Crate axiolid_nurbs

Expand description

General NURBS algorithms over Axiolid’s format-neutral B-spline values.

This crate builds on the portable scalar oracle: evaluation comes from axiolid-evaluate and is not reimplemented here. It owns differential geometry and exact shape-preserving transformations; importers and tessellators are consumers, not the capability boundary.

Every tolerance-sensitive solver takes explicit, bounded options (work ceilings, resolutions, tolerances) and reports an unresolved outcome or refuses when they run out. A shape-preserving transform is tested against independent evaluation samples of the original, not its own recurrence.

Modules§

extrema: Extrema between points, curves and surfaces (#119, B7): the smallest distance between two pieces of geometry, certified.

Structs§

BoundedResult: Outcome of a lossy operation: the curve, and the error it introduced.
BoundedSurface: A surface changed within a stated bound.
CertifiedCurveIntersectionOptions: Accuracy and work policy for certified planar root isolation.
CertifiedCurveSurfaceIntersectionOptions: Bounded policy for certified curve/surface root isolation.
CertifiedProjectionOptions: Explicit work and accuracy policy for globally certified projection.
CertifiedRegion: One classified leaf of the certified subdivision.
CertifiedSurfaceArcs3: Result of certified curved surface/surface analysis.
CertifiedSurfaceArcsOptions: Explicit policy for certified curved analysis.
CertifiedSurfaceProjectionOptions: Explicit accuracy and work policy for globally certified surface projection.
CertifiedSurfaceSurfaceIntersectionOptions: Bounded policy for certified surface/surface intersection and affine tracing.
ClassifiedCurveContact2: One classified non-transverse contact, owned by exactly one parameter box.
ConstructedCurveSurfacePoint3: A certified curve/surface crossing, reported as a point rather than a curve.
ConstructedIntersectionCurve3: An intersection curve constructed from a certified trace.
CurveCurveHit: One point where two curves meet, with its parameter on each.
CurveDifferential2: Parameter-invariant differential properties of a planar curve.
CurveDifferential3: Parameter-invariant differential properties of a spatial curve.
CurveDistanceCertificate2: Globally bounded minimum-distance result for two planar curves.
CurveDistanceCertificate3: Globally bounded minimum-distance result for two spatial curves.
CurvePairParameterBox: Product-domain box that may contain a globally closest curve pair.
CurveProjection2: Best planar-curve projection candidate found within the supplied budget.
CurveProjection3: Best spatial-curve projection candidate found within the supplied budget.
CurveProjectionCertificate2: Globally bounded closest-point result for a planar curve.
CurveProjectionCertificate3: Globally bounded closest-point result for a spatial curve.
CurveSurfaceParameterBox: Native parameter box for a curve and a tensor-product surface patch.
ExactCurveHit: One intersection point.
ExactIntersectionCurve: The exact intersection curve of two elementary surfaces, when one exists in closed form.
FundamentalForm: Coefficients (e, f, g) of a quadratic fundamental form.
Isolated: A parameter isolated by certified subdivision, held as the exact double it was refined to (so parameters compare exactly, bit for bit).
ParameterInterval: Closed native-parameter interval that may contain a global minimizer.
PeriodicBSplineSurface: An owned tensor-product B-spline surface with validated cyclic axes.
PeriodicCurve2: Verified closed-seam extension of a planar B-spline curve.
PeriodicCurve3: Verified closed-seam extension of a spatial B-spline curve.
ProjectionOptions: Explicit work and convergence policy for bounded projection.
SurfaceDifferential: First/second-order differential properties of an oriented surface.
SurfaceInversionCertificate3: Unique native parameters proven to name a point on the surface.
SurfaceKnotRemoval: The outcome of removing one knot value from a surface up to some number of times.
SurfaceParameterBox: Closed native (u, v) box that may contain a global minimizer.
SurfaceProjection: Best surface projection candidate found within the supplied budget.
SurfaceProjectionCertificate3: Globally bounded closest-point certificate for a spatial surface.
SurfaceSurfaceParameterBox: Native four-parameter box for a pair of tensor-product surfaces.
SurfaceSurfaceTraceEndpoint3: Certified endpoint enclosure for an affine surface/surface trace.
TransverseCurveIntersection2: One isolated transverse planar intersection.
TransverseCurveSurfaceIntersection3: Existence-and-uniqueness certificate for one transverse intersection.
TransverseSurfaceSurfaceTrace3: Certificate for one complete regular affine intersection segment.

