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STEP import: spindle and horn tori, and a negative major radius
A TOROIDAL_SURFACE whose tube reaches its axis (major radius at most the minor, or written with a negative major radius) and a DEGENERATE_TOROIDAL_SURFACE were refused. They are read as what they are: the tube's meridian circle (centre C + R·X, its angle from X towards Z) revolved about the axis, the same points and normal as ISO 10303-42's formula, a negative R putting the tube's centre across the axis. A revolved circle or ellipse that meets its axis is now its whole arc on the face's side, pole to pole, in closed form (where s0 + M cos(t - phi) = 0), and its NURBS form is cut there exactly (Boehm knot insertion, bspline::segment): the parameter stays the quarter grid's, so the edges' forms and straight pcurves are unchanged, and the surface ends at the poles instead of running on to whole quarters past the axis (which folded the surface over itself, and left a face with one bound around the axis without its pole). The face's boundary picks the apple or the lemon. On Poppy Humanoid 22 solids were refused for these tori; with the SMLib fixes before this none of their torus faces fails: Poppy 42 -> 27 solids not imported, 194 -> 215 bodies. Tests (hand-written files, analytic answers): a horn torus round of radius 1 on a pin (V = 8 pi + pi(5/3 + pi/2)); a spindle torus pin end (major 1, minor 2, its apex in a dimple at z = sqrt 3, V = 3 sqrt3 pi + 8 pi^2/3 on the cylinder) as TOROIDAL and DEGENERATE_TOROIDAL, with a seam to the pole and with one bound; a nearly round end (0.005 / 0.345) in two halves with SolidWorks's apex vertex; the lemon of a spindle torus as one seam-bounded face with major radius -1 and as a degenerate torus with its lemon selected (V = pi(6 sqrt3 - 8 pi/3)). Volumes and areas within 1e-3. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01LUXeKMoxpM7Vuv8Rb6E3K2
This commit is contained in:
jyviko
@@ -1061,6 +1061,216 @@ fn horn_torus_written_as_one_spline_face() {
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assert!(rel(measure(&imp.bodies[0].body).unwrap().volume, v) < 1e-3);
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}
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/// How a torus-capped cylinder ([`torus_capped_cylinder`]) ends.
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enum Tip {
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/// The tube's quarter from its outside over to its top, at `z`, and a disc there of radius `r`.
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Disc { z: f64, r: f64 },
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/// The tube on to where it meets the axis: the pole, a vertex at height `apex` on the axis
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/// reached by the tube's meridian as the torus face's seam, or (`seam` false) not, its one
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/// bound the circle at z = 0.
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Pole { apex: f64, seam: bool },
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}
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/// A cylinder about Z of radius `major + minor` from z = -2 to 0, its top a torus about Z with
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/// those radii (`torus`: the surface entity at #5 on placement #4) ending as `tip` says.
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fn torus_capped_cylinder(torus: &str, major: f64, minor: f64, tip: Tip) -> String {
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let outer = major + minor;
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let mut t = String::from(HEAD);
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t += "#1=CARTESIAN_POINT('',(0.,0.,0.));\n#2=DIRECTION('',(0.,0.,1.));\n#3=DIRECTION('',(1.,0.,0.));\n#4=AXIS2_PLACEMENT_3D('',#1,#2,#3);\n";
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t += &format!("{torus}\n#6=CYLINDRICAL_SURFACE('',#4,{outer:.16});\n");
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t += "#7=CARTESIAN_POINT('',(0.,0.,-2.));\n#8=AXIS2_PLACEMENT_3D('',#7,#2,#3);\n#9=PLANE('',#8);\n";
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t += &format!(
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"#13=CARTESIAN_POINT('',({outer:.16},0.,-2.));\n#14=VERTEX_POINT('',#13);\n#15=CARTESIAN_POINT('',({outer:.16},0.,0.));\n#16=VERTEX_POINT('',#15);\n"
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);
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t += &format!(
