Module evaluate 

General NURBS analysis, inverse-query, and exact transformation algorithms. Scalar evaluation for parametric curves and surfaces.

Modules

arc_length

Arc-length evaluation of intrinsic (natural-equation) curves and of the planar-plus-elevation composition.

arc_parameter

Arc length along any evaluable curve, and its inverse.

banked

Evaluation of banked curves: point, tangent and the rolled section frame.

bound

Certified derivative and chord bounds (#232).

chain

Evaluation of arc-length chains (Chain2).

curve

Scalar reference implementation of curve evaluation (ADR 0012).

elevated

Derivatives, certified bounds and seams of elevated and banked curves in plan distance (#252).

elevation

Heights, grades and chord bounds of elevation laws, including the profile given by its own curvature, which has no closed form (#238).

frenet

Frame and position of a space curve given by curvature and torsion.

intrinsic_relation

Relations over Intrinsic3: trimming, offsetting, and joining.

polyline_length

Exact distance-to-parameter conversion for polylines.

provider

The reference curve-evaluation provider.

station

Stations: a position at a distance along a curve, framed by the curve’s section (#241, ADR 0082).

surface

Scalar reference implementation of surface evaluation (ADR 0012).

Structs

BankedSection

The section of a banked curve at one station.

CompositeBasis

Pieces of curves laid end to end as one station basis; see the module documentation.

Mitre

The plane a section stands in where a run crosses a seam whose tangents differ; see the module documentation.

Patch

A finite parameter rectangle for tessellation.

ReferenceCurveEvaluator

Reference curve evaluator.

ScalarCurve

Portable scalar curve evaluator.

ScalarSurface

The axiolid_surface::SurfaceEvaluator implementation, so a caller can dispatch through the trait rather than the free functions.

SectionFrame

A point on a curve and the section axes there: tangent, left lateral and up, unit and right-handed (up = tangent x lateral).

StationPiece

One piece of a CompositeBasis: the span [start, end] of an atomic curve, in that curve’s station measure, traversed forwards or backwards, optionally placed by a rigid motion; see the module documentation.

StationSeam

A place inside a curve where two of its pieces meet; see the module documentation.

Enums

StationCurve

The atomic curve under a StationPiece.

Constants

ARC_LENGTH_TOLERANCE

Relative tolerance of every arc length and arc-length inverse this module returns: the absolute tolerance for a length l is ARC_LENGTH_TOLERANCE * max(1, |l|), in the curve’s length unit.

Functions

arc_length2

Signed arc length of a 2D curve from parameter from to to: negative when to < from. See the module documentation for the tolerance.

arc_length3

Signed arc length of a 3D curve from parameter from to to; see arc_length2.

banked_derivative

Derivative of banked_point in plan distance: (p, g + e'). Not unit: its length is sqrt(1 + (g + e')^2).

banked_point

Position on a banked curve at plan distance d: base(d) + e(d) z.

banked_second_derivative

Second derivative of banked_point in plan distance (#252): the centreline’s (p'', z'') plus the pivot’s e'' vertically.

banked_section

The section at plan distance d: rotation point, rolled frame, cant, bank angle and roll.

banked_tangent

Unit tangent of a banked curve at plan distance d.

chain_point

Point on a chain at arc length s from its start. See the module documentation for the accuracy contract and refusals.

chain_tangent

Unit tangent of a chain at arc length s (unit when the start frame is orthonormal; a skewed frame maps it as it maps an intrinsic curve’s).

derivative2

First derivative of a 2D curve.

derivative3

First derivative of a 3D curve.

elevated_chord_bound

Certified 3D chord bound of an elevated curve over plan distances [a, b]: sqrt(P^2 + Z^2), P = h^2 / 8 sup |k| the plan’s and Z the profile’s chord bound at equal plan distance (see the module documentation for the derivation).

elevated_derivative

Derivative of an elevated curve in plan distance: (p', z'). Not unit: its length is sqrt(1 + g^2) on an orthonormal plan frame.

elevated_derivative_bounds

Certified suprema of |c'|, |c''|, |c'''| of an elevated curve in plan distance over [a, b]: sqrt(P_j^2 + Z_j^2) (module documentation). None where the curve may not be C^2 strictly inside the span, or where either half is not bounded.

elevated_point

Position on an elevated curve at plan distance d.

elevated_second_derivative

Second derivative of an elevated curve in plan distance: (k n, z''), the plan’s curvature vector and the profile’s z''.

elevated_tangent

Unit tangent of an elevated curve at plan distance d.

elevation_chord_bound

Certified bound on how far an elevation law strays from the chord of its heights over the plan-distance span [a, b]: sup |z(d) - L(d)|, L the straight line through (a, z(a)) and (b, z(b)).

elevation_grade

Grade dz/dd at plan distance distance, for every law in the family.

elevation_height

Height at plan distance distance, for every law in the family.

evaluate2

Position on a 2D curve.

evaluate3

Position on a 3D curve.

exact_station_seams2

station_seams2, refusing a curve with a seam whose distance is not read from stored data alone.

exact_station_seams3

station_seams3, refusing a curve with a seam whose distance is not read from stored data alone.

flatten2

Flatten a 2D curve over domain so the chord never deviates from the true curve by more than chord_tolerance.

frenet_frame

Frame of a space curve at arc length s from its start.

frenet_point

Position on a space curve at arc length s from its start.

frenet_tangent

Unit tangent of a space curve at arc length s from its start.

grade_corners3

Where an elevated or banked curve turns a corner: the seams (of its profile, and of a banked curve’s pivot) across which the grade of its point path jumps by more than angle radians, ascending.

intrinsic_point

Position on an intrinsic curve at arc length s from its start.

intrinsic_tangent

Unit tangent of an intrinsic curve at arc length s.

join_intrinsic3

Join two space curves into one, when the second continues the first.

offset_intrinsic3

Offset a space curve by distance along its principal normal.

parameter_at_arc_length2

The parameter at signed arc length length from parameter from along a 2D curve: in increasing parameter for a positive length, decreasing for a negative one.

parameter_at_arc_length3

parameter_at_arc_length2 for a 3D curve.

partials

Analytic first partial derivatives (∂S/∂u, ∂S/∂v) at (u, v).

station_frame_is_exact2

Whether a station frame on this 2D curve is exact (#264): its point and axes at the station’s distance itself, in closed form, rounding aside, with no quadrature or root find behind them.

station_frame_is_exact3

station_frame_is_exact2 for a 3D curve: only a line.

station_length2

The length a station on a 2D curve is measured against: None for a line (unbounded), one turn for a circle or an ellipse, the arc length of its domain for a polyline or a B-spline, the stated length of an intrinsic curve or a chain.

station_length3

The length a station on a 3D curve is measured against, as station_length2; an elevated curve’s is its plan’s, a banked curve’s the span of its cant law.

station_seams2

The seams of a 2D curve, every one located (see the module documentation); a B-spline’s corner knots by quadrature, flagged not exact.

station_seams3

The seams of a 3D curve, every one located; see station_seams2.

station_section2

The section of a 2D curve at arc length distance from its start; see the module documentation for the conventions.

station_section3

The section of a 3D curve at distance from its start: plan distance on an elevated or banked curve, arc length on any other; see the module documentation.

station_section2_on

station_section2 reading side of a seam the station lies on (see the module documentation); off a seam the side does not matter.

station_section3_on

station_section3 reading side of a seam the station lies on (see the module documentation); off a seam the side does not matter.

trim_intrinsic3

Restrict a space curve to [start, end] of its arc length.