Module curve

Modules

conic

Exact conic curve data.

elevation

Elevation laws and the composition of a planar curve with one.

evaluate

Backend-open curve evaluation capability.

implicit

Curves given implicitly: where a field over a surface’s parameters is zero (ADR 0077).

linear

Linear curve values.

linear_vocabulary

The focused linear vocabulary, re-exported for consumers that want to name its origin explicitly. A line-only consumer should depend on axiolid-linear directly instead of paying for this aggregate.

pair_section

Where two parametric surfaces meet, carried by nodes on both (ADR 0077).

quadric_section

Where a quadric cuts a cylinder or cone, read in the ruled surface’s own parameters (ADR 0076).

sinusoid

The height wave a plane cuts across a cylinder, in the cylinder’s own parameters.

spline

B-spline and rational B-spline curve data.

spline_surface

Polynomial and rational B-spline surfaces.

torus_section

Where a plane or sphere cuts a torus, read in the torus’s own parameters (ADR 0076).

Structs

AngleGraph2

The solution u(t) of a(t) cos u + b(t) sin u = c(t) chosen by branch, as a graph over its second coordinate: the point at t is (u(t), t).

BSplineCurve

Exact B-spline data. Rational curves carry one weight per control point.

BSplineSurface

Tensor-product B-spline surface preserving exact knot and weight data.

Circle2

Circle in a two-dimensional frame.

Circle3

Circle in a three-dimensional plane frame.

Elevated3

A planar curve carrying an independent elevation law.

Ellipse2

Ellipse in a two-dimensional frame.

Ellipse3

Ellipse in a three-dimensional plane frame.

Harmonic

One sinusoidal term of a curvature law: amplitude * sin(angular_frequency * s + phase).

ImplicitCell

One stretch of an ImplicitCurve2: as the free parameter runs from from to to, the curve is the unique zero of the field for the other parameter in [low, high], where the field is strictly monotone in it.

ImplicitCurve2

A stretch of a field’s zero set, in the parameters of the surface the field lives on. The parameter t runs over [0, cells.len()]: cell i covers [i, i + 1], its free parameter moving linearly from from to to.

ImplicitSection3

An ImplicitCurve2 on its carrier, in space: the point at t is the carrier’s point at curve.point(t).

Intrinsic2

A plane curve given by its natural equation: a curvature law anchored to a start frame and run for a finite arc length.

Intrinsic3

A space curve given by its natural equations.

Jet2

A field’s value, gradient and Hessian at one point.

LiftedCurve2

A curve in space read in an analytic surface’s parameters: the pcurve at t is the carrier’s parameters of curve’s point at t, so it shares the edge’s parameter exactly. This is the pcurve, on the analytic face, of a section that only the other face’s surface can carry (a B-spline’s section, ADR 0077): the inverse is in closed form for planes, ruled surfaces, spheres and tori.

Line

Infinite parametric line origin + t * direction.

PairNode

A point on both surfaces, with its parameters on each.

PairSection3

A stretch of the curve where two surfaces meet. The parameter runs over [0, nodes.len() - 1], one unit per chord.

PatchField2

A piecewise polynomial field: on each cell of the grid of u_breaks by v_breaks, a tensor-product Bernstein polynomial of degree (u_degree, v_degree) in the cell’s local coordinates s, t in [0, 1]. Its coefficients bound it (the convex hull property), which is what makes a trace on it certified.

Polyline

Piecewise-linear curve preserving source vertex order.

QuadraticGraph2

The graph of one root of a(t) v^2 + b(t) v + c(t) = 0, parameterised by its first coordinate: the point at t is (t, v(t)).

RuledCarrier

A ruled carrier surface, as the curve needs it: a cylinder (rx = ry, slope = 0), an elliptical cylinder (slope = 0) or a cone (rx = ry, slope = tan(semi-angle)), in the same parameterisation as the matching axiolid_surface family.

RuledSection3

A quadric’s section of a ruled carrier, in space: the point at t is the carrier’s point at (t, graph.height(t)).

SeriesField2

A field over the parameter plane: sum c[i][j] B_i(u) B_j(v), with the bases of Basis along each parameter. The form a plane’s, quadric’s or torus’s equation takes on an analytic surface.

Sinusoid2

The graph v = mean + cosine cos(t) + sine sin(t), parameterised by t.

SurfaceJet

A point’s partial derivatives on a Carrier, to second order.

TorusCarrier

A torus, as the curve needs it, in axiolid_surface::Torus’s parameterisation: O + (R + r cos v)(cos u X + sin u Y) + r sin v Z.

TorusSection3

A plane’s or sphere’s section of a torus, in space: the torus point at (graph.angle(t), t).

Trig2

constant + cos cos(t) + sin sin(t) + cos2 cos(2t) + sin2 sin(2t).

Enums

Axis

Which parameter a cell runs along; the other is solved for.

Basis

How a SeriesField2 varies along one parameter.

Branch

Which root of the quadratic a graph follows.

Carrier

The surface a traced curve lies on, as the curve needs it, in the same parameterisation as the matching axiolid_surface family.

CurvatureLaw

Curvature as a closed-form function of arc length.

Curve2

Atomic two-dimensional curve values.

Curve3

Atomic three-dimensional curve values.

ElevationLaw

Height as a function of distance along the plan.

Field2

A field over a surface’s parameters whose zero set is a section curve: another surface’s equation read in this surface’s parameters.

KnotSpec

How the knot vector was specified by the source representation.

Traits

CurveEvaluator

Evaluate and differentiate one curve representation.

Type Aliases

BSplineCurve2

Two-dimensional B-spline curve.

BSplineCurve3

Three-dimensional B-spline curve.

Line2

Two-dimensional line.

Line3

Three-dimensional line.

Polyline2

Two-dimensional polyline.

Polyline3

Three-dimensional polyline.