A region's corners are its interior angles below 135 degrees, and an
O-grid's 45-degree cuts meet straight sides at exactly that angle. The
computed angle then rounds either way with the last bits of its points,
which differ between platforms' sin and cos and between tessellations:
one ulp in three points of the slot test's arcs, Windows' sin against
glibc's, turned a mapped region into a triangle and the whole blocking
into a different one with a corner scaled Jacobian of 0.375 for 0.707.
Angles within 1e-9 rad of the corner and reflex thresholds now count as
on them, and on a threshold is smooth (neither a corner nor reflex),
which keeps the slot's intended O-grid of 9 regions and 848 quads on
Linux, macOS and Windows. The region classification and the O-grid's
own corner tests share the rule, the slot test pins the blocking, and
its arc helper uses the mesher's portable trig.
Part of #556.
move_nodes_with takes the region's quality before the move from an earlier run
and a coarser guard bisection, for a live preview; each pass measures the
elements in parallel (fixed blocks). The relaxation's state sizes its elements
(a certified check each) only for the strong mode, which alone uses the size:
on the crank arm's hex20 mesh that was 114 ms of every 130 ms preview.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
relax::move_weights gives each node its share of a displacement (the grabbed
nodes all of it, the nodes within the radius strength x falloff, or the
harmonic function of the element-edge graph, zero beyond the radius and at
held nodes); relax::move_nodes applies it as the relaxation's constraints let
each node move (faces in UV, edges along, vertices held), scaled back by
bisection until no valid element inverts, and reports each element's scaled
Jacobian before and after.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The dihedral range and mesh.quality's scaled Jacobian were both right:
they are computed by the same function on the same final corners (tet4
and tet10 give identical numbers), but a dihedral range does not bound
the corner scaled Jacobian. A needle has dihedral angles near 60 and 90
degrees and a nearly flat apex corner. Before 417c0c88 sphere-on-plate
at size 4 had dihedrals 36.3-141.6 and 106 needles below SJ 0.2 (min
0.095); now 36.0-137.6 and min SJ 0.351.
The mesher's report now carries min_scaled_jacobian so it cannot read
as all-good while needles remain.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The improvement objective was the smallest dihedral sine, which misses
needles: every dihedral angle fine while a corner is nearly flat, so
the corpus meshes had scaled Jacobians down to 0.01-0.07. The objective
is now the smaller of the dihedral sine and the scaled Jacobian at the
worst corner (the measure analysts check, Knupp 2001), weighted so a
Jacobian of 0.3 (the skill's limit) counts as a 30 degree dihedral
angle (the schedule's target): the Jacobian decides only near that
limit. The existing edge removal, multi-face removal, smoothing and
insertion then remove the needles.
Skill tet10 min SJ: sphere-on-plate 0.092 -> 0.335, filleted-bracket
0.021 -> 0.318 (both pass, nothing marked). Default-size tet10:
thin-ribs 0.240, shallow-groove 0.321, rounded-box 0.311.
The strong-relaxation test relaxes below 0.45: nothing is left below
0.3. Literature note in docs/meshing/literature.md.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Owner's rule (#438): move the bad nodes, interpolate, keep the morph as long as no
element inverts (guards "valid", the default); the old guards stay as "strict". The
run keeps its best round (highest smallest scaled Jacobian, then fewest elements below
the threshold, then highest mean) and never ends below the start. Default reach five
mean edge lengths of the bad elements (was three); on the Pi 5 base reach 3, 5 and 7
end at the same quality, 5 moving fewer nodes than 7 while leaving none below 0.7.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Deleting a cap tetrahedron (two boundary faces of one B-rep face) gives each of its
two other neighbours a boundary face; a neighbour that had three was left with every
face on the boundary, joined to the mesh by its vertices alone. On Linux the dome on
a plate (cmd::plan::decompose::tests::a_dome_on_a_plate...) got one and the static
solve found the stiffness singular. The kernel's tessellation and sphere parameters
differ in their last bits between macOS and Linux (SolidCraft, outside this repo);
given the same input the tet mesher gives the same mesh on both (checked by replaying
Linux's surface and spheres on macOS, which reproduced the floating tetrahedron).
The deletion now refuses when a neighbour would float, and the linear validity gate
fails a mesh with a tetrahedron that shares no face with the rest, saying so.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
In the max-min phase a valid element's term q^-16 reached 1e96 as q -> 0+, far above
an invalid element's 2e8, so the descent kept elements inverted rather than pass
through flat: the distorted plate stayed tangled (4 invalid) once its mesh was the
same on every platform. The shape term now continues as its tangent line below
q = 0.3 (finite, steep) and an invalid element costs 1e11, above any valid one.
Adds a test that the plate's mesh, its perturbation and the strong relaxation are
the same bits with 1 and 4 threads and match a fingerprint taken on macOS (CI checks
it on Linux).