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"#19=CIRCLE('',#8,{outer:.16});\n#20=EDGE_CURVE('',#14,#14,#19,.T.);\n#21=CIRCLE('',#4,{outer:.16});\n#22=EDGE_CURVE('',#16,#16,#21,.T.);\n"
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);
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t += "#25=VECTOR('',#2,1.);\n#26=LINE('',#13,#25);\n#27=EDGE_CURVE('',#14,#16,#26,.T.);\n";
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t += "#40=ORIENTED_EDGE('',*,*,#20,.F.);\n#41=EDGE_LOOP('',(#40));\n#42=FACE_OUTER_BOUND('',#41,.T.);\n#43=ADVANCED_FACE('',(#42),#9,.F.);\n";
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t += "#44=ORIENTED_EDGE('',*,*,#20,.T.);\n#45=ORIENTED_EDGE('',*,*,#27,.T.);\n#46=ORIENTED_EDGE('',*,*,#22,.F.);\n#47=ORIENTED_EDGE('',*,*,#27,.F.);\n";
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t += "#48=EDGE_LOOP('',(#44,#45,#46,#47));\n#49=FACE_OUTER_BOUND('',#48,.T.);\n#50=ADVANCED_FACE('',(#49),#6,.T.);\n#51=ORIENTED_EDGE('',*,*,#22,.T.);\n";
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// The tube's meridian at u = 0 from (outer, 0, 0) to `end`, the torus face's seam: centre
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// (major, 0, 0), angle from X towards Z (its axis -Y).
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let meridian = |t: &mut String, end: [f64; 2]| {
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*t += &format!("#17=CARTESIAN_POINT('',({:.16},0.,{:.16}));\n#18=VERTEX_POINT('',#17);\n", end[0], end[1]);
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*t += &format!(
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"#28=CARTESIAN_POINT('',({major:.16},0.,0.));\n#29=DIRECTION('',(0.,-1.,0.));\n#30=AXIS2_PLACEMENT_3D('',#28,#29,#3);\n#31=CIRCLE('',#30,{minor:.16});\n#32=EDGE_CURVE('',#16,#18,#31,.T.);\n"
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);
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*t += "#52=ORIENTED_EDGE('',*,*,#32,.T.);\n#54=ORIENTED_EDGE('',*,*,#32,.F.);\n";
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};
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let faces = match tip {
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Tip::Disc { z, r } => {
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meridian(&mut t, [r, z]);
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t += &format!("#10=CARTESIAN_POINT('',(0.,0.,{z:.16}));\n#11=AXIS2_PLACEMENT_3D('',#10,#2,#3);\n#12=PLANE('',#11);\n");
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t += &format!("#23=CIRCLE('',#11,{r:.16});\n#24=EDGE_CURVE('',#18,#18,#23,.T.);\n#53=ORIENTED_EDGE('',*,*,#24,.F.);\n");
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t += "#55=EDGE_LOOP('',(#51,#52,#53,#54));\n#56=FACE_OUTER_BOUND('',#55,.T.);\n#57=ADVANCED_FACE('',(#56),#5,.T.);\n";
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t += "#58=ORIENTED_EDGE('',*,*,#24,.T.);\n#59=EDGE_LOOP('',(#58));\n#60=FACE_OUTER_BOUND('',#59,.T.);\n#61=ADVANCED_FACE('',(#60),#12,.T.);\n";
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"#43,#50,#57,#61"
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}
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Tip::Pole { apex, seam } => {
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if seam {
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meridian(&mut t, [0.0, apex]);
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t += "#55=EDGE_LOOP('',(#51,#52,#54));\n";
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} else {
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t += "#55=EDGE_LOOP('',(#51));\n";
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}
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t += "#56=FACE_OUTER_BOUND('',#55,.T.);\n#57=ADVANCED_FACE('',(#56),#5,.T.);\n";
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"#43,#50,#57"
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}
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};
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t += &format!("#62=CLOSED_SHELL('',({faces}));\n#63=MANIFOLD_SOLID_BREP('Pin',#62);\n#64=ADVANCED_BREP_SHAPE_REPRESENTATION('',(#63),#70);\n");
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t += &context(70, "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))");
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t += TAIL;
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t
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}
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/// The one closed body of `text`, its volume and area against the closed forms; `warnings`
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/// the import's warnings.
