over the base: enter the rectangle, diameter, height and the x and y offset of the circle. One-piece triangulated pattern.

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1,217.1 mm702.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

621.3mm

Approximate, within ±2.9 mm

Cut length
In the app
Top edge (chords)
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Find the tangent points

    Draw the plan with the circle moved by ex and ey. On each side of the rectangle, mark the circle point where the tangent is parallel to that side.

  2. Divide the corner arcs

    Divide the arc between two tangent points into the chosen number of sections for each corner.

  3. Work out the true lengths

    For each corner, measure in plan to every point on its arc and combine with H; each corner has its own set of lengths.

  4. Lay out the strip

    Start with the seam line from the middle of an A side, then add corner fans and flat triangles in turn, each triangle from three true lengths.

  5. Close and finish

    End with the second half side and seam line, curve the round edge through its points and add your allowances.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: No published source checked for this shape. Method: outer envelope of the two openings (flat triangles and oblique cone corners), triangulated; checked against a separate reference implementation in Trueflat.

Method and formula

The surface is the outer envelope of the two openings: four flat triangles, one on each side of the rectangle, and four oblique cone pieces with their apex at the corners. Moving the circle makes every corner different, so the four fans and the four flat triangles all have their own lengths. The seam stays in the middle of an A side and runs up to the circle point where the tangent is parallel to that side.

  • Offsets: the circle centre must stay over the base, |ex| ≤ A/2 and |ey| ≤ B/2. Further out is a double-offset boot.
  • With ex = ey = 0 the pattern is identical to the centred square to round.
  • Accuracy: the round edge is drawn as n chords per corner, so it is shorter than πD by at most π³D ÷ (96 n²).

With sheet thickness and inside or outside dimensions, each opening is moved by one amount to the middle of the sheet. This is approximate: the calculator shows how far the opening can be off, and asks for middle-of-sheet dimensions if that is more than 1 mm.

Worked example

A = 600, B = 400, D = 300, H = 300 mm, ex = 80, ey = −40 mm, two sections per corner. The seam line from the middle of the near A side to the circle is √(80² + 10² + 300²) = 310.64 mm, so both seam edges total 621.29 mm. On the other three sides the lines from the middle to the tangent point are 310.64, 323.26 and 380.13 mm. The round edge in chords is 918.44 mm, 24.04 mm short of πD and inside the 24.22 mm bound.

Questions

How is this different from square to round and the double-offset boot?

Square to round has the circle centred over the rectangle. Here the circle may move anywhere as long as its centre stays over the base. If the round end has to sit further out, overhanging the rectangle, use the double-offset boot.

Is the pattern exact?

The flat triangles are exact. The cone corners are drawn with n chords per corner, so the round edge is short of πD by at most π³D ÷ (96 n²). Thickness conversion for inside or outside dimensions is approximate and the deviation is shown.

Why are all four corners different?

Moving the circle changes the plan distance from each corner to the circle, so each corner fan gets its own true lengths and each flat side its own height. Lay them out in order from the seam; do not copy one corner to the others.

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