* Add a one-surface fill of closed 3D loops to geom
A closed loop of curves that does not lie in a plane has no exact surface;
the usual answer is one smooth face fitted over it. fill_loop does that:
- the loop's best-fit plane (Newell normal), with a frame chosen from the
loop itself so the result does not depend on where the loop starts, its
direction, or where the part sits
- the loop seen along that normal must be simple and must not fold or run
along the normal; otherwise it is refused ("not supported yet"), never
filled with wrong geometry
- one non-rational bicubic B-spline height field over the loop's box,
fitted by least squares to the loop's samples (The NURBS Book 9.4.1,
9.4.3, eq. 9.62/9.65) with a thin-plate smoothness term
lambda*A*int(h_uu^2 + 2 h_uv^2 + h_vv^2), A one grid cell's area, so the
fit is the same at any scale; only planes are reproduced exactly
- span counts per direction (long narrow loops fit), refined until the
loop is within tolerance, else refused with the deviation reached
bspline: bisected span search, basis functions on a stack array, one
clamping helper shared by curves and surfaces, one binomial helper.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
* Patch fills non-planar loops of edges with one smooth face (#250)
surface.patch with edges refused any loop that is not planar ("not
supported yet: patching a loop that is not planar"). It now fills it:
- planar loops still get one exact planar face, but planarity is certified
conservatively: lines by their ends, B-spline/NURBS edges by their control
points, intersection curves by their samples lying on a support plane
within tolerance; a loop that can't be certified is filled instead
- other loops get one face from geom's fill_loop, bounded by the body's own
chained edges, whole (no split): its history is one generated face whose
edges are the body's, and it stitches back into a closed solid
- intersection-curve edges are sampled by a seeded, guarded double
projection shared by the planarity test and the fill (plane_fit)
- the face tolerance is 10x the planarity tolerance (documented: later
operations take the face to contain its edges within it)
- edge picking runs inside the guard; the geom->truck conversion is shared
with the T-spline sheets (spline_conv); the Newell plane fit is shared with
STEP import
Tests: 3- to 8-sided, concave (dart, arrow, plus), flat-corner, two-edge and
imported rims fill as one face and stitch closed (volumes against an
independent integral); finite mesh normals, same result for any pick order
or placement; non-height-field loops and too-fine detail are refused.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
* Test the Patch dialog filling a non-planar loop of picked edges
The Patch dialog's only test used a sketch profile. Picking the four
curved rim edges of a box cut by a sideways cylinder now makes one
surface.patch command whose result is a single smooth face over the rim.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
---------
Co-authored-by: Claude Opus 5.5 <[email protected]>
This commit is contained in:
Irakli KourtisandClaude Opus 5.5 authored and GitHub committed
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201e9d5f9f
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-146
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@@ -13,7 +13,7 @@ pub static COMMANDS: &[CommandSpec] = &[
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CommandSpec::new("surface.patch", "Patch", patch)
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CommandSpec::new("surface.patch", "Patch", patch)
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.at("SURFACE", "CREATE")
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.at("SURFACE", "CREATE")
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.icon("patch")
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.icon("patch")
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.params("sketch?: id|name and profiles? (planar patches of sketch regions) | edges: [[x,y,z]] (points on a closed loop of a body's edges) and body?; name?, body_name?"),
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.params("sketch?: id|name and profiles? (planar patches of sketch regions) | edges: [[x,y,z]] (points on a closed loop of a body's edges: one face on them, planar when the loop is, else a smooth B-spline surface) and body?; name?, body_name?"),
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CommandSpec::new("surface.stitch", "Stitch", stitch)
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CommandSpec::new("surface.stitch", "Stitch", stitch)
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.at("SURFACE", "MODIFY")
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.at("SURFACE", "MODIFY")
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.icon("stitch")
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.icon("stitch")
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@@ -129,7 +129,8 @@ mod tests {
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solidcraft_kernel::measure(&st.body(name).unwrap().body).unwrap().volume
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solidcraft_kernel::measure(&st.body(name).unwrap().body).unwrap().volume
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}
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}
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/// A rectangle patched, trimmed by a plane and thickened; a box's faces stitched back.
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/// A rectangle patched, trimmed by a plane and thickened; a box's open top patched; a rim
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/// that is not planar patched.
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#[test]
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#[test]
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fn patch_trim_thicken_and_stitch() {
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fn patch_trim_thicken_and_stitch() {
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let mut s = Session::default();
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let mut s = Session::default();
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@@ -148,6 +149,24 @@ mod tests {
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run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [20, 0, 0], "body_name": "Cup"}));
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run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [20, 0, 0], "body_name": "Cup"}));
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run(&mut s, "surface.patch", json!({"edges": [[25, 0, 10], [30, 5, 10], [25, 10, 10], [20, 5, 10]], "body": "Cup", "body_name": "Lid"}));
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run(&mut s, "surface.patch", json!({"edges": [[25, 0, 10], [30, 5, 10], [25, 10, 10], [20, 5, 10]], "body": "Cup", "body_name": "Lid"}));
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assert!(s.world_state().body("Lid").unwrap().body.is_surface());
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assert!(s.world_state().body("Lid").unwrap().body.is_surface());
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// A rim that is not planar: a box with its top cut away by a sideways cylinder.
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run(&mut s, "solid.box", json!({"length": 28, "width": 28, "height": 20, "corner": [-14, -14, 0], "body_name": "Saddle"}));
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run(
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&mut s,
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"solid.cylinder",
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json!({"radius": 40, "height": 120, "base": [0, -60, 50], "axis": "Y", "operation": "cut", "targets": ["Saddle"]}),
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);
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let z = |x: f64| 50.0 - (1600.0 - x * x).sqrt();
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let rim = json!([[14, 0, z(14.0)], [0, 14, z(0.0)], [-14, 0, z(-14.0)], [0, -14, z(0.0)]]);
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run(&mut s, "surface.patch", json!({"edges": rim, "body": "Saddle", "body_name": "Cover"}));
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let st = s.world_state();
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let cover = &st.body("Cover").unwrap().body;
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assert!(cover.is_surface() && cover.face_count() == 1);
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// The cover is a smooth surface on the rim, close to the cylinder that cut it (its area
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// within 1% of the cylinder's inside the rim).
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let area = solidcraft_kernel::measure(cover).unwrap().area;
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let want = 28.0 * 40.0 * 2.0 * (14.0f64 / 40.0).asin();
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assert!((area - want).abs() < want * 1e-2, "{area} vs {want}");
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assert!(s.execute("surface.thicken", &json!({"bodies": ["Nope"], "thickness": 1})).is_err());
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assert!(s.execute("surface.thicken", &json!({"bodies": ["Nope"], "thickness": 1})).is_err());
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assert!(s.execute("surface.trim", &json!({"body": "Sheet"})).is_err());
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assert!(s.execute("surface.trim", &json!({"body": "Sheet"})).is_err());
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}
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}
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+111
-67
@@ -154,6 +154,18 @@ pub fn check_knots(knots: &[f64]) -> SplineResult<()> {
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/// A knot vector shorter than two knots gives zeros.
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/// A knot vector shorter than two knots gives zeros.
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pub fn local_basis(knots: &[f64], u: f64, side: Side, n: usize) -> Vec<f64> {
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pub fn local_basis(knots: &[f64], u: f64, side: Side, n: usize) -> Vec<f64> {
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let mut out = vec![0.0; n + 1];
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let mut out = vec![0.0; n + 1];
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let ders = local_basis_array(knots, u, side, n);
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for (o, d) in out.iter_mut().zip(ders) {
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*o = d;
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}
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out
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}
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/// [`local_basis`] into a fixed array (no allocation): element `k` is the `k`-th derivative,
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/// for `k ≤ min(n, MAX_SPLINE_DEGREE)`, the rest zero.
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pub(crate) fn local_basis_array(knots: &[f64], u: f64, side: Side, n: usize) -> [f64; MAX_SPLINE_DEGREE + 1] {
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const W: usize = MAX_SPLINE_DEGREE + 1;
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let mut out = [0.0; W];
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let Some(p) = knots.len().checked_sub(2) else { return out };
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let Some(p) = knots.len().checked_sub(2) else { return out };
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if p > MAX_SPLINE_DEGREE || !u.is_finite() {
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if p > MAX_SPLINE_DEGREE || !u.is_finite() {
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return out;
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return out;
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@@ -163,7 +175,6 @@ pub fn local_basis(knots: &[f64], u: f64, side: Side, n: usize) -> Vec<f64> {
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// table[k][j]: k-th derivative of N_{j,q} for the current degree q (j = 0..=p−q), updated
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// table[k][j]: k-th derivative of N_{j,q} for the current degree q (j = 0..=p−q), updated
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// in place: k descending (level k reads level k−1 of the previous degree), j ascending
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// in place: k descending (level k reads level k−1 of the previous degree), j ascending
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// (N_{j,q} reads N_{j+1,q−1}, not yet overwritten). Derivatives above p are zero.
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// (N_{j,q} reads N_{j+1,q−1}, not yet overwritten). Derivatives above p are zero.
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const W: usize = MAX_SPLINE_DEGREE + 1;
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let levels = n.min(p);
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let levels = n.min(p);
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let mut table = [[0.0f64; W]; W];
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let mut table = [[0.0f64; W]; W];
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for (j, slot) in table[0].iter_mut().enumerate().take(p + 1) {
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for (j, slot) in table[0].iter_mut().enumerate().take(p + 1) {
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@@ -286,15 +297,16 @@ pub fn find_span(knots: &[f64], p: usize, n: usize, u: f64) -> Option<usize> {
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if u < lo || u > hi {
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if u < lo || u > hi {
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return None;
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return None;
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}
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}
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// The last non-empty span in [p, n−1] that starts at or before u.
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// The last non-empty span in [p, n−1] that starts at or before u: by bisection (the knots
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let mut k = p;
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// are sorted), and at the domain end the last non-empty span.
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for i in p..n {
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let mut k = if u >= hi {
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if let (Some(&a), Some(&b)) = (knots.get(i), knots.get(i + 1))
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n - 1
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&& a <= u
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} else {
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&& a < b
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let below = knots.get(p..n)?.partition_point(|&x| x <= u);
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{
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p + below.checked_sub(1)?
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k = i;
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};
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}
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while k > p && !(knots.get(k)? < knots.get(k + 1)?) {
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k -= 1;
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}
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}
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Some(k)
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Some(k)
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}
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}
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@@ -331,16 +343,62 @@ pub fn insert_knot(p: usize, knots: &[f64], ctrl: &[HPoint], u: f64) -> SplineRe
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Ok((nk, q))
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Ok((nk, q))
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}
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}
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/// The binomial coefficient `(n k)` (zero for `k > n`).
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pub(crate) fn binomial(n: usize, k: usize) -> f64 {
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if k > n {
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return 0.0;
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}
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(0..k).fold(1.0, |c, m| c * (n - m) as f64 / (m + 1) as f64)
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}
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/// Bernstein polynomial `Bᵢ,ₚ(x)`.
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/// Bernstein polynomial `Bᵢ,ₚ(x)`.
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pub fn bernstein(p: usize, i: usize, x: f64) -> f64 {
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pub fn bernstein(p: usize, i: usize, x: f64) -> f64 {
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if i > p {
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if i > p {
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return 0.0;
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return 0.0;
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}
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}
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let mut c = 1.0;
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binomial(p, i) * x.powi(i as i32) * (1.0 - x).powi((p - i) as i32)
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for m in 0..i {
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}
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c = c * (p - m) as f64 / (m + 1) as f64;
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/// One row of a B-spline (degree `p`, knots, homogeneous control points) clamped on its domain
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/// `[knots[p], knots[n]]`: each domain end inserted until it repeats `p` times (§5.2), then the
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/// basis functions that vanish on the domain dropped (a basis function's last span does not
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/// depend on its first knot, so that knot moves to the domain end). The curve on the domain is
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/// unchanged.
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pub(crate) fn clamp_row(p: usize, knots: &[f64], row: &[HPoint]) -> SplineResult<(Vec<f64>, Vec<HPoint>)> {
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let n = row.len();
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let (Some(&a), Some(&b)) = (knots.get(p), knots.get(n)) else { return invalid("too few knots") };
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let (mut knots, mut row) = (knots.to_vec(), row.to_vec());
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for (at_end, x) in [(false, a), (true, b)] {
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let mult = |k: &[f64]| k.iter().filter(|&&y| y == x).count();
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let mut guard = 0;
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while mult(&knots) < p {
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guard += 1;
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if guard > MAX_SPLINE_DEGREE + 1 {
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return invalid("clamping did not converge");
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}
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(knots, row) = insert_knot(p, &knots, &row, x)?;
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}
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let n = row.len();
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let (first, last) = if at_end {
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// Functions i with i ≥ (first index of x) start at or past the end.
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(0, knots.iter().position(|&y| y == x).unwrap_or(n).min(n))
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} else {
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// Functions i with i + p + 1 ≤ (last index of x) end at or before the start.
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(knots.iter().rposition(|&y| y == x).unwrap_or(p).saturating_sub(p), n)
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};
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if last <= first + p {
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return invalid("too few control points remain after clamping");
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}
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let mut nk: Vec<f64> = knots.get(first..last + p + 1).map(<[f64]>::to_vec).unwrap_or_default();
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if at_end {
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nk.last_mut().into_iter().for_each(|y| *y = x);
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} else {
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nk.first_mut().into_iter().for_each(|y| *y = x);
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}
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row = row.get(first..last).map(<[HPoint]>::to_vec).unwrap_or_default();
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knots = nk;
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}
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}
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c * x.powi(i as i32) * (1.0 - x).powi((p - i) as i32)
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Ok((knots, row))
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}
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}
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/// A Bézier curve's point at `x ∈ [0, 1]` (de Casteljau, NURBS Book §1.4).
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/// A Bézier curve's point at `x ∈ [0, 1]` (de Casteljau, NURBS Book §1.4).
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@@ -543,66 +601,37 @@ impl NurbsSurface {
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}
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}
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/// The same surface on the same domain with clamped knot vectors (`p+1` equal knots at
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/// The same surface on the same domain with clamped knot vectors (`p+1` equal knots at
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/// each end, so the boundary curves are given by the boundary rows of control points):
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/// each end, so the boundary curves are given by the boundary rows of control points): each
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/// insert each domain end until it has multiplicity `p`, then drop the basis functions
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/// row of control points clamped in turn ([`clamp_row`]).
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/// that vanish on the domain (NURBS Book §5.2 knot insertion; a basis function's last span
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/// does not depend on its first knot, so that knot can be moved to the domain end).
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pub fn clamped(&self) -> SplineResult<NurbsSurface> {
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pub fn clamped(&self) -> SplineResult<NurbsSurface> {
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let mut s = self.clone();
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let mut s = self.clone();
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for dir in [Dir::S, Dir::T] {
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for d in 0..2 {
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let d = dir.pick(0, 1);
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let p = s.degree[d];
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let p = s.degree[d];
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for end in 0..2 {
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let [nu, nv] = s.count;
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let a = s.domain()[d][end];
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let (lines, len) = if d == 0 { (nv, nu) } else { (nu, nv) };
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while s.knots[d].iter().filter(|&&x| x == a).count() < p {
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let mut knots = Vec::new();
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s = s.insert_knot(dir, a)?;
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let mut rows = Vec::with_capacity(lines);
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}
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for line in 0..lines {
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s = s.trim_end(d, end, a)?;
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let row: Vec<HPoint> = (0..len).map(|k| if d == 0 { s.point(k, line) } else { s.point(line, k) }).collect();
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let (k, r) = clamp_row(p, &s.knots[d], &row)?;
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knots = k;
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rows.push(r);
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}
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}
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let new_len = rows.first().map_or(0, Vec::len);
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let mut ctrl = Vec::with_capacity(lines * new_len);
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if d == 0 {
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rows.iter().for_each(|r| ctrl.extend_from_slice(r));
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} else {
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for j in 0..new_len {
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ctrl.extend(rows.iter().map(|r| r.get(j).copied().unwrap_or(HPoint::ZERO)));
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}
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}
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let mut all = s.knots.clone();
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all[d] = knots;
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s = NurbsSurface::from_homogeneous(s.degree, all, ctrl)?;
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}
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}
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Ok(s)
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Ok(s)
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}
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}
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/// Drop the basis functions that vanish on the domain past the knot `a` (multiplicity ≥ p)
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/// at the start (`end == 0`) or the end of direction `d`.