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fn assert_closed_measures(text: &str, volume: f64, area: f64, warnings: &[&str]) {
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let imp = step_import(text).unwrap();
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assert_eq!(imp.bodies.len(), 1, "{:?}", imp.warnings);
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assert_eq!(imp.warnings, warnings, "{:?}", imp.warnings);
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assert!(imp.bodies[0].closed);
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let m = measure(&imp.bodies[0].body).unwrap();
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assert!(rel(m.volume, volume) < 1e-3, "volume {} vs {volume}", m.volume);
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assert!(rel(m.area, area) < 1e-3, "area {} vs {area}", m.area);
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}
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/// A horn torus (major radius = minor, its tube touching its axis) as a round of radius 1 on a
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/// cylinder of radius 2, from the cylinder's top edge over to a disc of radius 1 at z = 1 (a
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/// round pin tip). Under the round, the solid's radius at height z is 1 + √(1 − z²):
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/// V = 8π + π∫₀¹(1 + √(1 − z²))² dz = 8π + π(5/3 + π/2); the round's area is
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/// 2π∫₀^{π/2}(1 + cos v) dv = π² + 2π, with the cylinder's 8π and the discs' 4π and π.
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#[test]
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fn horn_torus_round_on_a_pin_imports_whole() {
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use std::f64::consts::PI;
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let t = torus_capped_cylinder("#5=TOROIDAL_SURFACE('',#4,1.,1.);", 1.0, 1.0, Tip::Disc { z: 1.0, r: 1.0 });
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assert_closed_measures(&t, 8.0 * PI + PI * (5.0 / 3.0 + PI / 2.0), 15.0 * PI + PI * PI, &[]);
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}
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/// The volume and area of a spindle torus's pin end ([`Tip::Pole`]): in the meridian plane the
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/// disc of radius `r` about (`major`, 0) above z = 0 and right of the axis, which the tube meets
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/// at z = c = √(r² − R²) (cos v = −R/r). With s = √(r² − z²) and S(a) = ∫₀^a s dz =
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/// (a√(r² − a²) + r² asin(a/r))/2: V = π∫₀^c (R + s)² dz + π∫_c^r 4Rs dz =
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/// π(R²c + r²c − c³/3 + 2R·S(c)) + 4πR(S(r) − S(c)); area 2πr(R·acos(−R/r) + c).
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fn pin_end(major: f64, r: f64) -> (f64, f64) {
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use std::f64::consts::PI;
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let c = (r * r - major * major).sqrt();
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let s = |a: f64| 0.5 * (a * (r * r - a * a).max(0.0).sqrt() + r * r * (a / r).asin());
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let volume = PI * (major * major * c + r * r * c - c.powi(3) / 3.0 + 2.0 * major * s(c)) + 4.0 * PI * major * (s(r) - s(c));
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(volume, 2.0 * PI * r * (major * (-major / r).acos() + c))
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}
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/// A spindle torus (major radius below the minor, its tube across its axis) as a pin's end: the
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/// apple's part from the cylinder at z = 0 up over the tube's top and down to where the tube
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/// meets the axis, a pole in a dimple ([`pin_end`], with the cylinder's side and its disc).
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/// Major 1, minor 2 (the tube meets the axis at z = √3: V = 3√3π + 8π²/3, area
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/// 4π(2π/3 + √3)), written as a TOROIDAL_SURFACE (as SolidWorks writes it) and as the schema's
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/// DEGENERATE_TOROIDAL_SURFACE, its apple selected; with a seam to the pole, and with the
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/// circle at z = 0 its one bound (the reader adds the seam).
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#[test]
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fn spindle_torus_pin_tip_imports_whole() {
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use std::f64::consts::PI;
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let s3 = 3f64.sqrt();
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let (volume, area) = pin_with_cylinder(1.0, 2.0);
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assert!(rel(volume, 18.0 * PI + 3.0 * s3 * PI + 8.0 * PI * PI / 3.0) < 1e-12 && rel(area, 21.0 * PI + 4.0 * PI * (2.0 * PI / 3.0 + s3)) < 1e-12);
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for torus in ["#5=TOROIDAL_SURFACE('',#4,1.,2.);", "#5=DEGENERATE_TOROIDAL_SURFACE('',#4,1.,2.,.T.);"] {
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for (seam, warnings) in [(true, &[][..]), (false, &["solid 'Pin': 1 seam edges added to faces that wind around their surface"][..])] {
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let t = torus_capped_cylinder(torus, 1.0, 2.0, Tip::Pole { apex: s3, seam });
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assert_closed_measures(&t, volume, area, warnings);
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}
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}
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}
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/// [`pin_end`] on its cylinder from z = -2 ([`torus_capped_cylinder`]): its volume and area.