Enums§

CertifiedCurveIntersection2: Planar curve/curve classification under the implemented proof paths.
CertifiedCurveSurfaceIntersection3: Certified curve/surface query outcome.
CertifiedSurfaceProjection3: Exhaustive bounded outcome for spatial surface projection.
CertifiedSurfaceSurfaceIntersection3: Certified surface/surface query outcome.
CoverageFault: Why a set of regions failed to account for the whole domain.
CurveIntersectionDegeneracy: Singular or not-yet-isolated curve relationship.
Derivation: The closed-form identity behind an exact intersection curve.
ExactCurveIntersection: The exact intersection of a curve with another operand.
ExactCurveParameter: Where on the first curve an intersection lies, exactly.
ExactCurveRefusal: Why an exact curve intersection was not computed.
ExactIntersectionRefusal: Why an elementary pair has no exact closed-form intersection curve here.
IntersectionCurveRefusal: Why a certified query produced no constructed intersection curve.
ProjectionStatus: Outcome of the selected bounded local solve.
RegionKind: What was certified about one leaf region of the parameter domain.
SeamContinuity: Highest endpoint continuity verified in the curve’s native parameter.
SurfaceInversionRefusal: Why a sound inversion query did not yield unique parameters.
SurfaceProjectionUnresolvedReason: Why a valid surface projection remains unresolved without exhausting work.

Constants§

MAX_AUDIT_DEPTH: Largest subdivision depth the coverage audit can represent exactly.
MAX_CERTIFIED_SURFACE_PROJECTION_DEPTH: Maximum accepted binary subdivision depth for certified surface projection.
MAX_CERTIFIED_SURFACE_PROJECTION_WORK: Maximum accepted shared work budget for certified surface projection.

