Module nurbs Copy item path Source extrema Extrema between points, curves and surfaces (#119, B7): the smallest
distance between two pieces of geometry, certified. 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. 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. 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. 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 ImplicitSection3None 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
PairSection3first (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.