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fn pin_with_cylinder(major: f64, minor: f64) -> (f64, f64) {
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use std::f64::consts::PI;
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let (v, a) = pin_end(major, minor);
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let outer = major + minor;
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(v + 2.0 * PI * outer * outer, a + 4.0 * PI * outer + PI * outer * outer)
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}
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/// A nearly round pin end as SolidWorks writes it: a spindle torus of major radius 0.005 and
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/// minor 0.345 on a cylinder of radius 0.35, its apple's part in two halves (u in [0, π] and
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/// [π, 2π]) between the meridians at u = 0 and π, which meet at an apex vertex written at the
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/// tube's top, z = 0.345: 3.6e-5 mm above the pole (z = √(0.345² − 0.005²)), in a file of
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/// uncertainty 1e-5 mm. The meridians end 1.7e-6 rad short of the pole, where the tube's
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/// circle about the axis is 1.2e-6 mm across: a pole to within the uncertainty, so each half's
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/// loop jumps from one meridian to the other there. Volume and area as [`pin_end`].
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#[test]
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fn nearly_round_spindle_torus_pin_end_in_halves_imports_whole() {
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let (major, minor) = (0.005, 0.345);
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let outer = major + minor;
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let mut t = String::from(HEAD);
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t += "#1=CARTESIAN_POINT('',(0.,0.,0.));\n#2=DIRECTION('',(0.,0.,1.));\n#3=DIRECTION('',(1.,0.,0.));\n#4=AXIS2_PLACEMENT_3D('',#1,#2,#3);\n";
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// The torus's angle from 45° below X: the halves are u in [π/4, 5π/4] and [5π/4, 9π/4] on
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// it, three quarters of its NURBS form each, the meridians two apart.
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t += "#88=DIRECTION('',(0.7071067811865476,-0.7071067811865476,0.));\n#89=AXIS2_PLACEMENT_3D('',#1,#2,#88);\n";
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t += &format!("#5=TOROIDAL_SURFACE('',#89,{major:.16},{minor:.16});\n#6=CYLINDRICAL_SURFACE('',#4,{outer:.16});\n");
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t += "#7=CARTESIAN_POINT('',(0.,0.,-2.));\n#8=AXIS2_PLACEMENT_3D('',#7,#2,#3);\n#9=PLANE('',#8);\n";
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t += &format!(
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"#13=CARTESIAN_POINT('',({outer:.16},0.,-2.));\n#14=VERTEX_POINT('',#13);\n#15=CARTESIAN_POINT('',({outer:.16},0.,0.));\n#16=VERTEX_POINT('',#15);\n"
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);
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t += &format!(
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"#65=CARTESIAN_POINT('',({:.16},0.,0.));\n#66=VERTEX_POINT('',#65);\n#17=CARTESIAN_POINT('',(0.,0.,{minor:.16}));\n#18=VERTEX_POINT('',#17);\n",
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-outer
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);
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t += &format!("#19=CIRCLE('',#8,{outer:.16});\n#20=EDGE_CURVE('',#14,#14,#19,.T.);\n#21=CIRCLE('',#4,{outer:.16});\n");
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t += "#22=EDGE_CURVE('',#16,#66,#21,.T.);\n#67=EDGE_CURVE('',#66,#16,#21,.T.);\n#25=VECTOR('',#2,1.);\n#26=LINE('',#13,#25);\n#27=EDGE_CURVE('',#14,#16,#26,.T.);\n";
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// The meridians, each angle from -Z: at u = 0 about (major, 0, 0) towards X (axis -Y); at
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// u = π about (-major, 0, 0) towards -X (axis +Y).