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fn trim_end(&self, d: usize, end: usize, a: f64) -> SplineResult<NurbsSurface> {
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let p = self.degree[d];
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let kn = &self.knots[d];
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let n = self.count[d];
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let (first, last) = match end {
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0 => {
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let last_a = kn.iter().rposition(|&x| x == a).ok_or_else(|| SplineError::Invalid("clamp".into()))?;
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// Functions i with i + p + 1 ≤ last_a vanish on [a, …).
|
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(last_a.saturating_sub(p), n)
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}
|
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_ => {
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let first_a = kn.iter().position(|&x| x == a).ok_or_else(|| SplineError::Invalid("clamp".into()))?;
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// Functions i with i ≥ first_a vanish on (…, a].
|
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(0, first_a.min(n))
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}
|
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};
|
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if last <= first + p {
|
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return invalid("clamp: too few control points remain");
|
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}
|
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let mut knots = self.knots.clone();
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|
||||||
let mut nk: Vec<f64> = kn.get(first..last + p + 1).map(<[f64]>::to_vec).unwrap_or_default();
|
|
||||||
match end {
|
|
||||||
0 => nk.first_mut().into_iter().for_each(|x| *x = a),
|
|
||||||
_ => nk.last_mut().into_iter().for_each(|x| *x = a),
|
|
||||||
}
|
|
||||||
knots[d] = nk;
|
|
||||||
let [nu, nv] = self.count;
|
|
||||||
let mut ctrl = Vec::new();
|
|
||||||
for j in 0..nv {
|
|
||||||
for i in 0..nu {
|
|
||||||
let k = if d == 0 { i } else { j };
|
|
||||||
if k >= first && k < last {
|
|
||||||
ctrl.push(self.point(i, j));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
NurbsSurface::from_homogeneous(self.degree, knots, ctrl)
|
|
||||||
}
|
|
||||||
}
|
}
|
||||||
|
|
||||||
#[cfg(test)]
|
#[cfg(test)]
|
||||||
@@ -666,6 +695,21 @@ pub(crate) mod tests {
|
|||||||
assert!(worst < 1e-5, "derivative error {worst}");
|
assert!(worst < 1e-5, "derivative error {worst}");
|
||||||
}
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn span_search_finds_the_last_non_empty_span_at_or_before_u() {
|
||||||
|
let p = 3;
|
||||||
|
let knots = [0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 0.5, 0.9, 0.9, 0.9, 1.0, 1.0, 1.0, 1.0];
|
||||||
|
let n = knots.len() - p - 1;
|
||||||
|
for k in 0..=1000 {
|
||||||
|
let u = k as f64 / 1000.0;
|
||||||
|
// The plain search: the last span [knots[i], knots[i+1]) with knots[i] ≤ u.
|
||||||
|
let want = (p..n).filter(|&i| knots[i] <= u && knots[i] < knots[i + 1]).max().unwrap();
|
||||||
|
assert_eq!(find_span(&knots, p, n, u), Some(want), "u = {u}");
|
||||||
|
}
|
||||||
|
assert_eq!(find_span(&knots, p, n, 1.5), None);
|
||||||
|
assert_eq!(find_span(&knots, p, n, f64::NAN), None);
|
||||||
|
}
|
||||||
|
|
||||||
#[test]
|
#[test]
|
||||||
fn single_function_knot_insertion_is_exact() {
|
fn single_function_knot_insertion_is_exact() {
|
||||||
let mut rng = Lcg(7);
|
let mut rng = Lcg(7);
|
||||||
|
|||||||
@@ -0,0 +1,742 @@
|
|||||||
|
//! Filling a closed loop of curves with one surface: a non-rational bicubic B-spline height
|
||||||
|
//! field over the loop's best-fit plane, fitted to the loop by least squares with a smoothness
|
||||||
|
//! term. A loop that cannot be seen as the boundary of a height field over that plane (it
|
||||||
|
//! crosses itself, folds back or runs along the plane's normal when seen along that normal) is
|
||||||
|
//! refused, never filled with wrong geometry.
|
||||||
|
//!
|
||||||
|
//! References: Piegl & Tiller, *The NURBS Book* (2nd ed.) — §9.4.1 and §9.4.3 (least squares
|
||||||
|
//! approximation: minimise the sum of squared residuals, eq. 9.62, through the normal
|
||||||
|
//! equations, eq. 9.65), §3.4 (tensor product B-spline surfaces), §3.3 (derivative of a
|
||||||
|
//! B-spline curve, eq. 3.4: control values at the knot averages reproduce a linear function),
|
||||||
|
//! A2.1 (span search).
|
||||||
|
|
||||||
|
use crate::Vec3;
|
||||||
|
use crate::bspline::{HPoint, NurbsSurface, Side, SplineError, SplineResult, find_span, invalid, local_basis_array};
|
||||||
|
|
||||||
|
/// Most loop points a fill takes.
|
||||||
|
pub const MAX_LOOP_POINTS: usize = 8192;
|
||||||
|
/// Most spans of the height field in each direction.
|
||||||
|
pub const MAX_FILL_SPANS: usize = 32;
|
||||||
|
/// Fewest spans of the height field in each direction (the first fit tried).
|
||||||
|
const MIN_FILL_SPANS: usize = 4;
|
||||||
|
/// The smoothness energy's terms: `(order in u, order in v, weight)` of `∫∫ (∂ h)²`.
|
||||||
|
const ENERGY: [(usize, usize, f64); 3] = [(2, 0, 1.0), (1, 1, 2.0), (0, 2, 1.0)];
|
||||||
|
/// Four-point Gauss–Legendre nodes and weights on `[−1, 1]` (exact to degree 7).
|
||||||
|
const GAUSS4: [(f64, f64); 4] = [
|
||||||
|
(-0.861_136_311_594_052_6, 0.347_854_845_137_453_8),
|
||||||
|
(-0.339_981_043_584_856_3, 0.652_145_154_862_546_2),
|
||||||
|
(0.339_981_043_584_856_3, 0.652_145_154_862_546_2),
|
||||||
|
(0.861_136_311_594_052_6, 0.347_854_845_137_453_8),
|
||||||
|
];
|
||||||
|
/// The smoothness term's weight per fitted point (see [`fill_loop`]).
|
||||||
|
const SMOOTHNESS: f64 = 1e-7;
|
||||||
|
/// A loop step shorter than this fraction of its length in space, seen along the normal, runs
|
||||||
|
/// along the normal (steeper than about 87° from the plane).
|
||||||
|
const MIN_STEP_SLOPE: f64 = 0.05;
|
||||||
|
/// Consecutive steps closer to reversed than this cosine fold the loop back on itself.
|
||||||
|
const FOLD_COS: f64 = -0.999;
|
||||||
|
|
||||||
|
/// A loop's fill: the surface (`S(u, v) = o + u·x + v·y + h(u, v)·n` over the plane with normal
|
||||||
|
/// `n`, so `∂S/∂u × ∂S/∂v` points along `n`), the plane's frame, whether the loop runs counter-
|
||||||
|
/// clockwise about it, the largest distance from a sampled loop point to the surface along `n`,
|
||||||
|
/// and how many points of the loop were evaluated.
|
||||||
|
#[derive(Clone, Debug, PartialEq)]
|
||||||
|
pub struct LoopFill {
|
||||||
|
pub surface: NurbsSurface,
|
||||||
|
/// The plane's origin and its axes `x`, `y` (the surface's parameter directions).
|
||||||
|
pub origin: Vec3,
|
||||||
|
pub axes: [Vec3; 2],
|
||||||
|
pub normal: Vec3,
|
||||||
|
pub counter_clockwise: bool,
|
||||||
|
pub deviation: f64,
|
||||||
|
pub evaluations: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Fill the closed loop of `sides` curves (side `k` given by `point(k, t)`, `t` from 0 at its
|
||||||
|
/// start to 1 at its end, which is where side `k+1` starts) with one surface passing within
|
||||||
|
/// `tol` of the loop.
|
||||||
|
///
|
||||||
|
/// - Sampling: each side at `t = i/s` (fitted) and halfway between (checked), `s` from 16
|
||||||
|
/// doubling while the fit needs denser points, at most [`MAX_LOOP_POINTS`] points in all. The
|
||||||
|
/// sample parameters are the same run either way, so the fill does not depend on where the
|
||||||
|
/// loop starts or which way it runs.
|
||||||
|
/// - The plane: through the fitted points' centroid, normal by Newell's method, turned so that
|
||||||
|
/// its largest component is positive; its first axis points to the fitted point farthest from
|
||||||
|
/// the centroid in the plane (the highest of points as far). So the plane and its axes, and with them the grid and the fill,
|
||||||
|
/// move with the loop (a reflected axis gives the same grid).
|
||||||
|
/// - Refused ("not supported yet"): a loop that, seen along the normal, has a step much shorter
|
||||||
|
/// than in space (it runs along the normal), turns straight back, or crosses or touches
|
||||||
|
/// itself; such a loop does not bound a height field over the plane.
|
||||||
|
/// - The height field: a bicubic B-spline with uniform knots over the projected loop's box
|
||||||
|
/// (widened by 1%); its control points sit at the knot averages in the plane, so its surface
|
||||||
|
/// parameters are plane coordinates, and their heights are the unknowns. The heights minimise
|
||||||
|
/// `Σ (h(uₖ, vₖ) − hₖ)² + λ·A · ∫∫ h_uu² + 2·h_uv² + h_vv²` over the fitted points — least
|
||||||
|
/// squares (eq. 9.62, normal equations eq. 9.65) plus the thin-plate bending energy over the
|
||||||
|
/// box, `A` the area of one grid cell (so each cell's energy counts like a squared second
|
||||||
|
/// difference of heights, and the balance is the same at any size). The energy decides the
|
||||||
|
/// inside, where there are no points; it is zero only for planes, so a plane through the
|
||||||
|
/// loop is reproduced exactly, and any other rim gets the least-bending surface on it, which
|
||||||
|
/// is free to turn at the rim (it is not the surface that made the rim). It does not depend
|
||||||
|
/// on the grid's directions. `λ = 10⁻⁷ ·` (fitted points) `/` (control points): just enough
|
||||||
|
/// to fix the inside, small enough not to pull the surface off the loop.
|
||||||
|
/// - Grids of 4, 8, 16, 32 spans across the box's longer side are tried, with as many across
|
||||||
|
/// the shorter side as keep the cells about square; a grid whose cells are under twice the
|
||||||
|
/// fitted points' largest step in a direction (cells between points would be left to the
|
||||||
|
/// energy alone) waits for denser sampling. The first grid within `tol` of every sampled
|
||||||
|
/// point (measured along the normal, which bounds the distance) is the fill; otherwise the
|
||||||
|
/// sampling doubles, and when that runs out, "not supported yet" with the closest deviation
|
||||||
|
/// reached.
|
||||||
|
pub fn fill_loop(sides: usize, point: &mut dyn FnMut(usize, f64) -> Option<Vec3>, tol: f64) -> SplineResult<LoopFill> {
|
||||||
|
if sides == 0 || sides.saturating_mul(16) > MAX_LOOP_POINTS / 2 {
|
||||||
|
return Err(SplineError::TooLarge(format!("a loop of {sides} sides (at most {})", MAX_LOOP_POINTS / 32)));
|
||||||
|
}
|
||||||
|
if !(tol.is_finite() && tol > 0.0) {
|
||||||
|
return invalid("the fill tolerance must be positive");
|
||||||
|
}
|
||||||
|
let mut evaluations = 0usize;
|
||||||
|
let mut eval = |k: usize, t: f64| -> SplineResult<Vec3> {
|
||||||
|
evaluations += 1;
|
||||||
|
point(k, t).filter(|p| p.is_finite()).ok_or_else(|| SplineError::Invalid(format!("side {k} has no finite point at {t}")))
|
||||||
|
};
|
||||||
|
let mut per = 16usize;
|
||||||
|
// Fitted points: side by side, per side at i/per (i < per).
|
||||||
|
let mut fit: Vec<Vec3> = Vec::with_capacity(sides * per);
|
||||||
|
for k in 0..sides {
|
||||||
|
for i in 0..per {
|
||||||
|
fit.push(eval(k, i as f64 / per as f64)?);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
let mut deviation = f64::INFINITY;
|
||||||
|
loop {
|
||||||
|
let mut check = Vec::with_capacity(fit.len());
|
||||||
|
for k in 0..sides {
|
||||||
|
for i in 0..per {
|
||||||
|
check.push(eval(k, (i as f64 + 0.5) / per as f64)?);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// The loop in order: fitted and checked points alternating.
|
||||||
|
let all: Vec<Vec3> = fit.iter().zip(&check).flat_map(|(a, b)| [*a, *b]).collect();
|
||||||
|
match fit_once(&fit, &all, tol)? {
|
||||||
|
Fit::Done(mut fill) => {
|
||||||
|
fill.evaluations = evaluations;
|
||||||
|
return Ok(*fill);
|
||||||
|
}
|
||||||
|
Fit::Denser(dev) => deviation = deviation.min(dev),
|
||||||
|
Fit::Exhausted(dev) => {
|
||||||
|
deviation = deviation.min(dev);
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if all.len() * 2 > MAX_LOOP_POINTS {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
fit = all;
|
||||||
|
per *= 2;
|
||||||
|
}
|
||||||
|
Err(SplineError::Unsupported(format!("filling a loop this wavy with one surface (it stays {deviation:e} off the loop, tolerance {tol:e})")))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// What one round of [`fill_loop`] gave.
|
||||||
|
enum Fit {
|
||||||
|
Done(Box<LoopFill>),
|
||||||
|
/// Within tolerance only with cells finer than the points allow: sample denser.
|
||||||
|
Denser(f64),
|
||||||
|
/// The finest grid tried is not within tolerance.
|
||||||
|
Exhausted(f64),
|
||||||
|
}
|
||||||
|
|
||||||
|
/// One round of [`fill_loop`]: fit the points `fit`, check every point of `all` (the loop in
|
||||||
|
/// order, `fit` among them).
|
||||||
|
fn fit_once(fit: &[Vec3], all: &[Vec3], tol: f64) -> SplineResult<Fit> {
|
||||||
|
let m = fit.len();
|
||||||
|
let o = fit.iter().fold(Vec3::ZERO, |a, p| a + *p) / m as f64;
|
||||||
|
let at = |k: usize| fit.get(k % m).copied().unwrap_or(Vec3::ZERO);
|
||||||
|
let area = (0..m).fold(Vec3::ZERO, |a, k| a + (at(k) - o).cross(at(k + 1) - o));
|
||||||
|
let Some(normal) = area.normalized() else { return invalid("the loop encloses no area") };
|
||||||
|
let largest = [normal.x, normal.y, normal.z].into_iter().fold(0.0f64, |a, c| if c.abs() > a.abs() { c } else { a });
|
||||||
|
let counter_clockwise = largest > 0.0;
|
||||||
|
let n = if counter_clockwise { normal } else { normal * -1.0 };
|
||||||
|
// The first axis towards the fitted point farthest from the centroid in the plane: the axes,
|
||||||
|
// the grid and so the fill move with the loop.
|
||||||
|
let flat = |p: &Vec3| {
|
||||||
|
let d = *p - o;
|
||||||
|
d - n * d.dot(n)
|
||||||
|
};
|
||||||
|
// Points as far as each other (within rounding) are told apart by their height, and points
|
||||||
|
// alike in both by their coordinates: the same point is chosen however the loop is given,
|
||||||
|
// and as the loop moves, but for ties its symmetry makes.
|
||||||
|
let key = |p: &Vec3| (flat(p).len(), (*p - o).dot(n));
|
||||||
|
let reach = fit.iter().map(|p| key(p).0).fold(0.0, f64::max);
|
||||||
|
let near = 1e-9 * reach;
|
||||||
|
let far = fit.iter().fold(None::<&Vec3>, |best, p| match best {
|
||||||
|
None => Some(p),
|
||||||
|
Some(b) => {
|
||||||
|
let ((db, hb), (dp, hp)) = (key(b), key(p));
|
||||||
|
let better = if (dp - db).abs() > near {
|
||||||
|
dp > db
|
||||||
|
} else if (hp - hb).abs() > near {
|
||||||
|
hp > hb
|
||||||
|
} else {
|
||||||
|
(p.x, p.y, p.z) > (b.x, b.y, b.z)
|
||||||
|
};
|
||||||
|
Some(if better { p } else { b })
|
||||||
|
}
|
||||||
|
});
|
||||||
|
let far = far.map(flat).unwrap_or(Vec3::ZERO);
|
||||||
|
let x = far.normalized().ok_or_else(|| SplineError::Invalid("the loop has no extent in its plane".into()))?;
|
||||||
|
let y = n.cross(x);
|
||||||
|
let project = |pts: &[Vec3]| -> (Vec<[f64; 2]>, Vec<f64>) {
|
||||||
|
(pts.iter().map(|p| [(*p - o).dot(x), (*p - o).dot(y)]).collect(), pts.iter().map(|p| (*p - o).dot(n)).collect())
|
||||||
|
};
|
||||||
|
let (uv, h) = project(all);
|
||||||
|
check_projectable(all, &uv)?;
|
||||||
|
let (fuv, fh) = project(fit);
|
||||||
|
let (mut lo, mut hi) = ([f64::INFINITY; 2], [f64::NEG_INFINITY; 2]);
|
||||||
|
for q in &uv {
|
||||||
|
for d in 0..2 {
|
||||||
|
lo[d] = lo[d].min(q[d]);
|
||||||
|
hi[d] = hi[d].max(q[d]);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for d in 0..2 {
|
||||||
|
let pad = 0.01 * (hi[d] - lo[d]);
|
||||||
|
lo[d] -= pad;
|
||||||
|
hi[d] += pad;
|
||||||
|
}
|
||||||
|
if !(lo[0] < hi[0] && lo[1] < hi[1] && (hi[0] - lo[0]).is_finite() && (hi[1] - lo[1]).is_finite()) {
|
||||||
|
return invalid("the loop's extent is not finite");
|
||||||
|
}
|
||||||
|
// Spans per direction: `level` across the longer side of the box, as many across the
|
||||||
|
// shorter as keep the cells about square (at least one). A grid finer than the fitted
|
||||||
|
// points can hold in a direction (cells under twice their largest step along it) is tried
|
||||||
|
// only after denser sampling; the coarsest is always tried.
