Pipe Cut Template Builder

Both cut types are the same problem: find where a cylinder's surface meets another surface, then unroll the cylinder flat. Unrolling is exact — a cylinder is a developable surface, so arc length around it becomes distance along the paper with no distortion whatsoever. A point at angle φ and axial position z lands at (R·φ, z), and the template is exactly π·OD wide.

The two profiles

Everything reduces to one function: the axial position of the cut as you go round the pipe. For an angled end cut, a plane tilted by θ from square gives a pure sinusoid, z = R·tan θ·(1 − sin φ). For a saddle, substituting the branch surface into the header's equation y² + z² = R_h² gives a quadratic whose relevant root is t = [√(R_h² − R²cos²φ) − R·sin φ·cos α] / sin α. Neither is a fitted curve or a table lookup; both follow directly from the geometry.

The two are not independent. Let the header grow without bound and its surface becomes a plane, so the saddle must reduce to the angled cut — and it does, at θ = 90° − α. That link is a test, and it is the test that caught a sign error which every other check passed: written with the wrong sign the miter is still a sinusoid of the right amplitude and period, so only the comparison against the saddle exposed that the same joint unwrapped mirrored depending on which mode you picked.

Why the export is approximate, and by how much

The intersection is solved analytically. The exported polyline is a sampled approximation of that curve, held within the maximum deviation you set.

So the question is not whether there is an error but whether it is bounded and reported. The sampler subdivides until no chord departs from the true curve by more than the deviation you asked for, putting vertices where the curvature is rather than spreading them evenly — which is why a template with a stated 0.05 mm needs a few hundred points rather than a few thousand. The achieved figure is then measured again afterwards, converging on the true maximum by search rather than reading it off the same grid the sampler used, so it is a check on the sampler rather than a restatement of its own stopping rule.

Most tools of this kind ask for a number of ordinates instead. That is a proxy for the thing that matters: on a 180 mm branch into a 200 mm header, sixteen ordinates is 2.46 mm out at its worst point — a visible scribing error, and nothing on screen says so. Asking for the deviation directly makes the trade-off the one you actually care about.

For marking by hand the tool does give ordinates, because a tape and a batten are what you have at the pipe. The table states the same figure for them — how far straight lines through the points would be from the true curve — so the choice of 8 or 32 points is an informed one. Counts are multiples of four, so with a named seam position and no extra rotation, the four quarter points of the cut always fall on a point.

The equal-diameter corner

When branch and header are the same size the intersection collapses to two flat ellipses that cross, so the cut has a genuine sharp corner on each side — the profile becomes R(|sin φ| − sin φ·cos α) / sin α, whose slope jumps where sin φ changes sign. Chord-tolerance subdivision cannot resolve a corner: it halves forever and still rounds the nose off. So those angles are declared in advance and a vertex is placed exactly on each. The tool tells you the corner is real rather than letting it look like a defect.

Angles, and saying which one

An angle field on a pipe tool is ambiguous unless it says what it is measured from, and both conventions are in common use. The cut angle here is measured from square, so 0° is a square cut. The branch angle is measured between the centrelines, so 90° is a square tee. Each has a diagram next to it rather than only a sentence.

A branch angle above 90° is accepted as typed rather than folded onto its supplement. 45° and 135° are the same physical joint measured to opposite ends of the header. The long and short seam references follow the joint, so with them the two templates come out identical; the side reference stays at the same angle, so with it the template runs the other way round the pipe — the same cut with the seam on the other side of the joint.

Printing

Each sheet is an SVG sized in millimetres with a viewBox spanning the same number of units, so one unit is one millimetre and the browser carries that to paper. Large pipes tile across several sheets with 10 mm of overlap and registration ticks to align to — ticks butt together far more accurately than cut paper edges. There is no PDF library involved: that would add a second rendering path outside the parity checks to make a file the browser prints anyway.

What no stylesheet can do is stop a print dialog applying "Fit to page". Hence the 100 mm ruler on every sheet. It costs nothing, and it turns "print at 100%" from an instruction you have to trust into one you can check with the tape already in your pocket.

What is in the file

One open POLYLINE on the CUT layer in DXF R12, and nothing else. Open rather than closed: joining the two ends would draw a straight line across the template that is not a cut. The seam edges and the datum line in the preview mark the boundary of the paper, not lines to cut on the pipe, and they are not exported. The vertices in the file are the same vertices the deviation figure was measured against — checked by re-parsing the file rather than by comparing objects in memory.