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t += "#82=DIRECTION('',(0.,0.,-1.));\n";
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t += &format!(
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"#28=CARTESIAN_POINT('',({major:.16},0.,0.));\n#29=DIRECTION('',(0.,-1.,0.));\n#30=AXIS2_PLACEMENT_3D('',#28,#29,#82);\n#31=CIRCLE('',#30,{minor:.16});\n#32=EDGE_CURVE('',#16,#18,#31,.T.);\n"
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);
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t += &format!(
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"#80=CARTESIAN_POINT('',({:.16},0.,0.));\n#81=DIRECTION('',(0.,1.,0.));\n#83=AXIS2_PLACEMENT_3D('',#80,#81,#82);\n#84=CIRCLE('',#83,{minor:.16});\n#85=EDGE_CURVE('',#66,#18,#84,.T.);\n",
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-major
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);
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t += "#40=ORIENTED_EDGE('',*,*,#20,.F.);\n#41=EDGE_LOOP('',(#40));\n#42=FACE_OUTER_BOUND('',#41,.T.);\n#43=ADVANCED_FACE('',(#42),#9,.F.);\n";
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t += "#44=ORIENTED_EDGE('',*,*,#20,.T.);\n#45=ORIENTED_EDGE('',*,*,#27,.T.);\n#46=ORIENTED_EDGE('',*,*,#67,.F.);\n#47=ORIENTED_EDGE('',*,*,#22,.F.);\n#48=ORIENTED_EDGE('',*,*,#27,.F.);\n";
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t += "#49=EDGE_LOOP('',(#44,#45,#46,#47,#48));\n#50=FACE_OUTER_BOUND('',#49,.T.);\n#51=ADVANCED_FACE('',(#50),#6,.T.);\n";
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t += "#52=ORIENTED_EDGE('',*,*,#22,.T.);\n#53=ORIENTED_EDGE('',*,*,#85,.T.);\n#54=ORIENTED_EDGE('',*,*,#32,.F.);\n#55=EDGE_LOOP('',(#52,#53,#54));\n#56=FACE_OUTER_BOUND('',#55,.T.);\n#57=ADVANCED_FACE('',(#56),#5,.T.);\n";
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t += "#58=ORIENTED_EDGE('',*,*,#67,.T.);\n#59=ORIENTED_EDGE('',*,*,#32,.T.);\n#60=ORIENTED_EDGE('',*,*,#85,.F.);\n#61=EDGE_LOOP('',(#58,#59,#60));\n#62=FACE_OUTER_BOUND('',#61,.T.);\n#63=ADVANCED_FACE('',(#62),#5,.T.);\n";
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t += "#64=CLOSED_SHELL('',(#43,#51,#57,#63));\n#86=MANIFOLD_SOLID_BREP('Pin',#64);\n#87=ADVANCED_BREP_SHAPE_REPRESENTATION('',(#86),#70);\n";
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t += &context(70, "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))").replace("LENGTH_MEASURE(1.E-6)", "LENGTH_MEASURE(1.E-5)");
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t += TAIL;
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let (volume, area) = pin_with_cylinder(major, minor);
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assert_closed_measures(&t, volume, area, &[]);
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}
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/// The lemon of a spindle torus (the tube's part across the axis: a closed surface with a pole
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/// at each end), one face bounded by its meridian used both ways, written with a negative major
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/// radius (-1, minor 2: the tube's centre on the other side of the axis, as some writers have
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/// it) and as the schema's DEGENERATE_TOROIDAL_SURFACE with its lemon selected (major radius 1,
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/// where the lemon is the tube's far side, R + r cos v < 0, and the surface's normal
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/// ∂S/∂u × ∂S/∂v points into it: `same_sense` .F.). Its radius at height z is √(4 − z²) − 1
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/// for |z| ≤ √3: V = π∫(5 − z² − 2√(4 − z²)) dz = π(6√3 − 8π/3); area
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/// 2π∫_{−π/3}^{π/3}(2 cos v − 1)·2 dv = 4π(2√3 − 2π/3).