|
||||||
|
let extent = [hi[0] - lo[0], hi[1] - lo[1]];
|
||||||
|
let mut step = [0.0f64; 2];
|
||||||
|
for k in 0..m {
|
||||||
|
let (p, q) = (fuv.get(k).copied().unwrap_or([0.0; 2]), fuv.get((k + 1) % m).copied().unwrap_or([0.0; 2]));
|
||||||
|
for d in 0..2 {
|
||||||
|
step[d] = step[d].max((q[d] - p[d]).abs());
|
||||||
|
}
|
||||||
|
}
|
||||||
|
let longer = extent[0].max(extent[1]);
|
||||||
|
let mut deviation = f64::INFINITY;
|
||||||
|
let mut level = MIN_FILL_SPANS;
|
||||||
|
while level <= MAX_FILL_SPANS {
|
||||||
|
let spans = [0, 1].map(|d| ((extent[d] / longer * level as f64).ceil() as usize).clamp(1, level));
|
||||||
|
let holds = (0..2).all(|d| extent[d] / spans[d] as f64 >= 2.0 * step[d]);
|
||||||
|
if !holds && level > MIN_FILL_SPANS {
|
||||||
|
return Ok(Fit::Denser(deviation));
|
||||||
|
}
|
||||||
|
let grid = Grid::new(spans, lo, hi);
|
||||||
|
let heights = grid.fit(&fuv, &fh)?;
|
||||||
|
let dev = uv.iter().zip(&h).map(|(q, hk)| (grid.height(&heights, *q) - hk).abs()).fold(0.0, f64::max);
|
||||||
|
if !dev.is_finite() {
|
||||||
|
return invalid("the fit is not finite");
|
||||||
|
}
|
||||||
|
deviation = deviation.min(dev);
|
||||||
|
if dev <= tol && holds {
|
||||||
|
let surface = grid.surface(&heights, o, x, y, n)?;
|
||||||
|
let fill = LoopFill { surface, origin: o, axes: [x, y], normal: n, counter_clockwise, deviation: dev, evaluations: 0 };
|
||||||
|
return Ok(Fit::Done(Box::new(fill)));
|
||||||
|
}
|
||||||
|
if !holds {
|
||||||
|
return Ok(Fit::Denser(deviation));
|
||||||
|
}
|
||||||
|
level *= 2;
|
||||||
|
}
|
||||||
|
Ok(Fit::Exhausted(deviation))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Refuse a loop that does not bound a height field over its plane (see [`fill_loop`]).
|
||||||
|
fn check_projectable(points: &[Vec3], uv: &[[f64; 2]]) -> SplineResult<()> {
|
||||||
|
let m = uv.len();
|
||||||
|
let q = |k: usize| uv.get(k % m).copied().unwrap_or([0.0; 2]);
|
||||||
|
let p = |k: usize| points.get(k % m).copied().unwrap_or(Vec3::ZERO);
|
||||||
|
let step = |k: usize| {
|
||||||
|
let (a, b) = (q(k), q(k + 1));
|
||||||
|
[b[0] - a[0], b[1] - a[1]]
|
||||||
|
};
|
||||||
|
for k in 0..m {
|
||||||
|
let d = step(k);
|
||||||
|
let flat = d[0].hypot(d[1]);
|
||||||
|
let space = p(k).dist(p(k + 1));
|
||||||
|
if space > 0.0 && flat < MIN_STEP_SLOPE * space {
|
||||||
|
return Err(SplineError::Unsupported("filling a loop that runs along its plane's normal".into()));
|
||||||
|
}
|
||||||
|
let e = step(k + 1);
|
||||||
|
let fe = e[0].hypot(e[1]);
|
||||||
|
if flat > 0.0 && fe > 0.0 && (d[0] * e[0] + d[1] * e[1]) < FOLD_COS * flat * fe {
|
||||||
|
return Err(SplineError::Unsupported("filling a loop that folds back on itself".into()));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// Non-adjacent segments must not meet: a sweep over the segments' u extents.
|
||||||
|
let mut segs: Vec<(f64, f64, usize)> = (0..m)
|
||||||
|
.map(|k| {
|
||||||
|
let (a, b) = (q(k), q(k + 1));
|
||||||
|
(a[0].min(b[0]), a[0].max(b[0]), k)
|
||||||
|
})
|
||||||
|
.collect();
|
||||||
|
segs.sort_by(|a, b| a.0.total_cmp(&b.0));
|
||||||
|
for (i, &(_, hi, k)) in segs.iter().enumerate() {
|
||||||
|
for &(lo2, _, l) in segs.get(i + 1..).into_iter().flatten() {
|
||||||
|
if lo2 > hi {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
let adjacent = (k + 1) % m == l || (l + 1) % m == k;
|
||||||
|
if !adjacent && segments_meet(q(k), q(k + 1), q(l), q(l + 1)) {
|
||||||
|
return Err(SplineError::Unsupported("filling a loop that crosses itself seen along its plane's normal".into()));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
Ok(())
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Whether the closed segments `ab` and `cd` share a point.
|
||||||
|
fn segments_meet(a: [f64; 2], b: [f64; 2], c: [f64; 2], d: [f64; 2]) -> bool {
|
||||||
|
let orient = |p: [f64; 2], q: [f64; 2], r: [f64; 2]| (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0]);
|
||||||
|
let within =
|
||||||
|
|p: [f64; 2], q: [f64; 2], r: [f64; 2]| r[0] >= p[0].min(q[0]) && r[0] <= p[0].max(q[0]) && r[1] >= p[1].min(q[1]) && r[1] <= p[1].max(q[1]);
|
||||||
|
let (d1, d2, d3, d4) = (orient(c, d, a), orient(c, d, b), orient(a, b, c), orient(a, b, d));
|
||||||
|
if ((d1 > 0.0 && d2 < 0.0) || (d1 < 0.0 && d2 > 0.0)) && ((d3 > 0.0 && d4 < 0.0) || (d3 < 0.0 && d4 > 0.0)) {
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
(d1 == 0.0 && within(c, d, a)) || (d2 == 0.0 && within(c, d, b)) || (d3 == 0.0 && within(a, b, c)) || (d4 == 0.0 && within(a, b, d))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A bicubic height field's grid: uniform clamped knots over `[lo, hi]` in each direction,
|
||||||
|
/// `count` control points along each.
|
||||||
|
struct Grid {
|
||||||
|
knots: [Vec<f64>; 2],
|
||||||
|
count: [usize; 2],
|
||||||
|
}
|
||||||
|
|
||||||
|
impl LoopFill {
|
||||||
|
/// The surface's point over (or under) `p`, along the normal.
|
||||||
|
pub fn point_over(&self, p: Vec3) -> SplineResult<Vec3> {
|
||||||
|
let d = p - self.origin;
|
||||||
|
let [x, y] = self.axes;
|
||||||
|
self.surface.eval(d.dot(x), d.dot(y))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Grid {
|
||||||
|
fn new(spans: [usize; 2], lo: [f64; 2], hi: [f64; 2]) -> Grid {
|
||||||
|
let knots = [0, 1].map(|d| {
|
||||||
|
let (a, b, s) = (lo[d], hi[d], spans[d]);
|
||||||
|
let mut k = vec![a; 4];
|
||||||
|
k.extend((1..s).map(|i| a + (b - a) * i as f64 / s as f64));
|
||||||
|
k.extend([b; 4]);
|
||||||
|
k
|
||||||
|
});
|
||||||
|
Grid { knots, count: spans.map(|s| s + 3) }
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The length of one span in direction `d`.
|
||||||
|
fn cell(&self, d: usize) -> f64 {
|
||||||
|
let (Some(k), Some(&c)) = (self.knots.get(d), self.count.get(d)) else { return 0.0 };
|
||||||
|
(k.last().copied().unwrap_or(0.0) - k.first().copied().unwrap_or(0.0)) / (c - 3) as f64
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The knot average `(kᵢ₊₁ + kᵢ₊₂ + kᵢ₊₃)/3` of control point `i` in direction `d`.
|
||||||
|
fn average(&self, d: usize, i: usize) -> f64 {
|
||||||
|
self.knots.get(d).map_or(0.0, |k| (1..=3).map(|t| k.get(i + t).copied().unwrap_or(0.0)).sum::<f64>() / 3.0)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The four non-zero basis functions' `r`-th derivatives and the first index, at `x` in
|
||||||
|
/// direction `d`.
|
||||||
|
fn basis_derivative(&self, d: usize, x: f64, r: usize) -> Option<(usize, [f64; 4])> {
|
||||||
|
let kn = self.knots.get(d)?;
|
||||||
|
let x = x.clamp(*kn.first()?, *kn.last()?);
|
||||||
|
let span = find_span(kn, 3, *self.count.get(d)?, x)?;
|
||||||
|
let side = if x >= *kn.last()? { Side::Left } else { Side::Right };
|
||||||
|
let first = span.checked_sub(3)?;
|
||||||
|
let mut out = [0.0; 4];
|
||||||
|
for (a, o) in out.iter_mut().enumerate() {
|
||||||
|
*o = kn.get(first + a..first + a + 5).map_or(0.0, |l| local_basis_array(l, x, side, r).get(r).copied().unwrap_or(0.0));
|
||||||
|
}
|
||||||
|
Some((first, out))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The height at `q` of the net `heights` (i fastest).
|
||||||
|
fn height(&self, heights: &[f64], q: [f64; 2]) -> f64 {
|
||||||
|
let (Some((i0, bu)), Some((j0, bv))) = (self.basis_derivative(0, q[0], 0), self.basis_derivative(1, q[1], 0)) else { return f64::NAN };
|
||||||
|
let mut s = 0.0;
|
||||||
|
for (b, wv) in bv.iter().enumerate() {
|
||||||
|
for (a, wu) in bu.iter().enumerate() {
|
||||||
|
s += wu * wv * heights.get((j0 + b) * self.count[0] + i0 + a).copied().unwrap_or(f64::NAN);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
s
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The control heights fitting the points (see [`fill_loop`]): the normal equations, banded
|
||||||
|
/// (unknowns i fastest, so coupled unknowns are at most `3·count[0] + 3` apart), solved by
|
||||||
|
/// Cholesky factorisation.
|
||||||
|
fn fit(&self, uv: &[[f64; 2]], h: &[f64]) -> SplineResult<Vec<f64>> {
|
||||||
|
let [cu, cv] = self.count;
|
||||||
|
let n = cu * cv;
|
||||||
|
let mut band = Band::new(n, 3 * cu + 3);
|
||||||
|
let mut rhs = vec![0.0; n];
|
||||||
|
let mut fitted = 0usize;
|
||||||
|
for (q, hk) in uv.iter().zip(h) {
|
||||||
|
let (Some((i0, bu)), Some((j0, bv))) = (self.basis_derivative(0, q[0], 0), self.basis_derivative(1, q[1], 0)) else {
|
||||||
|
return invalid("a loop point is off the grid");
|
||||||
|
};
|
||||||
|
let mut terms = [(0usize, 0.0f64); 16];
|
||||||
|
for (t, slot) in terms.iter_mut().enumerate() {
|
||||||
|
let (a, b) = (t % 4, t / 4);
|
||||||
|
*slot = ((j0 + b) * cu + i0 + a, bu.get(a).copied().unwrap_or(0.0) * bv.get(b).copied().unwrap_or(0.0));
|
||||||
|
}
|
||||||
|
for &(r, wr) in &terms {
|
||||||
|
if let Some(slot) = rhs.get_mut(r) {
|
||||||
|
*slot += wr * hk;
|
||||||
|
}
|
||||||
|
for &(s, ws) in &terms {
|
||||||
|
band.add(r, s, wr * ws);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
fitted += 1;
|
||||||
|
}
|
||||||
|
// The thin-plate energy ∫∫ h_uu² + 2·h_uv² + h_vv² over the grid's box, times the area of
|
||||||
|
// one cell: per cell that is the squared second difference of the heights, so it weighs
|
||||||
|
// against the data term (squared heights) alike at any size. Each term is a product of
|
||||||
|
// one-direction Gram matrices of the basis functions' derivatives.
|
||||||
|
let lambda = SMOOTHNESS * fitted as f64 / n as f64 * self.cell(0) * self.cell(1);
|
||||||
|
let gram = |d: usize, r: usize| -> Vec<f64> {
|
||||||
|
let c = self.count.get(d).copied().unwrap_or(0);
|
||||||
|
let mut g = vec![0.0; c * c];
|
||||||
|
let Some(k) = self.knots.get(d) else { return g };
|
||||||
|
for w in k.windows(2) {
|
||||||
|
let &[a, b] = w else { continue };
|
||||||
|
if !(b > a) {
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
for (gx, gw) in GAUSS4 {
|
||||||
|
let x = 0.5 * (a + b) + 0.5 * (b - a) * gx;
|
||||||
|
let Some((first, vals)) = self.basis_derivative(d, x, r) else { continue };
|
||||||
|
for (i, vi) in vals.iter().enumerate() {
|
||||||
|
for (j, vj) in vals.iter().enumerate() {
|
||||||
|
if let Some(slot) = g.get_mut((first + i) * c + first + j) {
|
||||||
|
*slot += 0.5 * (b - a) * gw * vi * vj;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
g
|
||||||
|
};
|
||||||
|
let grams: [[Vec<f64>; 3]; 2] = [0, 1].map(|d| [0, 1, 2].map(|r| gram(d, r)));
|
||||||
|
let g = |d: usize, r: usize, i: usize, k: usize| {
|
||||||
|
let c = self.count.get(d).copied().unwrap_or(0);
|
||||||
|
grams.get(d).and_then(|m| m.get(r)).and_then(|m| m.get(i * c + k)).copied().unwrap_or(0.0)
|
||||||
|
};
|
||||||
|
for j in 0..cv {
|
||||||
|
for i in 0..cu {
|
||||||
|
let r = j * cu + i;
|
||||||
|
for l in j.saturating_sub(3)..(j + 4).min(cv) {
|
||||||
|
for k in i.saturating_sub(3)..(i + 4).min(cu) {
|
||||||
|
let e: f64 = ENERGY.iter().map(|&(ru, rv, w)| w * g(0, ru, i, k) * g(1, rv, j, l)).sum();
|
||||||
|
band.add(r, l * cu + k, lambda * e);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
band.solve(rhs)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The surface of the net `heights` over the plane `o`, `x`, `y`, `n`: control point `(i, j)`
|
||||||
|
/// at the knot averages `(ξᵢ, ηⱼ)` in the plane, `heights[j·count[0] + i]` along `n`.
|
||||||
|
fn surface(&self, heights: &[f64], o: Vec3, x: Vec3, y: Vec3, n: Vec3) -> SplineResult<NurbsSurface> {
|
||||||
|
let [cu, cv] = self.count;
|
||||||
|
let mut ctrl = Vec::with_capacity(cu * cv);
|
||||||
|
for j in 0..cv {
|
||||||
|
for i in 0..cu {
|
||||||
|
let hij = heights.get(j * cu + i).copied().unwrap_or(f64::NAN);
|
||||||
|
ctrl.push(HPoint::weighted(o + x * self.average(0, i) + y * self.average(1, j) + n * hij, 1.0));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
NurbsSurface::from_homogeneous([3, 3], self.knots.clone(), ctrl)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A symmetric banded matrix: the upper band, row `r` holding columns `r ..= r + bw`.
|
||||||
|
struct Band {
|
||||||
|
n: usize,
|
||||||
|
bw: usize,
|
||||||
|
a: Vec<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Band {
|
||||||
|
fn new(n: usize, bw: usize) -> Band {
|
||||||
|
Band { n, bw, a: vec![0.0; n * (bw + 1)] }
|
||||||
|
}
|
||||||
|
fn index(&self, r: usize, s: usize) -> Option<usize> {
|
||||||
|
let (r, s) = if r <= s { (r, s) } else { (s, r) };
|
||||||
|
(s - r <= self.bw && s < self.n).then_some(r * (self.bw + 1) + (s - r))
|
||||||
|
}
|
||||||
|
fn get(&self, r: usize, s: usize) -> f64 {
|
||||||
|
self.index(r, s).and_then(|i| self.a.get(i)).copied().unwrap_or(0.0)
|
||||||
|
}
|
||||||
|
fn set(&mut self, r: usize, s: usize, v: f64) {
|
||||||
|
if let Some(x) = self.index(r, s).and_then(|i| self.a.get_mut(i)) {
|
||||||
|
*x = v;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
/// Add `v` at `(r, s)` with `r ≤ s` (the lower half is the same by symmetry: callers adding
|
||||||
|
/// a full outer product reach each stored entry once through `r ≤ s`).
|
||||||
|
fn add(&mut self, r: usize, s: usize, v: f64) {
|
||||||
|
if r <= s
|
||||||
|
&& let Some(x) = self.index(r, s).and_then(|i| self.a.get_mut(i))
|
||||||
|
{
|
||||||
|
*x += v;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
/// Solve `A·x = b` by banded Cholesky factorisation `A = Uᵀ·U`; an error when `A` is not
|
||||||
|
/// positive definite.
