* Add B-spline basis, knot insertion and NURBS surfaces to geom
Freeform faces need local refinement and gap-free joins between patches
with different knot vectors, which tensor B-spline grids cannot give;
T-splines can, and the first user is an N-sided Boundary Fill of
non-planar loops. This lays the univariate groundwork they rest on, in
the L0 geometry crate so it stays independent of the B-rep kernel:
- Cox-de Boor basis of one function from its local knot vector, on
half-open spans with a left-limit side for the domain end, with
derivatives (NURBS Book eq. 2.5, 2.9)
- knot insertion into a single basis function (Sederberg et al. 2004
section 3) and Bezier extraction of one function by repeated insertion
- Boehm knot insertion for curves (NURBS Book A5.1), de Casteljau
evaluation and sub-segments
- a rational tensor NURBS surface with evaluation, knot insertion and
clamping, and a rational Bezier patch type
All input is checked (finite, monotone knots, positive weights, size
caps) and returns SplineError; nothing indexes unchecked.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
* Add T-spline surfaces: T-mesh, evaluation, AS check, refinement, extraction
Tensor B-spline faces refine only by whole rows and columns and cannot
join patches with different knot vectors without gaps. T-splines allow
T-junctions in the control net, which fixes both; the first user is an
N-sided Boundary Fill. This adds the maths only (no command, no change
in behaviour):
- T-mesh in index space with knot values per line, validated (outer
rectangle, rectangular faces, no empty lines, size caps); local knot
vectors read off rays from each vertex, rays leaving the mesh repeat
the boundary (Sederberg et al. 2003 section 3)
- rational T-spline evaluation and first derivatives for odd bi-degree,
with a complete (p-1)/2-line frame and the domain inside it
- T-junction extensions and the analysis-suitability check (Scott et al.
2012 section 2)
- local refinement that keeps the surface exactly: requested knot lines
are cut in, then every original blending function is carried as a
record and split (violation 1) or the mesh gains edges (violations 2
and 3) until each record is a blending function of the refined mesh
(Sederberg et al. 2004 section 3); analysis-suitable input stays
analysis-suitable by carrying conflicting T-junctions across faces
- NURBS <-> T-spline conversion for meshes without T-junctions, and
Bezier extraction over the rectangles no blending-function knot line
crosses
Measured: regular T-spline vs NURBS < 1e-12, round trip exact, partition
of unity with T-junctions < 1e-14, refinement deviation <= 1.4e-14 over
40 random refinements, Bezier patches vs surface < 1e-14.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
* Convert T-splines to sewn NURBS sheet bodies in the kernel
A T-spline is only useful to the modeller once it is a B-rep face set.
tspline_sheet builds an open shell: a mesh without T-junctions becomes
one clamped NURBS face; otherwise each Bezier element is a face, and
sides are split at the T-points where neighbours' corners land, so all
faces share vertices and edges and the sheet is one oriented shell
(V - E + F = 1). Every truck call runs under guard. No command yet;
Boundary Fill will be the first caller.
Tests: one face for a regular surface, sewn Bezier faces with
T-junctions, tessellated points on the surface to ~1e-9 mm, and hostile
control nets (coincident, 1e300, needle-thin) never panic.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01J53sR6gEaVt56soFDpTck8
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Co-authored-by: Claude Opus 5.5 <[email protected]>