Part of #438.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The system maths library's sin, cos, atan2, log … are not correctly rounded and differ
between platforms: mesh.hex.generate gave the plate of the strong-relax test a different
mesh on Linux than on macOS (nodes from 2809 on), so the test passed on a Mac and failed
in CI. Every transcendental call in fieldcraft-mesh now goes through the libm crate (a
pure-Rust port of musl's), which gives the same bits everywhere.
Part of #438.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
SolidCraft lists a solid's faces in a different order from run to run
(the rounded box, for one), which reordered the triangle soup and the
face tags with every coordinate the same; welding keeps the first copy
it meets and every later stage visits ids in order, so the tet mesh
changed between runs. CanonicalSoup sorts the triangles by their
coordinates, numbers vertices by first use and face tags by first
appearance, and maps the tags back; mesh.tet.generate and the corpus
use it.
Tests: the washer's tet10 mesh has a fixed fingerprint (identical on
arm64 and x86-64 builds); a reordered, renumbered input gives the same
mesh; heavy: rounded-box and filleted-bracket mesh bit for bit the same
on repeated runs and with 1 and 8 threads.
The bracket oracle cases stay unfrozen: SolidCraft's tessellation
itself differs in the last bits between arm64 and x86-64. The coarse
case moves to 203.6 MPa with the canonical order; its band is 5%.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The platform maths libraries' atan2 and cbrt differ in the last bits
between macOS and glibc, so the dihedral angles and the shape measure a
mesh reports did too. The crate's own versions use + - * / and sqrt
only (correctly rounded everywhere) and agree with the platform's to a
few ulps.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
SizeField::range gives a field's smallest and largest size. The octree
starts its root cells at the largest instead of the size at the part's
centre, and refuses before building when the smallest needs more levels
than max_depth.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The thinnest wall (measured to a facing wall) and narrowest patch give the cell size the grid
needs; the requested size refined that deep comes first, a root shrunk so one level fewer is
exact second; beyond the levels or cells allowed meshing fails at once naming the wall, levels and
cells. max_depth is a cap (default 4); rebuilds stay within the planned levels; lattice positions
no longer depend on the lattice depth; the report gives root size, levels, wall, patch and cells
per level before and after closure.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A crease inside one face whose ends are not on other features (a tessellation crease across the
crank's r1.5 bore fillets) bounded nothing, so its open ends were corners no region border could
reach and the feature map failed on every build. Patch widths now count bounding curves only.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A merged face on several surfaces (a sliver absorbed into its neighbour)
had no exact surface, so the projection target fell back to its
triangles: flat curvature probes gave fewer divisions round the boss and
the enclosure base's symmetric mesh dropped from 0.70 to 0.51 once its
absorbs reached the cells. The target now projects a point of such a
face onto the exact surface of the B-rep piece it is on, trimmed to that
piece (Tessellation::with_pieces, Shape::tessellate_pieces); node
relaxation slides on it the same way.
Test from commands: the enclosure base's four slivers absorbed, meshed
whole and by symmetry, the absorbs kept in every cell.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
With "transition": "pyramid" (the default; "tie" keeps the old join) a tet
cell is meshed after the hex cells, with a pyramid on every hex face of its
cuts and its tetrahedra on the pyramids' sides: one conforming mesh, no tie.
Where it cannot be built the cell says why (no_pyramids) and is tied. The
apex height is 0.4 of the quad's edge, so pyramids on faces meeting at a
right angle do not cross.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
transition::pyramid_surface puts a pyramid on every hex interface quad and
builds the tet region's surface closed by the pyramid sides, re-stitching the
neighbouring faces to the hex rim nodes. QualityOptions::frozen_faces keeps
those sides exactly (TetComplex refuses changes that remove or add a frozen
face; their vertices are corners), and apex_points checks the result.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The owner's direction: bad nodes move to better places, the nodes within a reach follow by
the graph Laplacian's harmonic extension, edges held, nothing outside the reach moves.
mesh.node.relax strong mode takes below and reach and reports each round.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The extrude/revolve cross-section took both ends of every B-rep edge as curve ends. A closed
edge without a vertex on it (a hole's rim after geometry.faces.merge of its halves) starts
wherever its chain was picked up, the old seam vertex, so that point stayed a curve end and a
node column stayed on the merged boundary. Only open edges' ends (and the B-rep vertices) are
curve ends now; the layout and interval assignment place the rim's nodes.