|
||||||
|
fn solve(mut self, mut b: Vec<f64>) -> SplineResult<Vec<f64>> {
|
||||||
|
let (n, bw) = (self.n, self.bw);
|
||||||
|
for r in 0..n {
|
||||||
|
let mut d = self.get(r, r);
|
||||||
|
for k in r.saturating_sub(bw)..r {
|
||||||
|
let u = self.get(k, r);
|
||||||
|
d -= u * u;
|
||||||
|
}
|
||||||
|
if !(d > 0.0) {
|
||||||
|
return invalid("the fit's equations are singular");
|
||||||
|
}
|
||||||
|
let d = d.sqrt();
|
||||||
|
self.set(r, r, d);
|
||||||
|
for s in r + 1..(r + bw + 1).min(n) {
|
||||||
|
let mut v = self.get(r, s);
|
||||||
|
for k in s.saturating_sub(bw)..r {
|
||||||
|
v -= self.get(k, r) * self.get(k, s);
|
||||||
|
}
|
||||||
|
self.set(r, s, v / d);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
// Uᵀ·y = b, then U·x = y.
|
||||||
|
for r in 0..n {
|
||||||
|
let mut v = b.get(r).copied().unwrap_or(0.0);
|
||||||
|
for k in r.saturating_sub(bw)..r {
|
||||||
|
v -= self.get(k, r) * b.get(k).copied().unwrap_or(0.0);
|
||||||
|
}
|
||||||
|
if let Some(x) = b.get_mut(r) {
|
||||||
|
*x = v / self.get(r, r);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for r in (0..n).rev() {
|
||||||
|
let mut v = b.get(r).copied().unwrap_or(0.0);
|
||||||
|
for s in r + 1..(r + bw + 1).min(n) {
|
||||||
|
v -= self.get(r, s) * b.get(s).copied().unwrap_or(0.0);
|
||||||
|
}
|
||||||
|
if let Some(x) = b.get_mut(r) {
|
||||||
|
*x = v / self.get(r, r);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if b.iter().any(|x| !x.is_finite()) {
|
||||||
|
return invalid("the fit is not finite");
|
||||||
|
}
|
||||||
|
Ok(b)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
mod tests {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
/// The closed polygon through `corners` in space, side `k` from corner `k` to `k+1`.
|
||||||
|
fn polygon3(corners: &[Vec3]) -> impl FnMut(usize, f64) -> Option<Vec3> + '_ {
|
||||||
|
move |k, t| {
|
||||||
|
let n = corners.len();
|
||||||
|
Some(corners.get(k)?.lerp(*corners.get((k + 1) % n)?, t))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The polygon `corners` in the plane, lifted by `z(x, y)` all along.
|
||||||
|
fn lifted<'a>(corners: &'a [[f64; 2]], z: &'a dyn Fn(f64, f64) -> f64) -> impl FnMut(usize, f64) -> Option<Vec3> + 'a {
|
||||||
|
move |k, t| {
|
||||||
|
let n = corners.len();
|
||||||
|
let (a, b) = (corners.get(k)?, corners.get((k + 1) % n)?);
|
||||||
|
let (x, y) = (a[0] + (b[0] - a[0]) * t, a[1] + (b[1] - a[1]) * t);
|
||||||
|
Some(Vec3::new(x, y, z(x, y)))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn ring(n: usize, r: f64) -> Vec<[f64; 2]> {
|
||||||
|
(0..n).map(|k| k as f64 * std::f64::consts::TAU / n as f64).map(|a| [r * a.cos(), r * a.sin()]).collect()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The farthest the surface is from `z` over the polygon's inside (sampled on a grid).
|
||||||
|
fn off_inside(f: &LoopFill, corners: &[[f64; 2]], z: &dyn Fn(f64, f64) -> f64) -> f64 {
|
||||||
|
let inside = |x: f64, y: f64| {
|
||||||
|
let n = corners.len();
|
||||||
|
let mut w = false;
|
||||||
|
for k in 0..n {
|
||||||
|
let (a, b) = (corners[k], corners[(k + 1) % n]);
|
||||||
|
if (a[1] > y) != (b[1] > y) && x < a[0] + (y - a[1]) / (b[1] - a[1]) * (b[0] - a[0]) {
|
||||||
|
w = !w;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
w
|
||||||
|
};
|
||||||
|
let s = &f.surface;
|
||||||
|
let [du, dv] = s.domain();
|
||||||
|
let mut worst = 0.0f64;
|
||||||
|
for i in 0..=40 {
|
||||||
|
for j in 0..=40 {
|
||||||
|
let (u, v) = ((du[0] + (du[1] - du[0]) * i as f64 / 40.0).min(du[1]), (dv[0] + (dv[1] - dv[0]) * j as f64 / 40.0).min(dv[1]));
|
||||||
|
let p = s.eval(u, v).unwrap();
|
||||||
|
if inside(p.x, p.y) {
|
||||||
|
worst = worst.max((p.z - z(p.x, p.y)).abs());
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
worst
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn planes_are_reproduced_and_rims_of_quadrics_are_filled_closely() {
|
||||||
|
// A tilted plane over a hexagon: the smoothness energy vanishes on it, so the fill is it.
|
||||||
|
let hex = ring(6, 10.0);
|
||||||
|
let plane = |x: f64, y: f64| 0.3 * x - 0.2 * y + 1.0;
|
||||||
|
let f = fill_loop(6, &mut lifted(&hex, &plane), 1e-6).unwrap();
|
||||||
|
let inside = off_inside(&f, &hex, &plane);
|
||||||
|
eprintln!("plane: deviation {:e}, inside off by {inside:e}, {} evaluations", f.deviation, f.evaluations);
|
||||||
|
assert!(f.deviation <= 1e-6 && inside < 1e-9);
|
||||||
|
// A saddle and a dome: the least-bending fill through the rim is not the quadric (only
|
||||||
|
// planes are reproduced), but stays near it (the plate is free to turn at the rim).
|
||||||
|
let saddle = |x: f64, y: f64| 0.05 * x * y;
|
||||||
|
let dome = |x: f64, y: f64| 3.0 - 0.02 * (x * x + y * y);
|
||||||
|
for (name, z, bound) in [("saddle", &saddle as &dyn Fn(f64, f64) -> f64, 0.1), ("dome", &dome, 1.0)] {
|
||||||
|
let f = fill_loop(6, &mut lifted(&hex, z), 2e-5).unwrap();
|
||||||
|
let inside = off_inside(&f, &hex, z);
|
||||||
|
eprintln!("{name}: deviation {:e}, inside off by {inside:e}", f.deviation);
|
||||||
|
assert!(f.deviation <= 2e-5 && inside < bound, "{name}: {inside}");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn concave_loops_fill_and_the_result_does_not_depend_on_where_the_loop_starts() {
|
||||||
|
// A dart, an arrow-head pentagon and a plus, on a cylinder.
|
||||||
|
let z = |x: f64, _: f64| 50.0 - (1600.0 - x * x).sqrt();
|
||||||
|
let dart = vec![[0.0, 0.0], [20.0, -10.0], [8.0, 0.0], [20.0, 10.0]];
|
||||||
|
let arrow = vec![[0.0, 0.0], [10.0, -8.0], [10.0, -3.0], [20.0, 0.0], [10.0, 3.0]];
|
||||||
|
let plus = vec![
|
||||||
|
[-3.0, -9.0],
|
||||||
|
[3.0, -9.0],
|
||||||
|
[3.0, -3.0],
|
||||||
|
[9.0, -3.0],
|
||||||
|
[9.0, 3.0],
|
||||||
|
[3.0, 3.0],
|
||||||
|
[3.0, 9.0],
|
||||||
|
[-3.0, 9.0],
|
||||||
|
[-3.0, 3.0],
|
||||||
|
[-9.0, 3.0],
|
||||||
|
[-9.0, -3.0],
|
||||||
|
[-3.0, -3.0],
|
||||||
|
];
|
||||||
|
let flat_corner = vec![[-10.0, -10.0], [0.0, -10.0], [10.0, -10.0], [10.0, 10.0], [-10.0, 10.0]];
|
||||||
|
for (name, c) in [("dart", dart), ("arrow", arrow), ("plus", plus), ("flat corner", flat_corner)] {
|
||||||
|
let n = c.len();
|
||||||
|
let f = fill_loop(n, &mut lifted(&c, &z), 1e-4).unwrap();
|
||||||
|
let inside = off_inside(&f, &c, &z);
|
||||||
|
eprintln!("{name}: deviation {:e}, inside off the cylinder by {inside:e}, {} evaluations", f.deviation, f.evaluations);
|
||||||
|
// The least-bending fill, not the cylinder: within a few tenths of a millimetre of it.
|
||||||
|
assert!(f.deviation <= 1e-4 && inside < 0.2, "{name}: {inside}");
|
||||||
|
// The same loop from another corner and the other way round.
|
||||||
|
let mut back = c.clone();
|
||||||
|
back.rotate_left(2);
|
||||||
|
back.reverse();
|
||||||
|
let g = fill_loop(n, &mut lifted(&back, &z), 1e-4).unwrap();
|
||||||
|
assert_ne!(f.counter_clockwise, g.counter_clockwise);
|
||||||
|
for (x, y) in [(4.0, 0.0), (6.0, 1.0), (5.0, -1.0)] {
|
||||||
|
let p = Vec3::new(x, y, z(x, y));
|
||||||
|
let gap = f.point_over(p).unwrap().dist(g.point_over(p).unwrap());
|
||||||
|
assert!(gap < 1e-7, "{name}: {gap}");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn the_fill_is_the_same_at_any_size_and_place() {
|
||||||
|
// The arrow on the cylinder, scaled by 100 and by 1/100, turned and moved: the same fill,
|
||||||
|
// scaled and moved alike.
|
||||||
|
let z = |x: f64, _: f64| 50.0 - (1600.0 - x * x).sqrt();
|
||||||
|
let arrow = [[0.0, 0.0], [10.0, -8.0], [10.0, -3.0], [20.0, 0.0], [10.0, 3.0]];
|
||||||
|
let f = fill_loop(5, &mut lifted(&arrow, &z), 1e-4).unwrap();
|
||||||
|
let axis = Vec3::new(1.0, -2.0, 0.5).normalized().unwrap();
|
||||||
|
let shift = Vec3::new(30.0, -12.0, 7.0);
|
||||||
|
for scale in [100.0, 0.01] {
|
||||||
|
let place = |p: Vec3| {
|
||||||
|
// Scaled, turned by 0.9 about `axis` (Rodrigues), moved.
|
||||||
|
let p = p * scale;
|
||||||
|
let (c, s) = (0.9f64.cos(), 0.9f64.sin());
|
||||||
|
p * c + axis.cross(p) * s + axis * (axis.dot(p) * (1.0 - c)) + shift * scale
|
||||||
|
};
|
||||||
|
let mut moved = |k: usize, t: f64| lifted(&arrow, &z)(k, t).map(place);
|
||||||
|
let g = fill_loop(5, &mut moved, 1e-4 * scale).unwrap();
|
||||||
|
let mut worst = 0.0f64;
|
||||||
|
for (x, y) in [(4.0, 0.0), (6.0, 1.0), (5.0, -1.0), (9.0, -2.0), (12.0, 0.5)] {
|
||||||
|
let p = Vec3::new(x, y, z(x, y));
|
||||||
|
worst = worst.max(g.point_over(place(p)).unwrap().dist(place(f.point_over(p).unwrap())) / scale);
|
||||||
|
}
|
||||||
|
eprintln!("arrow scaled by {scale}, turned and moved: {} evaluations, surfaces apart by {worst:e} (relative)", g.evaluations);
|
||||||
|
assert!(worst < 1e-7, "scale {scale}: {worst}");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn a_long_narrow_slot_fills() {
|
||||||
|
// A 200 × 1 mm slot on a cylinder of radius 300 running along it.
|
||||||
|
let z = |x: f64, _: f64| 300.0 - (90_000.0 - (x - 100.0) * (x - 100.0)).sqrt();
|
||||||
|
let slot = [[0.0, 0.0], [200.0, 0.0], [200.0, 1.0], [0.0, 1.0]];
|
||||||
|
let f = fill_loop(4, &mut lifted(&slot, &z), 2e-4).unwrap();
|
||||||
|
let inside = off_inside(&f, &slot, &z);
|
||||||
|
eprintln!("slot: deviation {:e}, inside off the cylinder by {inside:e}, {} evaluations", f.deviation, f.evaluations);
|
||||||
|
assert!(f.deviation <= 2e-4 && inside < 1e-2);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn loops_that_do_not_bound_a_height_field_are_refused() {
|
||||||
|
let unsupported = |r: SplineResult<LoopFill>| matches!(r, Err(SplineError::Unsupported(_)));
|
||||||
|
let flat = |_: f64, _: f64| 0.0;
|
||||||
|
// A figure eight (lobes of different sizes).
|
||||||
|
let eight = [[0.0, 0.0], [10.0, 10.0], [10.0, 0.0], [0.0, 6.0]];
|
||||||
|
assert!(unsupported(fill_loop(4, &mut lifted(&eight, &flat), 1e-4)));
|
||||||
|
// A loop with a vertical spike in it (up along the normal and down again).
|
||||||
|
let spike = [
|
||||||
|
Vec3::ZERO,
|
||||||
|
Vec3::new(10.0, 0.0, 0.0),
|
||||||
|
Vec3::new(10.0, 10.0, 0.0),
|
||||||
|
Vec3::new(5.0, 10.0, 0.0),
|
||||||
|
Vec3::new(5.0, 10.0, 3.0),
|
||||||
|
Vec3::new(5.0, 10.0, 0.0),
|
||||||
|
Vec3::new(0.0, 10.0, 0.0),
|
||||||
|
];
|
||||||
|
assert!(unsupported(fill_loop(7, &mut polygon3(&spike), 1e-4)));
|
||||||
|
// A loop that runs back over itself.
|
||||||
|
let back = [[0.0, 0.0], [10.0, 0.0], [4.0, 0.0], [10.0, 10.0], [0.0, 10.0]];
|
||||||
|
assert!(unsupported(fill_loop(5, &mut lifted(&back, &flat), 1e-4)));
|
||||||
|
// A loop too wavy for one surface.
|
||||||
|
let wavy = |x: f64, y: f64| (x * 9.0).sin() * (y * 7.0).cos();
|
||||||
|
assert!(unsupported(fill_loop(64, &mut lifted(&ring(64, 10.0), &wavy), 1e-6)));
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn hostile_loops_are_refused() {
|
||||||
|
let flat = |_: f64, _: f64| 0.0;
|
||||||
|
let five = ring(5, 10.0);
|
||||||
|
assert!(fill_loop(0, &mut lifted(&five, &flat), 1e-4).is_err());
|
||||||
|
assert!(fill_loop(5, &mut |_, _| Some(Vec3::X), 1e-4).is_err(), "no area");
|
||||||
|
assert!(fill_loop(5, &mut |_, _| None, 1e-4).is_err());
|
||||||
|
assert!(fill_loop(5, &mut |k, t| Some(Vec3::new(k as f64, t, f64::NAN)), 1e-4).is_err());
|
||||||
|
assert!(fill_loop(5, &mut lifted(&five, &flat), 0.0).is_err() && fill_loop(5, &mut lifted(&five, &flat), f64::NAN).is_err());
|
||||||
|
assert!(fill_loop(10_000, &mut lifted(&five, &flat), 1e-4).is_err());
|
||||||
|
let huge = |x: f64, y: f64| (x * y) * 1e300;
|
||||||
|
let _ = fill_loop(5, &mut lifted(&five, &huge), 1e-4);
|
||||||
|
let tiny: Vec<[f64; 2]> = five.iter().map(|p| [p[0] * 1e-300, p[1] * 1e-300]).collect();
|
||||||
|
let _ = fill_loop(5, &mut lifted(&tiny, &flat), 1e-4);
|
||||||
|
let big: Vec<[f64; 2]> = five.iter().map(|p| [p[0] * 1e300, p[1] * 1e300]).collect();
|
||||||
|
let _ = fill_loop(5, &mut lifted(&big, &flat), 1e-4);
|
||||||
|
}
|
||||||
|
}
|
||||||
@@ -1,7 +1,7 @@
|
|||||||
//! Geometry foundation for SolidCraft: 2D/3D vectors, sketch planes, axis-aligned boxes,
|
//! Geometry foundation for SolidCraft: 2D/3D vectors, sketch planes, axis-aligned boxes,
|
||||||
//! triangle meshes with their measures (volume, area, centroid), and freeform surface maths
|
//! triangle meshes with their measures (volume, area, centroid), and freeform surface maths
|
||||||
//! (B-spline basis and NURBS surfaces in [`bspline`], T-splines in [`tspline`]). Units are
|
//! (B-spline basis and NURBS surfaces in [`bspline`], one-surface fills of closed loops in
|
||||||
//! millimetres.
|
//! [`fill`], T-splines in [`tspline`]). Units are millimetres.
|
||||||
//!
|
//!
|
||||||
//! This crate has no knowledge of sketches, documents or the B-rep kernel; every other crate
|
//! This crate has no knowledge of sketches, documents or the B-rep kernel; every other crate
|
||||||
//! builds on it.
|
//! builds on it.