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#[test]
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fn spindle_torus_lemon_with_a_negative_major_radius_imports_whole() {
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use std::f64::consts::PI;
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let s3 = 3f64.sqrt();
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for (torus, sense) in [("#5=TOROIDAL_SURFACE('',#4,-1.,2.);", "T"), ("#5=DEGENERATE_TOROIDAL_SURFACE('',#4,1.,2.,.F.);", "F")] {
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let mut t = String::from(HEAD);
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t += "#1=CARTESIAN_POINT('',(0.,0.,0.));\n#2=DIRECTION('',(0.,0.,1.));\n#3=DIRECTION('',(1.,0.,0.));\n#4=AXIS2_PLACEMENT_3D('',#1,#2,#3);\n";
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t += torus;
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// The meridian at u = 0: the circle about (-1, 0, 0) from v = -π/3 to π/3, angle from X
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// towards Z (its axis -Y).
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t += &format!(
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"\n#6=CARTESIAN_POINT('',(0.,0.,{:.16}));\n#7=VERTEX_POINT('',#6);\n#8=CARTESIAN_POINT('',(0.,0.,{s3:.16}));\n#9=VERTEX_POINT('',#8);\n",
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-s3
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);
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t += "#10=CARTESIAN_POINT('',(-1.,0.,0.));\n#11=DIRECTION('',(0.,-1.,0.));\n#12=AXIS2_PLACEMENT_3D('',#10,#11,#3);\n#13=CIRCLE('',#12,2.);\n#14=EDGE_CURVE('',#7,#9,#13,.T.);\n";
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t += "#15=ORIENTED_EDGE('',*,*,#14,.T.);\n#16=ORIENTED_EDGE('',*,*,#14,.F.);\n#17=EDGE_LOOP('',(#15,#16));\n#18=FACE_OUTER_BOUND('',#17,.T.);\n";
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t += &format!("#19=ADVANCED_FACE('',(#18),#5,.{sense}.);\n");
|
||||
t += "#20=CLOSED_SHELL('',(#19));\n#21=MANIFOLD_SOLID_BREP('Lemon',#20);\n#22=ADVANCED_BREP_SHAPE_REPRESENTATION('',(#21),#70);\n";
|
||||
t += &context(70, "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))");
|
||||
t += TAIL;
|
||||
assert_closed_measures(&t, PI * (6.0 * s3 - 8.0 * PI / 3.0), 4.0 * PI * (2.0 * s3 - 2.0 * PI / 3.0), &[]);
|
||||
}
|
||||
}
|
||||
|
||||
/// Booleans and blends build the same body every time, so an export is byte-identical from
|
||||
/// run to run (an export once listed a boolean's faces in hash order of their addresses). The
|
||||
/// tee of oracle 35 with its rolling-ball fillet round the junction.
|
||||
|
||||
@@ -668,8 +668,10 @@ impl<'a> Reader<'a> {
|
||||
"TOROIDAL_SURFACE" | "DEGENERATE_TOROIDAL_SURFACE" => {
|
||||
let major_radius = self.length(p.get(2), "major radius")?;
|
||||
let minor_radius = positive(self.length(p.get(3), "minor radius")?, "torus minor radius")?;
|
||||
if major_radius < 0.0 {
|
||||
return Err("torus major radius must not be negative".into());
|
||||
// A negative major radius (outside the schema, which some writers use for a
|
||||
// spindle torus) is the same formula: its tube on the other side of the axis.
|
||||
if !major_radius.is_finite() {
|
||||
return Err("torus major radius must be finite".into());
|
||||
}
|
||||
let position = position(self)?;
|
||||
if e.name() == "DEGENERATE_TOROIDAL_SURFACE" {
|
||||
|
||||
@@ -323,23 +323,101 @@ fn revolution(profile: &Curve, axis: &Axis1, ext: &Extent) -> R<BSurface> {
|
||||
Some(r) => Span::Open { inner: r, outer: r },
|
||||
None => span(&ts, &seam, is_closed(c))?,
|
||||
};
|
||||
// Stop where the profile crosses the axis outside the face.
|
||||
// Stop where the profile meets the axis outside the face: a circle or ellipse that
|
||||
// meets it is its whole arc on the face's side, pole to pole (closed form), so a face
|
||||
// with one bound around the axis reaches its pole and nothing folds over; another
|
||||
// profile stops where it crosses.