The hex test runs on a square plate and asserts the seams carry exactly as many nodes as the
same lines turned a quarter round the hole (10 and 10; before 5 and 10): the corner layout
puts arc-midpoint nodes there by symmetry, so 0 is not the right target.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A five-node pyramid, the conforming transition between a hexahedron's face
and tetrahedra: Bedrosian's rational shape functions with a collapsed (Duffy)
Gauss rule, a certified Jacobian on the base square with exact volume, a
scaled Jacobian, C3D5 / CPYRAM / LS-DYNA degenerate solid, VTK_PYRAMID and
the binary mesh code 13. A distorted hex8-pyramid5-tet4 transition mesh
passes the patch test and uniaxial tension exactly.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A patch of quads already meshed on a face of the body (a neighbour's mesh)
is matched to the block faces on it: block vertices to its nodes (its
singular nodes first, then along its grid lines), block edges along its
grid lines, faces filled quad by quad. Those faces take the patch's
divisions and nodes, held through smoothing. mesh.hex.project takes
"fixed": [face names] and builds the patch from other bodies' meshes.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
project_trimmed accepted the exact surface's point up to a fifth of the
nearest triangle's median edge off the face: on a tall fillet piece
(triangles 30 mm long) that let a point on a sibling piece of the same
cylinder count as on it, so every quad round the corner took the first
piece's name. The slack is now the triangle's own chordal gap to the
surface, doubled.
A face narrower than the elements (the sliver a corner boss leaves of the
inner fillet) gets one row of the quads it runs through, from the
neighbour with the most quads left. Tessellation::nearest_face finds the
face nearest a point.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The compass search after the sweeps moves the nodes of the worst elements one at a time, each to
its own best place. Since it lifts every element below 0.7 (#462) it moves many surface nodes,
and a column of them on a face ends at scattered places: the enclosure base's inner walls showed
zigzag element lines in a column next to each corner, full height. A last pass now moves each
surface node back toward the mean of its neighbours on the surface, as far as no element round
it falls below the lower of its own value and the mesh's smallest after the search, so the lines
straighten and the mesh's worst element is no worse.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Projecting a point onto one B-rep face searched one box tree over every triangle of the
boundary, skipping the other faces' triangles: when other faces lie nearer the point than the
target face, it walked most of the tree before reaching a triangle it could use. Smoothing a
projected mesh projects every boundary node many times, onto every face of its target group,
so the Pi 5 enclosure base spent 95 % of its 11 minutes there. Each face (and each face pair's
curve) now has a tree of its own: the same nearest triangle, found among its own boxes only.
Ties between triangles at the same distance went to whichever the tree's walk met first; they
now go to the lowest triangle, so the result no longer depends on how a tree is built. With
that rule the per-face trees and the whole-boundary tree give bitwise the same mesh.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
#462 visited nodes by a mirror-invariant key (distance from the centroid). On the cup with a
handle that order sweeps ring by ring round the axis and converges worse in its 100 sweeps: the
refined cup fell to a scaled Jacobian of 0.481 (needs 0.5, #440). In the lattice's own order
it holds, and the order gained the enclosure base little (its corners differ by 0.02 either
way), so it goes; the compass search's lift to 0.7 stays.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The compass search after the sweeps only lifted elements below 0.5 (the quality floor), so a
mesh whose worst elements sat just above it stayed there: every corner of an enclosure base
stopped at a scaled Jacobian of 0.50-0.52 where its walls meet the corner bosses. It now lifts
every element below 0.7, never lowering another below the lower of its own value and 0.5.
The sweeps and the search are Gauss-Seidel, so the node order shaped the result and mirror
image corners smoothed differently. Nodes are now visited by a key that a mirror or a quarter
turn about the nodes' centroid keeps (distance from it, then the sorted offsets along the
axes). What spread is left between mirrored corners (0.686 vs 0.702 on the test base) is most likely the projection onto the body's
tessellation, which the kernel does not make mirror symmetric (not yet proven).
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The crank ends at 8, 16, 20 and 22 mm, so no one-to-one sweep takes it.
The sweep met one of those caps as a linking face and reported "linking
face has no top side". A plane parallel to the source that only part of a
ring reaches is now named as what it is, with extrude pointed to. The arm's
profile alone sweeps as well as extrude does.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A smooth loop (straight sides running tangent into arcs, as a slot or a
rounded pocket) is meshed as a disk. Its middle block was a square halfway
to the loop's quarter points, which on the crank's 6:1 pocket floor
squashed elements to a scaled Jacobian of 0.16. The block is now a
rectangle on the region's principal axes, inset by the same distance all
round (the old square on a circle), its corners paired with the loop nodes
nearest their diagonals, its sides spaced as the nodes they pair with, and
the O-grid is smoothed (untangled first) before the validity check.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
project_trimmed accepted the analytic projection within a fifth of the nearest
triangle's size; a plane face's triangles can span the whole face, so nodes in a
3 mm fillet landed on the untrimmed box planes (mesh volume = the unfilleted box).
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Topology::split cuts a block at given fractions and every block chained to it
through parallel edges, orienting the fractions through the chain, so the
topology stays conforming. A certified-invalid element is reported with its
block, cell, centre and the block vertex and blocks meeting there; the mesh is
never emitted.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Each source node follows its own path (a direction or the section normal)
to the target, found by Newton on the target's tangent plane; layers are
graded by a bias; side faces, when given, hold the boundary nodes of every
layer (alternating projections at the target), and interior nodes take the
boundary-residual correction. Source nodes are kept, so a section taken from
a neighbouring mesh conforms with it.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Christian Svensson