|
||||||
@@ -10,6 +10,7 @@
|
|||||||
|
|
||||||
pub mod bspline;
|
pub mod bspline;
|
||||||
pub mod env;
|
pub mod env;
|
||||||
|
pub mod fill;
|
||||||
mod mesh;
|
mod mesh;
|
||||||
mod plane;
|
mod plane;
|
||||||
mod profile;
|
mod profile;
|
||||||
|
|||||||
@@ -0,0 +1,527 @@
|
|||||||
|
//! Filling a closed loop of a body's edges that is not planar with one face: a B-spline height
|
||||||
|
//! field over the loop's best-fit plane (`solidcraft_geom::fill::fill_loop`), bounded by the
|
||||||
|
//! body's own edges, whole. Loops that do not bound a height field over a plane are refused.
|
||||||
|
|
||||||
|
use solidcraft_geom::Vec3;
|
||||||
|
use solidcraft_geom::bspline::SplineError;
|
||||||
|
use truck_modeling as mt;
|
||||||
|
|
||||||
|
use crate::body::{Body, from_p3};
|
||||||
|
use crate::plane_fit::EdgeSampler;
|
||||||
|
use crate::record::{Rebuild, rebuilt_body};
|
||||||
|
use crate::{KernelError, Result};
|
||||||
|
|
||||||
|
/// A surface body of one face filling the closed loop `chain` of `body`'s edges (each edge
|
||||||
|
/// oriented along the loop, each ending where the next starts), within [`face_tolerance`] of
|
||||||
|
/// every edge. Its history is over `[body]`: the face is new, its edges the body's own. Call it
|
||||||
|
/// under [`crate::guard`].
|
||||||
|
pub(crate) fn fill_loop(body: &Body, chain: &[mt::Edge]) -> Result<Body> {
|
||||||
|
let tol = face_tolerance(body);
|
||||||
|
let mut sides: Vec<(EdgeSampler, Vec3)> = Vec::with_capacity(chain.len());
|
||||||
|
for e in chain {
|
||||||
|
let sampler = EdgeSampler::new(e).ok_or_else(|| KernelError::Invalid("an edge has no parameter range".into()))?;
|
||||||
|
sides.push((sampler, from_p3(e.front().point())));
|
||||||
|
}
|
||||||
|
let mut point = |k: usize, t: f64| -> Option<Vec3> {
|
||||||
|
let (sampler, start) = sides.get_mut(k)?;
|
||||||
|
// The loop's corners are its vertices (an imported edge's curve may end a little off).
|
||||||
|
if t <= 0.0 { Some(*start) } else { sampler.at(t) }
|
||||||
|
};
|
||||||
|
let fill = solidcraft_geom::fill::fill_loop(chain.len(), &mut point, tol).map_err(|e| match e {
|
||||||
|
SplineError::Unsupported(m) => KernelError::Invalid(format!("not supported yet: {m}")),
|
||||||
|
other => KernelError::Invalid(format!("cannot fill the loop: {other}")),
|
||||||
|
})?;
|
||||||
|
// The wire runs counter-clockwise about the surface's normal.
|
||||||
|
let wire: mt::Wire =
|
||||||
|
if fill.counter_clockwise { chain.to_vec().into() } else { chain.iter().rev().map(mt::Edge::inverse).collect::<Vec<_>>().into() };
|
||||||
|
let face = mt::Face::try_new(vec![wire], crate::spline_conv::surface(&fill.surface)?).map_err(|e| KernelError::Failed(format!("fill: {e}")))?;
|
||||||
|
let mut rec = Rebuild::default();
|
||||||
|
rec.made(&face, Vec::new());
|
||||||
|
Ok(rebuilt_body(crate::surfaces::surface_body(vec![face]), &[&body.solid], &rec))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// How far a loop's edges may be from a plane for its patch to be that plane: `10⁻⁷` of the
|
||||||
|
/// body's size, at least the linear tolerance (`10⁻⁶` mm) — the body's own "same point"
|
||||||
|
/// tolerance, since a planar face is exact and other operations treat it as containing its
|
||||||
|
/// edges to that tolerance. A fitted face gets [`face_tolerance`], ten times looser.
|
||||||
|
pub(crate) fn planarity_tolerance(body: &Body) -> f64 {
|
||||||
|
(body.size() * 1e-7).max(solidcraft_geom::LINEAR_TOL)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// How far the fill's surface may be from the loop's edges: `10⁻⁶` of the body's size, at least
|
||||||
|
/// `10⁻⁵` mm — ten times [`planarity_tolerance`]. Truck meshes a face from its edges' own
|
||||||
|
/// polylines (shared with the neighbouring faces), so the mesh stays watertight whatever the
|
||||||
|
/// gap: measured on a five-sided rim, fills whose edges were up to `4.5·10⁻⁴` mm off the surface
|
||||||
|
/// meshed cleanly and stitched back into closed solids. Ten times the linear tolerance because a
|
||||||
|
/// fitted surface approaches curved edges like a cubic spline, so each further factor of ten
|
||||||
|
/// costs about twice the spans each way, and imported edges may already lie `10⁻⁵` mm or more off
|
||||||
|
/// their vertices; two orders below what meshing tolerates. Later operations must take the face
|
||||||
|
/// to contain its edges within this tolerance, not the linear one: the face's edges are the
|
||||||
|
/// body's exact edges, the surface between them is the fit.
|
||||||
|
pub(crate) fn face_tolerance(body: &Body) -> f64 {
|
||||||
|
(body.size() * 1e-6).max(1e-5)
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
mod tests {
|
||||||
|
use mt::{BoundedCurve, InnerSpace, MetricSpace, ParametricCurve, ParametricSurface};
|
||||||
|
use solidcraft_geom::{Loop2, Plane, Region2, Vec2, Vec3};
|
||||||
|
use truck_modeling as mt;
|
||||||
|
|
||||||
|
use crate::body::{Body, from_p3, p3};
|
||||||
|
use crate::boolean_record::tests::{Reach, checked};
|
||||||
|
use crate::history::{Change, EdgeOrigin};
|
||||||
|
use crate::{BoolOp, boolean, copy_faces, cylinder, extrude, measure, patch_edges, stitch};
|
||||||
|
|
||||||
|
/// The cutting cylinder: axis along y at x = 0, z = 50, radius 40, so the top of a prism
|
||||||
|
/// within 20 of the axis and 20 high is cut away everywhere (to between 10 and 15.4 mm).
|
||||||
|
fn cut_height(x: f64) -> f64 {
|
||||||
|
50.0 - (1600.0 - x * x).sqrt()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A prism on the polygon `corners`, 20 high, its top cut by the cylinder; the cut solid, the
|
||||||
|
/// open cup without its top, and a point on each rim edge (the edges' midpoints in plan).
|
||||||
|
/// `inside` is a point inside the polygon.
|
||||||
|
fn cup(corners: &[Vec2], inside: Vec2) -> (Body, Body, Vec<Vec3>) {
|
||||||
|
let prism = extrude(&Plane::XY, &[Region2 { outer: Loop2::polygon(corners), holes: vec![] }], 0.0, 20.0).unwrap().pop().unwrap();
|
||||||
|
let tool = cylinder(Vec3::new(0.0, -60.0, 50.0), Vec3::Y, 40.0, 120.0).unwrap();
|
||||||
|
let solid = boolean(&prism, &tool, BoolOp::Cut).unwrap().unwrap();
|
||||||
|
let n = corners.len();
|
||||||
|
let mut keep = vec![inside.extend(0.0)];
|
||||||
|
let mut rim = Vec::new();
|
||||||
|
for k in 0..n {
|
||||||
|
let m = corners[k].lerp(corners[(k + 1) % n], 0.5);
|
||||||
|
keep.push(m.extend(5.0));
|
||||||
|
rim.push(m.extend(cut_height(m.x)));
|
||||||
|
}
|
||||||
|
let open = copy_faces(&solid, &keep).unwrap();
|
||||||
|
assert!(open.is_surface());
|
||||||
|
(solid, open, rim)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn regular(n: usize, phase: f64) -> Vec<Vec2> {
|
||||||
|
(0..n).map(|k| Vec2::from_angle(phase + k as f64 * std::f64::consts::TAU / n as f64) * 20.0).collect()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The distance from `p` to the surface: the nearest of a grid of samples, then Gauss–Newton
|
||||||
|
/// within the domain.
|
||||||
|
fn to_surface(s: &mt::Surface, p: mt::Point3) -> f64 {
|
||||||
|
let (Some((u0, u1)), Some((v0, v1))) = s.try_range_tuple() else { panic!("a bounded surface") };
|
||||||
|
let n = 80;
|
||||||
|
let mut best = (f64::MAX, u0, v0);
|
||||||
|
for i in 0..=n {
|
||||||
|
for j in 0..=n {
|
||||||
|
let (u, v) = (u0 + (u1 - u0) * i as f64 / n as f64, v0 + (v1 - v0) * j as f64 / n as f64);
|
||||||
|
let d = s.subs(u, v).distance(p);
|
||||||
|
if d < best.0 {
|
||||||
|
best = (d, u, v);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
let (_, mut u, mut v) = best;
|
||||||
|
for _ in 0..50 {
|
||||||
|
let (q, a, b) = (s.subs(u, v), s.uder(u, v), s.vder(u, v));
|
||||||
|
let r = q - p;
|
||||||
|
let (aa, ab, bb) = (a.dot(a), a.dot(b), b.dot(b));
|
||||||
|
let det = aa * bb - ab * ab;
|
||||||
|
if det.abs() < 1e-300 {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
let (ga, gb) = (a.dot(r), b.dot(r));
|
||||||
|
u = (u - (bb * ga - ab * gb) / det).clamp(u0, u1);
|
||||||
|
v = (v - (aa * gb - ab * ga) / det).clamp(v0, v1);
|
||||||
|
}
|
||||||
|
s.subs(u, v).distance(p)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The farthest point along the face's edges from its surface.
|
||||||
|
fn edges_off_surface(face: &mt::Face) -> f64 {
|
||||||
|
let s = face.surface();
|
||||||
|
let mut worst = 0.0f64;
|
||||||
|
for e in face.boundaries().iter().flat_map(|w| w.edge_iter()) {
|
||||||
|
let c = e.curve();
|
||||||
|
let (t0, t1) = c.range_tuple();
|
||||||
|
for k in 0..=24 {
|
||||||
|
worst = worst.max(to_surface(&s, c.subs(t0 + (t1 - t0) * k as f64 / 24.0)));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
worst
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The fill's mesh: every normal finite, and no triangle folded over (all face the same way
|
||||||
|
/// as the mesh's total area vector, by a clear margin).
|
||||||
|
fn mesh_is_clean(fill: &Body) -> f64 {
|
||||||
|
let m = fill.tessellate(0.01).unwrap();
|
||||||
|
assert!(!m.triangles.is_empty());
|
||||||
|
assert!(m.normals.iter().all(|n| n.is_finite() && n.len() > 0.5), "a mesh normal is not finite");
|
||||||
|
let tri = |t: &[u32; 3]| m.tri(t).unwrap();
|
||||||
|
let total = m.triangles.iter().map(|t| {
|
||||||
|
let [a, b, c] = tri(t);
|
||||||
|
(b - a).cross(c - a)
|
||||||
|
});
|
||||||
|
let total = total.fold(Vec3::ZERO, |s, v| s + v);
|
||||||
|
let n = total.normalized().unwrap();
|
||||||
|
for t in &m.triangles {
|
||||||
|
let [a, b, c] = tri(t);
|
||||||
|
let v = (b - a).cross(c - a);
|
||||||
|
if v.len() > 1e-12 {
|
||||||
|
assert!(v.dot(n) > 0.0, "a folded triangle");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
measure(fill).unwrap().area
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Fill the rim, check the face, stitch it back: (the fill, the closed solid's volume).
|
||||||
|
fn fill_rim(open: &Body, rim: &[Vec3]) -> (Body, f64) {
|
||||||
|
let fill = patch_edges(open, rim).unwrap();
|
||||||
|
assert!(fill.is_surface());
|
||||||
|
assert_eq!(fill.face_count(), 1, "one face");
|
||||||
|
let face = fill.solid.face_iter().next().unwrap().clone();
|
||||||
|
assert!(!matches!(face.surface(), mt::Surface::Plane(_)));
|
||||||
|
// Its edges are the open body's own, by identity, and nothing else.
|
||||||
|
let own: Vec<mt::EdgeID> = open.solid.edge_iter().map(|e| e.id()).collect();
|
||||||
|
assert!(fill.solid.edge_iter().all(|e| own.contains(&e.id())), "an edge that is not the body's");
|
||||||
|
let h = checked(&fill, &[open], 0.05, Reach { made: 0.0, moved: 0.0 }, &|_| true);
|
||||||
|
assert!(h.faces.iter().all(|f| f.change == Change::Generated && f.origins.is_empty()));
|
||||||
|
assert!(h.edges.iter().all(|e| matches!(e.origins.as_slice(), [EdgeOrigin::Edge { operand: 0, .. }])));
|
||||||
|
let off = edges_off_surface(&face);
|
||||||
|
let tol = super::face_tolerance(open);
|
||||||
|
assert!(off <= tol, "an edge is {off} off the face (tolerance {tol})");
|
||||||
|
mesh_is_clean(&fill);
|
||||||
|
let closed = stitch(&[open, &fill], 0.0).unwrap();
|
||||||
|
assert!(!closed.is_surface(), "the fill closes the cup");
|
||||||
|
(fill, measure(&closed).unwrap().volume)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The fill's height over the point `(x, y)`: Newton's method on the surface's `x`, `y` from
|
||||||
|
/// the nearest of a grid of samples.
|
||||||
|
fn height_over(s: &mt::Surface, x: f64, y: f64, start: &mut Option<(f64, f64)>) -> Option<f64> {
|
||||||
|
let (Some((u0, u1)), Some((v0, v1))) = s.try_range_tuple() else { return None };
|
||||||
|
let (mut u, mut v) = start.unwrap_or(((u0 + u1) / 2.0, (v0 + v1) / 2.0));
|
||||||
|
for _ in 0..30 {
|
||||||
|
let (q, a, b) = (s.subs(u, v), s.uder(u, v), s.vder(u, v));
|
||||||
|
let (rx, ry) = (q.x - x, q.y - y);
|
||||||
|
let det = a.x * b.y - a.y * b.x;
|
||||||
|
if det.abs() < 1e-300 {
|
||||||
|
return None;
|
||||||
|
}
|
||||||
|
u = (u - (b.y * rx - b.x * ry) / det).clamp(u0, u1);
|
||||||
|
v = (v - (a.x * ry - a.y * rx) / det).clamp(v0, v1);
|
||||||
|
}
|
||||||
|
let q = s.subs(u, v);
|
||||||
|
*start = Some((u, v));
|
||||||
|
((q.x - x).hypot(q.y - y) < 1e-9).then_some(q.z)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The volume the cut prism gains with the fill for its top: the fill's height above the
|
||||||
|
/// cylinder integrated over the polygon (midpoint rule on a 300 × 300 grid; the integrand
|
||||||
|
/// vanishes on the rim, so cells across it add little error).
|
||||||
|
fn gained(fill: &Body, corners: &[Vec2]) -> f64 {
|
||||||
|
let s = fill.solid.face_iter().next().unwrap().surface();
|
||||||
|
let (lo, hi) = corners.iter().fold((Vec2::new(f64::MAX, f64::MAX), Vec2::new(f64::MIN, f64::MIN)), |(lo, hi), p| {
|
||||||
|
(Vec2::new(lo.x.min(p.x), lo.y.min(p.y)), Vec2::new(hi.x.max(p.x), hi.y.max(p.y)))
|
||||||
|
});
|
||||||
|
let n = 300;
|
||||||
|
let (dx, dy) = ((hi.x - lo.x) / n as f64, (hi.y - lo.y) / n as f64);
|
||||||
|
let inside = |x: f64, y: f64| {
|
||||||
|
let mut w = false;
|
||||||
|
for k in 0..corners.len() {
|
||||||
|
let (a, b) = (corners[k], corners[(k + 1) % corners.len()]);
|
||||||
|
if (a.y > y) != (b.y > y) && x < a.x + (y - a.y) / (b.y - a.y) * (b.x - a.x) {
|
||||||
|
w = !w;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
w
|
||||||
|
};
|
||||||
|
let mut sum = 0.0;
|
||||||
|
let mut start = None;
|
||||||
|
for i in 0..n {
|
||||||
|
let x = lo.x + (i as f64 + 0.5) * dx;
|
||||||
|
for j in 0..n {
|
||||||
|
let y = lo.y + (j as f64 + 0.5) * dy;
|
||||||
|
if inside(x, y) {
|
||||||
|
let h = height_over(&s, x, y, &mut start).expect("the fill covers the polygon");
|
||||||
|
sum += (h - cut_height(x)) * dx * dy;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
sum
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The closed solid's volume against the cut prism's plus what the fill adds over the
|
||||||
|
/// cylinder (integrated independently, [`gained`]); they agree to the integration's error
|
||||||
|
/// (0.1% of what the fill adds) plus the error of measuring both solids on meshes
|
||||||
|
/// (`5·10⁻⁵` of the volume).