|
||||
let face_mid = match s {
|
||||
Span::Open { inner, .. } => 0.5 * (inner.0 + inner.1),
|
||||
Span::Turn { start } => start + (mid - start).rem_euclid(TAU),
|
||||
};
|
||||
let arc = conic_side_arc(c, o, e, face_mid);
|
||||
let side = |t: f64| probe(t).map(|q| (q - o).dot(e));
|
||||
let s = match s {
|
||||
Span::Open { inner, outer } => {
|
||||
let s = match (s, arc) {
|
||||
(_, Some(arc)) => Span::Open { inner: arc, outer: arc },
|
||||
(Span::Open { inner, outer }, None) => {
|
||||
let lo = crossing(&side, inner.0, outer.0).unwrap_or(outer.0);
|
||||
let hi = crossing(&side, inner.1, outer.1).unwrap_or(outer.1);
|
||||
Span::Open { inner, outer: (lo, hi) }
|
||||
}
|
||||
turn => turn,
|
||||
(turn, None) => turn,
|
||||
};
|
||||
bounded(c, s)?
|
||||
let curve = bounded(c, s)?;
|
||||
match arc {
|
||||
Some(arc) => clip_form(curve, arc)?,
|
||||
None => curve,
|
||||
}
|
||||
}
|
||||
};
|
||||
let identity = [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]];
|
||||
Ok(BSurface::PlacedRevolution { profile: Box::new(curve), origin: p3(o), axis: p3(k), matrix: identity, forward: false })
|
||||
}
|
||||
|
||||
/// A torus whose tube reaches its axis (a spindle or horn torus: major radius at most the
|
||||
/// minor, or written with a negative major radius, its tube on the other side of the axis) as
|
||||
/// what it is, its tube's meridian circle revolved about its axis: ISO 10303-42 gives the torus
|
||||
/// `C + (R + r cos v)(cos u X + sin u Y) + r sin v Z`, the revolution of the circle about `C`'s
|
||||
/// Z through `C + R X` with the same normal (∂S/∂u × ∂S/∂v). The revolution keeps the tube's
|
||||
/// arc on the face's side of the axis, pole to pole (`revolution`): the face's boundary, not a
|
||||
/// degenerate torus's `select_outer`, says which part (the apple or the lemon) it is on.
|
||||
fn torus_revolved(position: &Placement, major: f64, minor: f64, ext: &Extent) -> R<BSurface> {
|
||||
// The circle in the X–Z half-plane: its parameter from X towards Z, as the torus's v.
|
||||
let circle = Curve::Circle {
|
||||
position: Placement {
|
||||
origin: crate::geom::add(position.origin, crate::geom::scale(position.ref_direction, major)),
|
||||
axis: crate::geom::scale(position.y(), -1.0),
|
||||
ref_direction: position.ref_direction,
|
||||
},
|
||||
radius: minor,
|
||||
};
|
||||
revolution(&circle, &Axis1 { origin: position.origin, direction: position.axis }, ext)
|
||||
}
|
||||
|
||||
/// The arc of a circle or ellipse profile on the positive side of the plane through the axis
|
||||
/// point `o` square to `e` (the face's side of its axis), as angles: the one round `near`, its
|
||||
/// ends where the profile meets that plane; `None` for another profile, or one that does not
|
||||
/// meet it. On the conic `O + a cos t X + b sin t Y` the side is `s₀ + A cos t + B sin t =
|
||||
/// s₀ + M cos(t − φ)`, zero at `φ ± acos(−s₀/M)`; a profile that only touches the axis (a horn
|
||||
/// torus's tube) has its arc a whole turn, both ends at the touching point.