Functions§

analyze_curve2: Analyze a regular planar curve at t.
analyze_curve3: Analyze a regular spatial curve at t.
analyze_surface: Analyze a regular oriented surface at (u, v).
audit_coverage: Verify that the regions tile the root parameter box exactly.
bezier_segments2: Decompose a planar B-spline into exact rational/polynomial Bézier segments.
bezier_segments3: Decompose a spatial B-spline into exact rational/polynomial Bézier segments.
certify_surface_arcs: Certify the transversality structure of a curved surface pair.
construct_curve_surface_points: Construct curve/surface intersection points for a clamped NURBS pair.
construct_surface_surface_curves: Construct intersection curves for two clamped NURBS surfaces.
curve2_seam_continuity: Verify native-parameter endpoint continuity of a planar B-spline curve.
curve3_seam_continuity: Verify native-parameter endpoint continuity of a spatial B-spline curve.
distance_curve2_certified: Certify the global minimum distance between two planar B-spline curves.
distance_curve3_certified: Certify the global minimum distance between two spatial B-spline curves.
elevate_degree2: Raise a planar curve’s degree by one without changing its image.
elevate_degree3: Raise a spatial curve’s degree by one without changing its image.
elevate_surface_degree_u: Raise the surface’s u degree by one without changing it.
elevate_surface_degree_v: Raise the surface’s v degree by one; as elevate_surface_degree_u.
exact_curve_curve_intersection2: The exact intersection of two analytic plane curves.
exact_curve_curve_intersection3: The exact intersection of two analytic space curves.
exact_curve_surface_intersection: The exact intersection of an analytic curve with an elementary surface.
exact_surface_intersection: Derive the exact intersection curve of two elementary surfaces.
extract_stretch: The stretch of one of curves that runs from start through first and then second to end (all in parameters, each possibly a whole period off), as a curve of its own running from start to end. closed asks for a whole loop from start back to itself, in the direction that meets first before second.
implicit_surface_intersection: Every component of the section of carrier by other in a window of carrier’s parameters, as implicit curves on carrier.
implicit_view: A section-family curve over span as an ImplicitSection3, with the same point set and direction; None for other families or where the trace is refused.
insert_knot2: Insert one interior knot into a planar curve in homogeneous coordinates.
insert_knot3: Insert one interior knot into a spatial curve in homogeneous coordinates.
insert_surface_knot_u: Insert one U-axis knot into every homogeneous control-net column.
insert_surface_knot_v: Insert one V-axis knot into every homogeneous control-net row.
interpolate_curve3: Interpolate a cubic B-spline through points in order.
intersect_curve2_certified: Classify intersections of two clamped planar B-spline curves.
intersect_curve_surface_certified: Certify all isolated transverse roots of curve(t) = surface(u, v).
intersect_surface_surface_certified: Certify bounded intersections of two clamped, internally continuous NURBS surfaces.
invert_periodic_surface_certified: Globally invert a point against one canonical period of a cyclic surface.
invert_surface_certified: Globally invert a point against a clamped B-spline surface.
iso_curve_at_u: The iso-curve u = parameter, parametrised by v.
iso_curve_at_v: The iso-curve v = parameter, parametrised by u; as iso_curve_at_u.
loft_surface: Loft a surface through ordered section curves.
project_curve2: Find the best planar-curve projection candidate within explicit budgets.
project_curve3: Find the best spatial-curve projection candidate within explicit budgets.
project_curve2_certified: Globally bound the closest point on a clamped planar B-spline curve.
project_curve3_certified: Globally bound the closest point on a clamped spatial B-spline curve.
project_periodic_surface_certified: Exhaustively bound the global point-to-surface minimum over one canonical period of an explicitly validated cyclic B-spline surface.
project_surface: Find the best tensor-product surface projection candidate within budgets.
project_surface_certified: Exhaustively bound the global point-to-surface minimum over the closed native domain of a finite clamped NURBS surface.
reduce_degree2: Lower a planar curve’s degree by one, or refuse.
reduce_degree3: Lower a spatial curve’s degree by one, or refuse.
reduce_surface_degree_u: Lower the surface’s u degree by one, within tolerance, or refuse.
reduce_surface_degree_v: Lower the surface’s v degree by one; as reduce_surface_degree_u.
remove_knot2: Remove one interior knot from a planar curve, or refuse.
remove_knot3: Remove one interior knot from a spatial curve, or refuse.
remove_surface_knot_u: Remove the u knot parameter up to times times, keeping the surface within tolerance of the input.
remove_surface_knot_v: Remove the v knot parameter up to times times; as remove_surface_knot_u.
reverse2: Reverse a planar B-spline curve without changing its image.
reverse3: Reverse a spatial B-spline curve without changing its image.
reverse_surface_u: Reverse the surface’s U parameter without changing its image.
reverse_surface_v: Reverse the surface’s V parameter without changing its image.
section_curve_curve_intersection2: Where two plane curves meet, each over its span.
section_curve_curve_intersection3: Where two space curves meet, each over its span, within tolerance.
section_curve_surface_intersection: Where a section-family curve meets a surface, with parameters on the curve itself.
section_field_of: other’s implicit equation read in carrier’s parameters, where both are analytic: zero exactly where carrier’s point lies on other (for a cone, on either nappe).
spline_pair_intersection: Every component of the section of two B-spline surfaces within windows of their parameters (their whole domains when None), each a PairSection3 whose first surface is first (ADR 0077).
split2: Split a planar curve exactly at an interior parameter.
split3: Split a spatial curve exactly at an interior parameter.
trace_section_pcurves: Every component of the section of surface by other in a window of surface’s parameters, as curves in those parameters.
wrap_curve2_parameter: Wrap a finite planar-curve parameter into its active domain.
wrap_curve3_parameter: Wrap a finite spatial-curve parameter into its active domain.