|
||||||
|
fn check_volume(name: &str, solid: &Body, fill: &Body, corners: &[Vec2], got: f64) {
|
||||||
|
let prism = measure(solid).unwrap().volume;
|
||||||
|
let extra = gained(fill, corners);
|
||||||
|
let want = prism + extra;
|
||||||
|
let bound = 1e-3 * extra.abs() + 5e-5 * want;
|
||||||
|
eprintln!("{name}: closed volume {got:.4}, cut prism {prism:.4} + fill above the cylinder {extra:.4} = {want:.4} (bound ±{bound:.4})");
|
||||||
|
assert!((got - want).abs() <= bound, "{name}: {got} vs {want}");
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn regular_rims_of_three_to_eight_sides_fill_with_one_face_and_close_the_cup() {
|
||||||
|
for n in 3..=8 {
|
||||||
|
let corners = regular(n, 0.3);
|
||||||
|
let (solid, open, rim) = cup(&corners, Vec2::ZERO);
|
||||||
|
let (fill, got) = fill_rim(&open, &rim);
|
||||||
|
assert_eq!(fill.edge_count(), n, "the rim's own edges");
|
||||||
|
check_volume(&format!("{n} sides"), &solid, &fill, &corners, got);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn concave_rims_fill_with_one_face() {
|
||||||
|
let v = |x: f64, y: f64| Vec2::new(x, y);
|
||||||
|
let shapes = [
|
||||||
|
("dart", vec![v(-10.0, 0.0), v(15.0, -12.0), v(3.0, 0.0), v(15.0, 12.0)], v(0.0, 0.0)),
|
||||||
|
("arrow", vec![v(-12.0, 0.0), v(0.0, -10.0), v(0.0, -4.0), v(14.0, 0.0), v(0.0, 4.0)], v(0.0, 0.0)),
|
||||||
|
(
|
||||||
|
"plus",
|
||||||
|
vec![
|
||||||
|
v(-4.0, -14.0),
|
||||||
|
v(4.0, -14.0),
|
||||||
|
v(4.0, -4.0),
|
||||||
|
v(14.0, -4.0),
|
||||||
|
v(14.0, 4.0),
|
||||||
|
v(4.0, 4.0),
|
||||||
|
v(4.0, 14.0),
|
||||||
|
v(-4.0, 14.0),
|
||||||
|
v(-4.0, 4.0),
|
||||||
|
v(-14.0, 4.0),
|
||||||
|
v(-14.0, -4.0),
|
||||||
|
v(-4.0, -4.0),
|
||||||
|
],
|
||||||
|
v(0.0, 0.0),
|
||||||
|
),
|
||||||
|
];
|
||||||
|
for (name, corners, inside) in shapes {
|
||||||
|
let (solid, open, rim) = cup(&corners, inside);
|
||||||
|
let (fill, got) = fill_rim(&open, &rim);
|
||||||
|
assert_eq!(fill.edge_count(), corners.len(), "{name}: the rim's own edges");
|
||||||
|
check_volume(name, &solid, &fill, &corners, got);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn a_flat_corner_between_two_edges_is_kept() {
|
||||||
|
// A rim of five straight edges, two of them in line (a 180° corner between them), the
|
||||||
|
// four true corners at different heights; walls hang below it.
|
||||||
|
let p = |x: f64, y: f64, z: f64| mt::Vertex::new(mt::Point3::new(x, y, z));
|
||||||
|
let v = [p(-14.0, -14.0, 12.0), p(0.0, -14.0, 12.0), p(14.0, -14.0, 12.0), p(14.0, 14.0, 15.0), p(-14.0, 14.0, 10.0)];
|
||||||
|
let line = |a: &mt::Vertex, b: &mt::Vertex| mt::Edge::new(a, b, mt::Curve::Line(mt::Line(a.point(), b.point())));
|
||||||
|
let wire: mt::Wire = (0..5).map(|k| line(&v[k], &v[(k + 1) % 5])).collect::<Vec<_>>().into();
|
||||||
|
let low = mt::builder::translated(&wire, mt::Vector3::new(0.0, 0.0, -10.0));
|
||||||
|
let walls = mt::builder::try_wire_homotopy(&wire, &low).unwrap();
|
||||||
|
let body = crate::surfaces::surface_body(walls.face_iter().cloned().collect());
|
||||||
|
let rim: Vec<Vec3> = (0..5).map(|k| from_p3(v[k].point()).lerp(from_p3(v[(k + 1) % 5].point()), 0.5)).collect();
|
||||||
|
let fill = patch_edges(&body, &rim).unwrap();
|
||||||
|
assert_eq!((fill.face_count(), fill.edge_count()), (1, 5), "one face on all five edges");
|
||||||
|
let face = fill.solid.face_iter().next().unwrap().clone();
|
||||||
|
assert!(edges_off_surface(&face) <= super::face_tolerance(&body));
|
||||||
|
let area = mesh_is_clean(&fill);
|
||||||
|
eprintln!("flat corner: one face of area {area}");
|
||||||
|
assert!(area > 28.0 * 28.0 * 0.99 && area < 28.0 * 28.0 * 1.05, "{area}");
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn the_fill_does_not_depend_on_pick_order_or_where_the_body_is() {
|
||||||
|
let (_, open, rim) = cup(®ular(5, 0.3), Vec2::ZERO);
|
||||||
|
let (a, _) = fill_rim(&open, &rim);
|
||||||
|
let mut shuffled = rim.clone();
|
||||||
|
shuffled.rotate_left(3);
|
||||||
|
shuffled.swap(0, 1);
|
||||||
|
let (b, _) = fill_rim(&open, &shuffled);
|
||||||
|
let (sa, sb) = (a.solid.face_iter().next().unwrap().surface(), b.solid.face_iter().next().unwrap().surface());
|
||||||
|
let (Some((u0, u1)), Some((v0, v1))) = sa.try_range_tuple() else { panic!() };
|
||||||
|
let mut gap = 0.0f64;
|
||||||
|
for (x, y) in [(0.2, 0.3), (0.5, 0.5), (0.7, 0.9)] {
|
||||||
|
let (u, v) = (u0 + (u1 - u0) * x, v0 + (v1 - v0) * y);
|
||||||
|
gap = gap.max(sa.subs(u, v).distance(sb.subs(u, v)));
|
||||||
|
}
|
||||||
|
assert!(gap < 1e-7, "pick order moved the surface by {gap}");
|
||||||
|
let (area_a, area_b) = (mesh_is_clean(&a), mesh_is_clean(&b));
|
||||||
|
assert!((area_a - area_b).abs() < area_a * 1e-9);
|
||||||
|
// Moved and turned: the same area.
|
||||||
|
let moved = crate::transform(&open, Vec3::new(130.0, -70.0, 40.0), Vec3::ZERO, Vec3::new(1.0, 2.0, 3.0), 0.7).unwrap();
|
||||||
|
let ax = Vec3::new(1.0, 2.0, 3.0).normalized().unwrap();
|
||||||
|
let turn = |p: Vec3| {
|
||||||
|
// Rodrigues' rotation by 0.7 about `ax`, then the shift.
|
||||||
|
let (c, s) = (0.7f64.cos(), 0.7f64.sin());
|
||||||
|
p * c + ax.cross(p) * s + ax * (ax.dot(p) * (1.0 - c)) + Vec3::new(130.0, -70.0, 40.0)
|
||||||
|
};
|
||||||
|
let moved_rim: Vec<Vec3> = rim.iter().map(|p| turn(*p)).collect();
|
||||||
|
let (c, _) = fill_rim(&moved, &moved_rim);
|
||||||
|
let area_c = mesh_is_clean(&c);
|
||||||
|
eprintln!("pick order: surfaces within {gap:e}; areas {area_a} / {area_b} / moved {area_c}");
|
||||||
|
assert!((area_a - area_c).abs() < area_a * 1e-6, "{area_a} vs moved {area_c}");
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn a_saddle_rim_of_two_intersection_curves_fills() {
|
||||||
|
// A round post with its top cut by the sideways cylinder: the rim is two intersection
|
||||||
|
// curves; the fill is one face on them.
|
||||||
|
let post = cylinder(Vec3::ZERO, Vec3::Z, 10.0, 20.0).unwrap();
|
||||||
|
let tool = cylinder(Vec3::new(0.0, -60.0, 50.0), Vec3::Y, 40.0, 120.0).unwrap();
|
||||||
|
let solid = boolean(&post, &tool, BoolOp::Cut).unwrap().unwrap();
|
||||||
|
let sides: Vec<Vec3> = (0..8).map(|k| Vec2::from_angle(k as f64 * 0.8).extend(0.0) * 10.0 + Vec3::new(0.0, 0.0, 5.0)).collect();
|
||||||
|
let open = copy_faces(&solid, &[&[Vec3::ZERO][..], &sides].concat()).unwrap();
|
||||||
|
let rim: Vec<Vec3> = [-0.98, 2.18]
|
||||||
|
.map(|a: f64| {
|
||||||
|
let (x, y) = (10.0 * a.cos(), 10.0 * a.sin());
|
||||||
|
Vec3::new(x, y, cut_height(x))
|
||||||
|
})
|
||||||
|
.to_vec();
|
||||||
|
let (fill, got) = fill_rim(&open, &rim);
|
||||||
|
let circle: Vec<Vec2> = (0..720).map(|k| Vec2::from_angle(k as f64 * std::f64::consts::TAU / 720.0) * 10.0).collect();
|
||||||
|
check_volume("saddle rim", &solid, &fill, &circle, got);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn imported_edges_whose_vertices_are_off_their_curves_fill() {
|
||||||
|
// The cup's vertices moved 2·10⁻⁵ mm off their curves, as a file might give them.
|
||||||
|
let corners = regular(5, 0.3);
|
||||||
|
let (solid, open, rim) = cup(&corners, Vec2::ZERO);
|
||||||
|
let shell = open.solid.boundaries()[0].mapped(
|
||||||
|
|p: &mt::Point3| *p + mt::Vector3::new(2e-5, 0.0, 0.0),
|
||||||
|
|c: &mt::Curve| c.clone(),
|
||||||
|
|s: &mt::Surface| s.clone(),
|
||||||
|
);
|
||||||
|
let imported = crate::surfaces::surface_body(shell.face_iter().cloned().collect());
|
||||||
|
let (fill, got) = fill_rim(&imported, &rim);
|
||||||
|
check_volume("imported", &solid, &fill, &corners, got);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn a_spline_edge_bulging_out_of_plane_is_never_given_a_flat_face() {
|
||||||
|
// A flat rectangle of edges but for one cubic edge with a control point raised 1.5 mm: no
|
||||||
|
// plane can be certified. A one-span bump is followed by the fitted face; a narrow one
|
||||||
|
// (64 spans, about 1 mm wide, its third derivative jumping at every knot) may be beyond
|
||||||
|
// a 32 × 32 grid, and then it is refused.
|
||||||
|
for (spans, raised, must_fill) in [(1, 1, true), (64, 30, false)] {
|
||||||
|
let count = spans + 3;
|
||||||
|
let pts: Vec<mt::Point3> =
|
||||||
|
(0..count).map(|i| mt::Point3::new(20.0 * i as f64 / (count - 1) as f64, 0.0, if i == raised { 1.5 } else { 0.0 })).collect();
|
||||||
|
let spline = mt::BSplineCurve::new(mt::KnotVec::uniform_knot(3, spans), pts);
|
||||||
|
let v: Vec<mt::Vertex> =
|
||||||
|
[(0.0, 0.0), (20.0, 0.0), (20.0, 10.0), (0.0, 10.0)].iter().map(|&(x, y)| mt::Vertex::new(mt::Point3::new(x, y, 0.0))).collect();
|
||||||
|
let line = |a: &mt::Vertex, b: &mt::Vertex| mt::Edge::new(a, b, mt::Curve::Line(mt::Line(a.point(), b.point())));
|
||||||
|
let bottom = mt::Edge::new(&v[0], &v[1], mt::Curve::BSplineCurve(spline.clone()));
|
||||||
|
let wire: mt::Wire = vec![bottom, line(&v[1], &v[2]), line(&v[2], &v[3]), line(&v[3], &v[0])].into();
|
||||||
|
let top = mt::builder::translated(&wire, mt::Vector3::new(0.0, 0.0, -5.0));
|
||||||
|
let walls = mt::builder::try_wire_homotopy(&wire, &top).unwrap();
|
||||||
|
let body = crate::surfaces::surface_body(walls.face_iter().cloned().collect());
|
||||||
|
let peak = from_p3(spline.subs((raised as f64 + 1.0) / (count + 1) as f64));
|
||||||
|
let rim = [from_p3(spline.subs(0.5)), Vec3::new(20.0, 5.0, 0.0), Vec3::new(10.0, 10.0, 0.0), Vec3::new(0.0, 5.0, 0.0)];
|
||||||
|
match patch_edges(&body, &rim) {
|
||||||
|
Ok(fill) => {
|
||||||
|
let face = fill.solid.face_iter().next().unwrap().clone();
|
||||||
|
assert!(!matches!(face.surface(), mt::Surface::Plane(_)), "a plane would miss the bulge");
|
||||||
|
let (off, tol) = (edges_off_surface(&face), super::face_tolerance(&body));
|
||||||
|
eprintln!("{spans}-span bump: filled, edges within {off:e} of the face");
|
||||||
|
assert!(off <= tol && to_surface(&face.surface(), p3(peak)) <= tol);
|
||||||
|
mesh_is_clean(&fill);
|
||||||
|
}
|
||||||
|
Err(e) => {
|
||||||
|
eprintln!("{spans}-span bump: {e}");
|
||||||
|
assert!(!must_fill && e.to_string().contains("not supported yet"), "{e}");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A point on each edge that bounds one face of `body` (its free edges).
|
||||||
|
fn free_edge_points(body: &Body) -> Vec<Vec3> {
|
||||||
|
let mut uses: std::collections::HashMap<mt::EdgeID, (usize, mt::Edge)> = std::collections::HashMap::new();
|
||||||
|
for f in body.solid.face_iter() {
|
||||||
|
for e in f.boundaries().iter().flat_map(|w| w.edge_iter()) {
|
||||||
|
uses.entry(e.id()).or_insert((0, e.clone())).0 += 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
uses.values()
|
||||||
|
.filter(|(n, _)| *n == 1)
|
||||||
|
.map(|(_, e)| {
|
||||||
|
let c = e.curve();
|
||||||
|
let (t0, t1) = c.range_tuple();
|
||||||
|
from_p3(c.subs(0.5 * (t0 + t1)))
|
||||||
|
})
|
||||||
|
.collect()
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn a_loop_that_does_not_bound_a_height_field_is_refused() {
|
||||||
|
// Half a round post's side: two straight edges up and two half circles, whose plane
|
||||||
|
// stands on the post's axis; the half circles run along its normal at their ends.
|
||||||
|
let post = cylinder(Vec3::ZERO, Vec3::Z, 10.0, 20.0).unwrap();
|
||||||
|
let halves = crate::split_by_plane(&post, &Plane::from_normal(Vec3::ZERO, Vec3::X).unwrap()).unwrap();
|
||||||
|
let half = halves.into_iter().find(|b| measure(b).unwrap().bbox.min.x > -1e-6).unwrap();
|
||||||
|
let at: Vec<Vec3> =
|
||||||
|
(-4..=4).map(|k| Vec2::from_angle(k as f64 * 0.35).extend(10.0) * 1.0).map(|p| Vec3::new(p.x * 10.0, p.y * 10.0, 10.0)).collect();
|
||||||
|
let side = copy_faces(&half, &at).unwrap();
|
||||||
|
let rim = free_edge_points(&side);
|
||||||
|
let err = patch_edges(&side, &rim).unwrap_err().to_string();
|
||||||
|
eprintln!("half a post's side: {err}");
|
||||||
|
assert!(err.contains("not supported yet"), "{err}");
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn planar_loops_of_intersection_curves_are_one_planar_face() {
|
||||||
|
// A round post cut by planes tilted every way, gently to steeply: each rim is an ellipse
|
||||||
|
// of intersection curves (split where the post's side has seams) lying on the cutting
|
||||||
|
// plane, so the patch is one planar face, and the post closes again.