|
||||
fn conic_side_arc(c: &Curve, o: Vec3, e: Vec3, near: f64) -> Option<(f64, f64)> {
|
||||
let (position, a, b) = match c {
|
||||
Curve::Circle { position, radius } => (position, *radius, *radius),
|
||||
Curve::Ellipse { position, semi_axis_1, semi_axis_2 } => (position, *semi_axis_1, *semi_axis_2),
|
||||
_ => return None,
|
||||
};
|
||||
let s0 = (v3(position.origin) - o).dot(e);
|
||||
let (ca, cb) = (a * v3(position.ref_direction).dot(e), b * v3(position.y()).dot(e));
|
||||
let m = ca.hypot(cb);
|
||||
let ratio = -s0 / m;
|
||||
if !(m > 0.0 && (-1.0..=1.0).contains(&ratio)) {
|
||||
return None;
|
||||
}
|
||||
let half = ratio.acos();
|
||||
let phi = cb.atan2(ca);
|
||||
let centre = phi + ((near - phi) / TAU).round() * TAU;
|
||||
(centre.is_finite() && half > 0.0).then_some((centre - half, centre + half))
|
||||
}
|
||||
|
||||
/// A conic's NURBS form (on its quarter grid) cut to the angles `arc` where it reaches past
|
||||
/// them: the same curve at the same parameters (`bspline::segment`, exact knot insertion), so
|
||||
/// it keeps the grid its edges' forms share and stops where the profile meets the axis.
|
||||
fn clip_form(curve: BCurve, (a0, a1): (f64, f64)) -> R<BCurve> {
|
||||
use solidcraft_geom::bspline::{HPoint, segment};
|
||||
let BCurve::RationalSpline { knots, homogeneous } = curve else { return Ok(curve) };
|
||||
let (Some(&k0), Some(&k1)) = (knots.first(), knots.last()) else { return Err("a profile without knots".into()) };
|
||||
let (lo, hi) = (solidcraft_geom::brep::form::param(a0).max(k0), solidcraft_geom::brep::form::param(a1).min(k1));
|
||||
if lo <= k0 && hi >= k1 {
|
||||
return Ok(BCurve::RationalSpline { knots, homogeneous });
|
||||
}
|
||||
if !(lo < hi) {
|
||||
return Err(unsupported("a revolved profile on its axis"));
|
||||
}
|
||||
let degree = knots.len().checked_sub(homogeneous.len() + 1).ok_or("a profile's knots")?;
|
||||
let ctrl: Vec<HPoint> = homogeneous.iter().map(|h| HPoint { x: h[0], y: h[1], z: h[2], w: h[3] }).collect();
|
||||
let (knots, ctrl) = segment(degree, &knots, &ctrl, lo, hi).map_err(|e| format!("a revolved profile cut at its axis: {e}"))?;
|
||||
Ok(BCurve::RationalSpline { knots, homogeneous: ctrl.iter().map(|h| [h.x, h.y, h.z, h.w]).collect() })
|
||||
}
|
||||
|
||||
/// Going from `from` (where `side` is positive or zero) towards `to`, the first parameter
|
||||
/// where `side` reaches zero, if it does.
|
||||
fn crossing(side: &dyn Fn(f64) -> Option<f64>, from: f64, to: f64) -> Option<f64> {
|
||||
@@ -561,11 +639,13 @@ fn map_surface_in(s: &Surface, ext: &Extent, tol: f64, depth: usize, reversed: &
|
||||
Surface::Sphere { position, radius } => BSurface::Sphere { frame: frame(position), radius: *radius },
|
||||
Surface::Torus { position, major_radius, minor_radius } => {
|
||||
if !(major_radius > minor_radius) {
|
||||
return Err(unsupported("a spindle or horn torus"));
|
||||
return torus_revolved(position, *major_radius, *minor_radius, ext);
|
||||
}
|
||||
BSurface::Torus { frame: frame(position), major_radius: *major_radius, minor_radius: *minor_radius }
|
||||
}
|
||||
Surface::DegenerateTorus { .. } => return Err(unsupported("DEGENERATE_TOROIDAL_SURFACE")),
|
||||
Surface::DegenerateTorus { position, major_radius, minor_radius, .. } => {
|
||||
return torus_revolved(position, *major_radius, *minor_radius, ext);
|
||||
}
|
||||
Surface::BSpline(b) => super::map_bspline_surface(b)?,
|
||||
Surface::RectangularTrimmed { basis, .. } => map_surface_in(basis, ext, tol, depth + 1, reversed)?,
|
||||
Surface::Revolution { profile, axis } => revolution(profile, axis, ext)?,
|
||||
|
||||
Reference in New Issue
Block a user