|
||||||
|
for tilt in [Vec3::new(0.0, -0.4, 1.0), Vec3::new(0.7, -0.9, 1.0), Vec3::new(1.3, 0.2, 1.0)] {
|
||||||
|
let post = cylinder(Vec3::ZERO, Vec3::Z, 10.0, 30.0).unwrap();
|
||||||
|
let n = tilt.normalized().unwrap();
|
||||||
|
let plane = Plane::from_normal(Vec3::new(0.0, 0.0, 15.0), n).unwrap();
|
||||||
|
let pieces = crate::split_by_plane(&post, &plane).unwrap();
|
||||||
|
let solid = pieces.into_iter().find(|b| measure(b).unwrap().bbox.min.z < 0.5).unwrap();
|
||||||
|
let height = |x: f64, y: f64| 15.0 - (tilt.x * x + tilt.y * y) / tilt.z;
|
||||||
|
let sides: Vec<Vec3> = (0..8).map(|k| Vec2::from_angle(k as f64 * 0.8).extend(0.0) * 10.0 + Vec3::new(0.0, 0.0, 1.0)).collect();
|
||||||
|
let open = copy_faces(&solid, &[&[Vec3::ZERO][..], &sides].concat()).unwrap();
|
||||||
|
let rim: Vec<Vec3> = (0..12)
|
||||||
|
.map(|k| {
|
||||||
|
let a = k as f64 * std::f64::consts::TAU / 12.0 + 0.2;
|
||||||
|
let (x, y) = (10.0 * a.cos(), 10.0 * a.sin());
|
||||||
|
Vec3::new(x, y, height(x, y))
|
||||||
|
})
|
||||||
|
.collect();
|
||||||
|
let lid = patch_edges(&open, &rim).unwrap();
|
||||||
|
assert_eq!(lid.face_count(), 1);
|
||||||
|
let edges = lid.edge_count();
|
||||||
|
assert!(matches!(lid.solid.face_iter().next().unwrap().surface(), mt::Surface::Plane(_)), "tilt {tilt:?}");
|
||||||
|
let closed = stitch(&[&open, &lid], 0.0).unwrap();
|
||||||
|
assert!(!closed.is_surface());
|
||||||
|
let (want, got) = (measure(&solid).unwrap().volume, measure(&closed).unwrap().volume);
|
||||||
|
eprintln!("rim cut at {tilt:?}: {edges} intersection curves, planar face, volume {got} against {want}");
|
||||||
|
assert!((got - want).abs() < want * 1e-6, "{got} vs {want}");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn planar_loops_are_still_one_planar_face() {
|
||||||
|
let b = crate::box_solid(Vec3::ZERO, Vec3::new(10.0, 10.0, 10.0)).unwrap();
|
||||||
|
let open = copy_faces(
|
||||||
|
&b,
|
||||||
|
&[Vec3::new(5.0, 5.0, 0.0), Vec3::new(5.0, 0.0, 5.0), Vec3::new(10.0, 5.0, 5.0), Vec3::new(5.0, 10.0, 5.0), Vec3::new(0.0, 5.0, 5.0)],
|
||||||
|
)
|
||||||
|
.unwrap();
|
||||||
|
let rim = [Vec3::new(5.0, 0.0, 10.0), Vec3::new(10.0, 5.0, 10.0), Vec3::new(5.0, 10.0, 10.0), Vec3::new(0.0, 5.0, 10.0)];
|
||||||
|
let lid = patch_edges(&open, &rim).unwrap();
|
||||||
|
assert_eq!(lid.face_count(), 1);
|
||||||
|
assert!(matches!(lid.solid.face_iter().next().unwrap().surface(), mt::Surface::Plane(_)));
|
||||||
|
let closed = stitch(&[&open, &lid], 0.0).unwrap();
|
||||||
|
assert!((measure(&closed).unwrap().volume - 1000.0).abs() < 1e-9);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn open_partial_or_hostile_picks_are_refused() {
|
||||||
|
let (_, open, rim) = cup(®ular(5, 0.3), Vec2::ZERO);
|
||||||
|
assert!(patch_edges(&open, &rim[..4]).is_err(), "a loop with a missing edge");
|
||||||
|
assert!(patch_edges(&open, &[]).is_err());
|
||||||
|
assert!(patch_edges(&open, &[Vec3::new(f64::NAN, 0.0, 0.0)]).is_err());
|
||||||
|
assert!(patch_edges(&open, &[Vec3::new(1e300, 0.0, 0.0)]).is_err());
|
||||||
|
assert!(patch_edges(&open, &vec![rim[0]; 20_000]).is_err());
|
||||||
|
}
|
||||||
|
}
|
||||||
@@ -26,6 +26,7 @@ mod delete_face;
|
|||||||
mod emboss;
|
mod emboss;
|
||||||
#[cfg(test)]
|
#[cfg(test)]
|
||||||
mod face_source_tests;
|
mod face_source_tests;
|
||||||
|
mod fill;
|
||||||
mod freeform;
|
mod freeform;
|
||||||
pub mod fuzz;
|
pub mod fuzz;
|
||||||
mod heal;
|
mod heal;
|
||||||
@@ -45,6 +46,7 @@ mod modify_history_tests;
|
|||||||
mod numbered;
|
mod numbered;
|
||||||
mod offset;
|
mod offset;
|
||||||
mod ops;
|
mod ops;
|
||||||
|
mod plane_fit;
|
||||||
mod polybool;
|
mod polybool;
|
||||||
mod polyhedron;
|
mod polyhedron;
|
||||||
mod prism;
|
mod prism;
|
||||||
@@ -54,6 +56,7 @@ pub mod provenance;
|
|||||||
mod record;
|
mod record;
|
||||||
mod sew;
|
mod sew;
|
||||||
mod smooth_edges;
|
mod smooth_edges;
|
||||||
|
mod spline_conv;
|
||||||
mod splitface;
|
mod splitface;
|
||||||
mod step;
|
mod step;
|
||||||
mod step_in;
|
mod step_in;
|
||||||
|
|||||||
@@ -0,0 +1,133 @@
|
|||||||
|
//! Planes fitted to points around a loop (Newell's method), for planar faces of polygons read
|
||||||
|
//! from files and for patches filling a planar loop of edges, and points sampled along edges
|
||||||
|
//! (shared with the fill of a loop that is not planar).
|
||||||
|
|
||||||
|
use mt::{BoundedCurve, EuclideanSpace, InnerSpace, MetricSpace, ParametricCurve};
|
||||||
|
use solidcraft_geom::Vec3;
|
||||||
|
use truck_modeling as mt;
|
||||||
|
|
||||||
|
use crate::body::{from_p3, p3};
|
||||||
|
use crate::{KernelError, Result};
|
||||||
|
|
||||||
|
/// The plane through points round a loop: its normal by Newell's method (turning with the
|
||||||
|
/// loop), through their centroid; `None` for fewer than three points or no area.
|
||||||
|
pub(crate) fn plane_through(pts: &[mt::Point3]) -> Option<mt::Plane> {
|
||||||
|
let n = pts.len();
|
||||||
|
if n < 3 {
|
||||||
|
return None;
|
||||||
|
}
|
||||||
|
let mut nrm = mt::Vector3::new(0.0, 0.0, 0.0);
|
||||||
|
let mut c = mt::Vector3::new(0.0, 0.0, 0.0);
|
||||||
|
for i in 0..n {
|
||||||
|
let (a, b) = (pts.get(i)?, pts.get((i + 1) % n)?);
|
||||||
|
nrm.x += (a.y - b.y) * (a.z + b.z);
|
||||||
|
nrm.y += (a.z - b.z) * (a.x + b.x);
|
||||||
|
nrm.z += (a.x - b.x) * (a.y + b.y);
|
||||||
|
c += a.to_vec();
|
||||||
|
}
|
||||||
|
let len = nrm.magnitude();
|
||||||
|
if !(len > 1e-12) {
|
||||||
|
return None;
|
||||||
|
}
|
||||||
|
let z = nrm / len;
|
||||||
|
let o = mt::Point3::from_vec(c / n as f64);
|
||||||
|
let a = if z.x.abs() < 0.9 { mt::Vector3::unit_x() } else { mt::Vector3::unit_y() };
|
||||||
|
let x = (a - z * a.dot(z)).normalize();
|
||||||
|
let y = z.cross(x);
|
||||||
|
Some(mt::Plane::new(o, o + x, o + y))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The point of `c` at `t` (`None` where an intersection curve cannot find it).
|
||||||
|
fn curve_point(c: &mt::Curve, t: f64) -> Option<Vec3> {
|
||||||
|
let p = match c {
|
||||||
|
mt::Curve::IntersectionCurve(ic) => ic.search_triple(t)?.0,
|
||||||
|
other => other.subs(t),
|
||||||
|
};
|
||||||
|
let p = from_p3(p);
|
||||||
|
p.is_finite().then_some(p)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Points along an edge, in its own direction, at `s ∈ [0, 1]` of its parameter range. An
|
||||||
|
/// intersection curve's point is searched from the surface parameters of the point found before
|
||||||
|
/// when that one is near (an eighth of the range), and kept only when it lies near the curve's
|
||||||
|
/// leader (a seeded search can slide to another branch of the surfaces' intersection); else the
|
||||||
|
/// unseeded search decides. `None` where no point is found.
|
||||||
|
pub(crate) struct EdgeSampler {
|
||||||
|
curve: mt::Curve,
|
||||||
|
range: (f64, f64),
|
||||||
|
hint: Option<(f64, mt::Point2, mt::Point2)>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl EdgeSampler {
|
||||||
|
pub(crate) fn new(edge: &mt::Edge) -> Option<EdgeSampler> {
|
||||||
|
let curve = edge.oriented_curve();
|
||||||
|
let range = curve.range_tuple();
|
||||||
|
(range.0.is_finite() && range.1.is_finite() && range.0 < range.1).then_some(EdgeSampler { curve, range, hint: None })
|
||||||
|
}
|
||||||
|
|
||||||
|
pub(crate) fn at(&mut self, s: f64) -> Option<Vec3> {
|
||||||
|
let (t0, t1) = self.range;
|
||||||
|
let t = if s >= 1.0 { t1 } else { t0 + (t1 - t0) * s };
|
||||||
|
let mt::Curve::IntersectionCurve(ic) = &self.curve else { return curve_point(&self.curve, t) };
|
||||||
|
let leader = ic.leader();
|
||||||
|
let (p, d) = (leader.subs(t), leader.der(t));
|
||||||
|
let near = |q: mt::Point3| q.distance(p) <= 4.0 * ic.tolerance() + 1e-6;
|
||||||
|
let seeded = self
|
||||||
|
.hint
|
||||||
|
.filter(|(tp, _, _)| (t - tp).abs() <= (t1 - t0) / 8.0)
|
||||||
|
.and_then(|(_, a, b)| mt::double_projection(ic.surface0(), Some((a.x, a.y)), ic.surface1(), Some((b.x, b.y)), p, d, 100))
|
||||||
|
.filter(|f| near(f.0));
|
||||||
|
let found = seeded.or_else(|| mt::double_projection(ic.surface0(), None, ic.surface1(), None, p, d, 100))?;
|
||||||
|
self.hint = Some((t, found.1, found.2));
|
||||||
|
let q = from_p3(found.0);
|
||||||
|
q.is_finite().then_some(q)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The planar face bounded by the closed loop `chain` (each edge oriented along it) when its
|
||||||
|
/// edges are certainly in one plane, `None` otherwise (also when an edge cannot be sampled).
|
||||||
|
/// The plane is fitted to points along the edges ([`plane_through`], the normal turning with the
|
||||||
|
/// loop); the edges are certified within `tol` of it conservatively: a line by its ends, a
|
||||||
|
/// B-spline or NURBS curve with positive weights by its control points (the curve lies in their
|
||||||
|
/// convex hull), an intersection curve only when one of its two surfaces is a plane that the
|
||||||
|
/// loop's points lie on and the fitted plane agrees with over the loop (the curve lies in that
|
||||||
|
/// plane). Samples alone are never trusted: a spline can bulge out of the plane between them.
|
||||||
|
pub(crate) fn planar_face(chain: &[mt::Edge], tol: f64) -> Result<Option<mt::Face>> {
|
||||||
|
const SAMPLES: usize = 16;
|
||||||
|
let mut pts = Vec::with_capacity(chain.len() * SAMPLES);
|
||||||
|
for e in chain {
|
||||||
|
let Some(mut sampler) = EdgeSampler::new(e) else { return Ok(None) };
|
||||||
|
for k in 0..SAMPLES {
|
||||||
|
let Some(p) = sampler.at(k as f64 / SAMPLES as f64) else { return Ok(None) };
|
||||||
|
pts.push(p3(p));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
let Some(plane) = plane_through(&pts) else { return Ok(None) };
|
||||||
|
let (o, n) = (plane.origin(), plane.normal());
|
||||||
|
let off = |p: mt::Point3, o: mt::Point3, n: mt::Vector3| (p - o).dot(n).abs();
|
||||||
|
let on_plane = |p: mt::Point3| off(p, o, n) <= tol;
|
||||||
|
if !pts.iter().all(|p| on_plane(*p)) {
|
||||||
|
return Ok(None);
|
||||||
|
}
|
||||||
|
// A support plane `q` of an intersection curve holds the loop when the loop's points lie on
|
||||||
|
// it and their feet on the fitted plane do too.
|
||||||
|
let holds = |q: &mt::Plane| {
|
||||||
|
let (qo, qn) = (q.origin(), q.normal());
|
||||||
|
pts.iter().all(|p| off(*p, qo, qn) <= tol && off(*p - n * (*p - o).dot(n), qo, qn) <= tol)
|
||||||
|
};
|
||||||
|
for e in chain {
|
||||||
|
let certified = match e.curve() {
|
||||||
|
mt::Curve::Line(l) => on_plane(l.0) && on_plane(l.1),
|
||||||
|
mt::Curve::BSplineCurve(b) => b.control_points().iter().all(|p| on_plane(*p)),
|
||||||
|
mt::Curve::NurbsCurve(c) => {
|
||||||
|
c.non_rationalized().control_points().iter().all(|h| h.w > 0.0 && on_plane(mt::Point3::new(h.x / h.w, h.y / h.w, h.z / h.w)))
|
||||||
|
}
|
||||||
|
mt::Curve::IntersectionCurve(ic) => [ic.surface0(), ic.surface1()].into_iter().any(|s| matches!(s, mt::Surface::Plane(q) if holds(q))),
|
||||||
|
};
|
||||||
|
if !certified {
|
||||||
|
return Ok(None);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
let wire: mt::Wire = chain.to_vec().into();
|
||||||
|
Ok(Some(mt::Face::try_new(vec![wire], mt::Surface::Plane(plane)).map_err(|e| KernelError::Failed(format!("patch: {e}")))?))
|
||||||
|
}
|
||||||
@@ -0,0 +1,36 @@
|
|||||||
|
//! geom's B-spline curves and surfaces as truck's NURBS geometry, weights kept (homogeneous
|
||||||
|
//! control points carried over as they are).
|
||||||
|
|
||||||
|
use solidcraft_geom::bspline::{HPoint, NurbsSurface};
|
||||||
|
use truck_modeling as mt;
|
||||||
|
|
||||||
|
use crate::{KernelError, Result};
|
||||||
|
|
||||||
|
fn fail(m: impl std::fmt::Display) -> KernelError {
|
||||||
|
KernelError::Failed(format!("spline geometry: {m}"))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A homogeneous control point as truck's.
|
||||||
|
pub(crate) fn h4(h: HPoint) -> mt::Vector4 {
|
||||||
|
mt::Vector4::new(h.x, h.y, h.z, h.w)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A NURBS curve of knots and homogeneous control points.
|
||||||
|
pub(crate) fn nurbs_curve(knots: mt::KnotVec, ctrl: &[HPoint]) -> Result<mt::Curve> {
|
||||||
|
let c = mt::BSplineCurve::try_new(knots, ctrl.iter().copied().map(h4).collect()).map_err(fail)?;
|
||||||
|
Ok(mt::Curve::NurbsCurve(mt::NurbsCurve::new(c)))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A NURBS surface of knots and homogeneous control points (`rows[i][j]`: i along u).
|
||||||
|
pub(crate) fn nurbs_surface(knots: (mt::KnotVec, mt::KnotVec), rows: Vec<Vec<mt::Vector4>>) -> Result<mt::Surface> {
|
||||||
|
let s = mt::BSplineSurface::try_new(knots, rows).map_err(fail)?;
|
||||||
|
Ok(mt::Surface::NurbsSurface(mt::NurbsSurface::new(s)))
|
||||||
|
}
|
||||||
|
|
||||||
|
/// geom's tensor surface as truck's.
|
||||||
|
pub(crate) fn surface(s: &NurbsSurface) -> Result<mt::Surface> {
|
||||||
|
let [nu, nv] = s.count();
|
||||||
|
let [ku, kv] = s.knots();
|
||||||
|
let rows: Vec<Vec<mt::Vector4>> = (0..nu).map(|i| (0..nv).map(|j| h4(s.point(i, j))).collect()).collect();
|
||||||
|
nurbs_surface((mt::KnotVec::from(ku.clone()), mt::KnotVec::from(kv.clone())), rows)
|
||||||
|
}
|
||||||
@@ -4,7 +4,7 @@
|
|||||||
|
|
||||||
use std::collections::HashMap;
|
use std::collections::HashMap;
|
||||||
|
|
||||||
use mt::{BoundedCurve, EuclideanSpace, InnerSpace, MetricSpace, ParametricCurve};
|
use mt::{BoundedCurve, InnerSpace, MetricSpace, ParametricCurve};
|
||||||
use truck_modeling as mt;
|
use truck_modeling as mt;
|
||||||
|
|
||||||
use super::Ctx;
|
use super::Ctx;
|
||||||
@@ -244,7 +244,7 @@ impl Builder {
|
|||||||
})
|
})
|
||||||
.collect();
|
.collect();
|
||||||
let surface = if e.name() == "FACE" {
|
let surface = if e.name() == "FACE" {
|
||||||
plane_through(&extent).ok_or("polygonal face without a plane")?
|
crate::plane_fit::plane_through(&extent).map(mt::Surface::Plane).ok_or("polygonal face without a plane")?
|
||||||
} else {
|
} else {
|
||||||
let sid = rid(p.get(2), "face geometry")?;
|
let sid = rid(p.get(2), "face geometry")?;
|
||||||
let sense = p.get(3).and_then(Param::as_bool).unwrap_or(true);
|
let sense = p.get(3).and_then(Param::as_bool).unwrap_or(true);
|
||||||
@@ -344,30 +344,6 @@ impl Builder {
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/// Plane through a polygon (Newell's normal).
|
|
||||||
fn plane_through(pts: &[mt::Point3]) -> Option<mt::Surface> {
|
|
||||||
let n = pts.len();
|
|
||||||
let mut nrm = mt::Vector3::new(0.0, 0.0, 0.0);
|
|
||||||
let mut c = mt::Vector3::new(0.0, 0.0, 0.0);
|
|
||||||
for i in 0..n {
|
|
||||||
let (a, b) = (pts.get(i)?, pts.get((i + 1) % n)?);
|
|
||||||
nrm.x += (a.y - b.y) * (a.z + b.z);
|
|
||||||
nrm.y += (a.z - b.z) * (a.x + b.x);
|
|
||||||
nrm.z += (a.x - b.x) * (a.y + b.y);
|
|
||||||
c += a.to_homogeneous().truncate();
|
|
||||||
}
|
|
||||||
let len = nrm.magnitude();
|
|
||||||
if !(len > 1e-12) || n == 0 {
|
|
||||||
return None;
|
|
||||||
}
|
|
||||||
let z = nrm / len;
|
|
||||||
let o = mt::Point3::from_vec(c / n as f64);
|
|
||||||
let a = if z.x.abs() < 0.9 { mt::Vector3::unit_x() } else { mt::Vector3::unit_y() };
|
|
||||||
let x = (a - z * a.dot(z)).normalize();
|
|
||||||
let y = z.cross(x);
|
|
||||||
Some(mt::Surface::Plane(mt::Plane::new(o, o + x, o + y)))
|
|
||||||
}
|
|
||||||
|
|
||||||
/// Read a solid-like representation item: MANIFOLD_SOLID_BREP, BREP_WITH_VOIDS, FACETED_BREP,
|
/// Read a solid-like representation item: MANIFOLD_SOLID_BREP, BREP_WITH_VOIDS, FACETED_BREP,
|
||||||
/// or a SHELL_BASED_SURFACE_MODEL (closed shells give solids, open ones open bodies).
|
/// or a SHELL_BASED_SURFACE_MODEL (closed shells give solids, open ones open bodies).
|
||||||
pub(crate) fn read_item(cx: &Ctx, id: u64) -> R<BrepOut> {
|
pub(crate) fn read_item(cx: &Ctx, id: u64) -> R<BrepOut> {
|
||||||
|
|||||||
@@ -1,5 +1,6 @@
|
|||||||
//! Surface bodies (open shells) and the operations that turn them into solids: Patch (a planar
|
//! Surface bodies (open shells) and the operations that turn them into solids: Patch (a face
|
||||||
//! face filling a closed loop of edges or a sketch region), Stitch (surfaces sharing edges sewn
|
//! filling a closed loop of edges — planar, or B-spline patches for a loop that is not — or a
|
||||||
|
//! planar sketch region), Stitch (surfaces sharing edges sewn
|
||||||
//! into one body, a solid when they close), Trim (a surface cut by a tool, one side kept),
|
//! into one body, a solid when they close), Trim (a surface cut by a tool, one side kept),
|
||||||
//! Thicken (a surface offset along its normals into a solid) and copying faces out of a body.
|
//! Thicken (a surface offset along its normals into a solid) and copying faces out of a body.
|
||||||
|
|
||||||
@@ -76,13 +77,31 @@ pub(crate) fn edge_near(body: &Body, p: Vec3) -> Option<mt::Edge> {
|
|||||||
best.filter(|(d, _)| *d <= body.size() * 0.05 + 1e-6).map(|(_, e)| e)
|
best.filter(|(d, _)| *d <= body.size() * 0.05 + 1e-6).map(|(_, e)| e)
|
||||||
}
|
}
|
||||||
|
|
||||||
/// A planar surface filling a closed loop of a body's edges (each picked by a point on it). Its
|
/// A surface filling a closed loop of a body's edges (each picked by a point on it): one face on
|
||||||
/// history is over `[body]`: the face is new, its edges the body's.
|
/// the body's own edges, planar when the loop is certainly planar ([`crate::plane_fit`]), else a
|
||||||
|
/// B-spline height field over the loop's plane ([`crate::fill`]; loops that do not bound one are
|
||||||
|
/// refused). Its history is over `[body]`: the face is new, its edges the body's own.
|
||||||
pub fn patch_edges(body: &Body, at: &[Vec3]) -> Result<Body> {
|
pub fn patch_edges(body: &Body, at: &[Vec3]) -> Result<Body> {
|
||||||
body.require_brep("patch")?;
|
body.require_brep("patch")?;
|
||||||
if at.is_empty() || at.len() > 10_000 {
|
if at.is_empty() || at.len() > 10_000 {
|
||||||
return Err(KernelError::Invalid("pick the edges of a closed loop".into()));
|
return Err(KernelError::Invalid("pick the edges of a closed loop".into()));
|
||||||
}
|
}
|
||||||
|
guard("patch", || {
|
||||||
|
let chain = picked_loop(body, at)?;
|
||||||
|
let Some(face) = crate::plane_fit::planar_face(&chain, crate::fill::planarity_tolerance(body))? else {
|
||||||
|
// Not certainly planar: a fitted surface.
|
||||||
|
return crate::fill::fill_loop(body, &chain);
|
||||||
|
};
|
||||||
|
// A new face on the body's own edges.
|
||||||
|
let mut rec = Rebuild::default();
|
||||||
|
rec.made(&face, Vec::new());
|
||||||
|
Ok(rebuilt_body(surface_body(vec![face]), &[&body.solid], &rec))
|
||||||
|
})
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The edges of `body` picked by points on them, chained into one closed loop (each turned to
|
||||||
|
/// run along it). Call it under [`guard`]: sampling an intersection curve can fail in truck.
|
||||||
|
pub(crate) fn picked_loop(body: &Body, at: &[Vec3]) -> Result<Vec<mt::Edge>> {
|
||||||
let mut edges: Vec<mt::Edge> = Vec::new();
|
let mut edges: Vec<mt::Edge> = Vec::new();
|
||||||
for p in at {
|
for p in at {
|
||||||
let e = edge_near(body, *p).ok_or_else(|| KernelError::Invalid(format!("no edge at {p:?}")))?;
|
let e = edge_near(body, *p).ok_or_else(|| KernelError::Invalid(format!("no edge at {p:?}")))?;
|
||||||
@@ -90,34 +109,25 @@ pub fn patch_edges(body: &Body, at: &[Vec3]) -> Result<Body> {
|
|||||||
edges.push(e);
|
edges.push(e);
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
guard("patch", || {
|
let mut pool = edges;
|
||||||
// Chain the edges into one loop (turning them round as needed).
|
let first = pool.pop().ok_or_else(|| KernelError::Invalid("no edges".into()))?;
|
||||||
let mut pool = edges;
|
let start = first.front().id();
|
||||||
let first = pool.pop().ok_or_else(|| KernelError::Invalid("no edges".into()))?;
|
let mut at_v = first.back().clone();
|
||||||
let start = first.front().id();
|
let mut chain = vec![first];
|
||||||
let mut at_v = first.back().clone();
|
while at_v.id() != start {
|
||||||
let mut chain = vec![first];
|
let k = pool
|
||||||
while at_v.id() != start {
|
.iter()
|
||||||
let k = pool
|
.position(|e| e.front().id() == at_v.id() || e.back().id() == at_v.id())
|
||||||
.iter()
|
.ok_or_else(|| KernelError::Invalid("the edges do not form a closed loop".into()))?;
|
||||||
.position(|e| e.front().id() == at_v.id() || e.back().id() == at_v.id())
|
let e = pool.remove(k);
|
||||||
.ok_or_else(|| KernelError::Invalid("the edges do not form a closed loop".into()))?;
|
let e = if e.front().id() == at_v.id() { e } else { e.inverse() };
|
||||||
let e = pool.remove(k);
|
at_v = e.back().clone();
|
||||||
let e = if e.front().id() == at_v.id() { e } else { e.inverse() };
|
chain.push(e);
|
||||||
at_v = e.back().clone();
|
}
|
||||||
chain.push(e);
|
if !pool.is_empty() {
|
||||||
}
|
return Err(KernelError::Invalid("the edges form more than one loop".into()));
|
||||||
if !pool.is_empty() {
|
}
|
||||||
return Err(KernelError::Invalid("the edges form more than one loop".into()));
|
Ok(chain)
|
||||||
}
|
|
||||||
let wire: mt::Wire = chain.into();
|
|
||||||
let face = mt::builder::try_attach_plane(&[wire])
|
|
||||||
.map_err(|_| KernelError::Invalid("not supported yet: patching a loop that is not planar".into()))?;
|
|
||||||
// A new face on the body's own edges.
|
|
||||||
let mut rec = Rebuild::default();
|
|
||||||
rec.made(&face, Vec::new());
|
|
||||||
Ok(rebuilt_body(surface_body(vec![face]), &[&body.solid], &rec))
|
|
||||||
})
|
|
||||||
}
|
}
|
||||||
|
|
||||||
/// Faces of a body copied out as a surface body (faces picked by points on them). Its history is
|
/// Faces of a body copied out as a surface body (faces picked by points on them). Its history is
|
||||||
|
|||||||
@@ -11,6 +11,7 @@ use solidcraft_geom::tspline::TSpline;
|
|||||||
use truck_modeling as mt;
|
use truck_modeling as mt;
|
||||||
|
|
||||||
use crate::body::Body;
|
use crate::body::Body;
|
||||||
|
use crate::spline_conv::{h4, nurbs_curve, nurbs_surface};
|
||||||
use crate::{KernelError, Result, guard};
|
use crate::{KernelError, Result, guard};
|
||||||
|
|
||||||
/// A T-spline as a surface body (an open shell of NURBS faces whose normals follow
|
/// A T-spline as a surface body (an open shell of NURBS faces whose normals follow
|
||||||
@@ -34,25 +35,11 @@ fn fail(m: impl std::fmt::Display) -> KernelError {
|
|||||||
KernelError::Failed(format!("t-spline sheet: {m}"))
|
KernelError::Failed(format!("t-spline sheet: {m}"))
|
||||||
}
|
}
|
||||||
|
|
||||||
fn h4(h: HPoint) -> mt::Vector4 {
|
|
||||||
mt::Vector4::new(h.x, h.y, h.z, h.w)
|
|
||||||
}
|
|
||||||
|
|
||||||
fn vertex(h: HPoint) -> Result<mt::Vertex> {
|
fn vertex(h: HPoint) -> Result<mt::Vertex> {
|
||||||
let p = h.project().ok_or_else(|| fail("a corner has no position"))?;
|
let p = h.project().ok_or_else(|| fail("a corner has no position"))?;
|
||||||
Ok(mt::builder::vertex(crate::body::p3(p)))
|
Ok(mt::builder::vertex(crate::body::p3(p)))
|
||||||
}
|
}
|
||||||
|
|
||||||
fn nurbs_curve(knots: mt::KnotVec, ctrl: &[HPoint]) -> Result<mt::Curve> {
|
|
||||||
let c = mt::BSplineCurve::try_new(knots, ctrl.iter().copied().map(h4).collect()).map_err(fail)?;
|
|
||||||
Ok(mt::Curve::NurbsCurve(mt::NurbsCurve::new(c)))
|
|
||||||
}
|
|
||||||
|
|
||||||
fn surface(knots: (mt::KnotVec, mt::KnotVec), rows: Vec<Vec<mt::Vector4>>) -> Result<mt::Surface> {
|
|
||||||
let s = mt::BSplineSurface::try_new(knots, rows).map_err(fail)?;
|
|
||||||
Ok(mt::Surface::NurbsSurface(mt::NurbsSurface::new(s)))
|
|
||||||
}
|
|
||||||
|
|
||||||
/// One face from a clamped tensor surface, bounded by its four boundary curves.
|
/// One face from a clamped tensor surface, bounded by its four boundary curves.
|
||||||
fn tensor_face(n: &NurbsSurface) -> Result<mt::Face> {
|
fn tensor_face(n: &NurbsSurface) -> Result<mt::Face> {
|
||||||
let [nu, nv] = n.count();
|
let [nu, nv] = n.count();
|
||||||
@@ -69,8 +56,7 @@ fn tensor_face(n: &NurbsSurface) -> Result<mt::Face> {
|
|||||||
let top = edge(v3, v2, nurbs_curve(ku.clone(), &row(nv - 1))?)?;
|
let top = edge(v3, v2, nurbs_curve(ku.clone(), &row(nv - 1))?)?;
|
||||||
let left = edge(v0, v3, nurbs_curve(kv.clone(), &column(0))?)?;
|
let left = edge(v0, v3, nurbs_curve(kv.clone(), &column(0))?)?;
|
||||||
let wire: mt::Wire = vec![bottom, right, top.inverse(), left.inverse()].into();
|
let wire: mt::Wire = vec![bottom, right, top.inverse(), left.inverse()].into();
|
||||||
let rows: Vec<Vec<mt::Vector4>> = (0..nu).map(|i| (0..nv).map(|j| h4(n.point(i, j))).collect()).collect();
|
mt::Face::try_new(vec![wire], crate::spline_conv::surface(n)?).map_err(fail)
|
||||||
mt::Face::try_new(vec![wire], surface((ku, kv), rows)?).map_err(fail)
|
|
||||||
}
|
}
|
||||||
|
|
||||||
/// A parameter point, exact (knot values are shared, so equal points have equal bits).
|
/// A parameter point, exact (knot values are shared, so equal points have equal bits).
|
||||||
@@ -148,7 +134,7 @@ fn patch_faces(patches: &[BezierPatch]) -> Result<Vec<mt::Face>> {
|
|||||||
}
|
}
|
||||||
let [ps, pt] = p.degree;
|
let [ps, pt] = p.degree;
|
||||||
let rows: Vec<Vec<mt::Vector4>> = (0..=ps).map(|i| (0..=pt).map(|j| h4(p.point(i, j))).collect()).collect();
|
let rows: Vec<Vec<mt::Vector4>> = (0..=ps).map(|i| (0..=pt).map(|j| h4(p.point(i, j))).collect()).collect();
|
||||||
let surf = surface((mt::KnotVec::bezier_knot(ps), mt::KnotVec::bezier_knot(pt)), rows)?;
|
let surf = nurbs_surface((mt::KnotVec::bezier_knot(ps), mt::KnotVec::bezier_knot(pt)), rows)?;
|
||||||
faces.push(mt::Face::try_new(vec![wire.into()], surf).map_err(fail)?);
|
faces.push(mt::Face::try_new(vec![wire.into()], surf).map_err(fail)?);
|
||||||
}
|
}
|
||||||
Ok(faces)
|
Ok(faces)
|
||||||
|
|||||||
@@ -709,6 +709,31 @@ fn surface_dialogs_make_their_commands() {
|
|||||||
assert!((v - 30.0 * 20.0 * 2.0).abs() < 1.0, "{v}");
|
assert!((v - 30.0 * 20.0 * 2.0).abs() < 1.0, "{v}");
|
||||||
}
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn patch_dialog_fills_a_loop_of_edges_that_is_not_planar() {
|
||||||
|
// A box with its top cut away by a sideways cylinder: its rim is a closed loop of four
|
||||||
|
// curved edges, not in a plane. Picking them in the Patch dialog fills it with one face.
|
||||||
|
let mut app = app_with(json!([
|
||||||
|
{"command": "solid.box", "params": {"length": 28, "width": 28, "height": 20, "corner": [-14, -14, 0], "body_name": "Saddle"}},
|
||||||
|
{"command": "solid.cylinder", "params": {"radius": 40, "height": 120, "base": [0, -60, 50], "axis": "Y", "operation": "cut", "targets": ["Saddle"]}}
|
||||||
|
]));
|
||||||
|
let z = |x: f64| 50.0 - (1600.0 - x * x).sqrt();
|
||||||
|
let rim = [Vec3::new(14.0, 0.0, z(14.0)), Vec3::new(0.0, 14.0, z(0.0)), Vec3::new(-14.0, 0.0, z(-14.0)), Vec3::new(0.0, -14.0, z(0.0))];
|
||||||
|
let mut d = start(&mut app, vec![], "surface.patch");
|
||||||
|
d.inputs[0].items = rim.iter().enumerate().map(|(i, p)| Sel::Edge { body: "Saddle".into(), index: i, point: *p }).collect();
|
||||||
|
let cmds = apply_commands(&app, &d).unwrap();
|
||||||
|
assert_eq!(cmds.len(), 1);
|
||||||
|
assert_eq!(cmds[0].0, "surface.patch");
|
||||||
|
app.session.execute(&cmds[0].0, &cmds[0].1).unwrap();
|
||||||
|
let st = app.session.model.state();
|
||||||
|
let fill = st.bodies.iter().find(|b| b.name != "Saddle").unwrap();
|
||||||
|
assert!(fill.body.is_surface() && fill.body.face_count() == 1);
|
||||||
|
// One smooth face over the rim: its area is close to the cylinder's inside the rim.
|
||||||
|
let area = fill.mesh().measure().area;
|
||||||
|
let want = 28.0 * 40.0 * 2.0 * (14.0f64 / 40.0).asin();
|
||||||
|
assert!((area - want).abs() < want * 1e-2, "{area} vs {want}");
|
||||||
|
}
|
||||||
|
|
||||||
#[test]
|
#[test]
|
||||||
fn split_body_by_a_curved_face_sends_it_as_a_tool() {
|
fn split_body_by_a_curved_face_sends_it_as_a_tool() {
|
||||||
let mut app = app_with(json!([
|
let mut app = app_with(json!([
|
||||||
|
|||||||
Reference in new issue
Block a user