ArcFrame is a C# library for generating, evaluating, and composing arc-length-parameterized curves in 2D, 3D, and higher dimensions. It centers on intrinsic descriptions of curves (curvature as a function of arc length) and integrates moving frames on SO(N) to recover position and orientation with stable, adaptive numerics. The library includes robust clothoid utilities based on the Bertolazzi–Frego formulations for G1 interpolation and extensions toward G2 spline construction.
IArcLengthCurve with Evaluate(s) → (P, R, k) where P is position, R is an orthonormal frame [T, N, …], and k are principal curvatures. This contract ensures the curve can be embedded in any spatial dimension.
IntrinsicCurve builds curves from a CurveSpec that couples initial pose (ND), frame model (Frenet or Bishop), and a curvature law (N-1 components).
A midpoint integrator on SO(N) with adaptive step control for stable propagation of pose over arc length. TODO: implement RK4 frame stepping.
Uses the Levenberg-Marquardt algorithm to solve a CompositeCurveProblem given a set of constraints.
Linear curvature laws and generalized Fresnel integral evaluators support accurate clothoid construction and sampling.
A generalized matrix based Spline object, works as a native IArcLengthCurve by caching an ArcLengthTable on creation. Works with any matrix based spline model.
Position found via right-multiplication: P(t) = GBt' where G is the control point window, B is the basis matrix and t' is the power monomial vector [1, t, t^2, ...]^T
Built in cubic B-Splines include: CatmullRomSpline, BezierSpline, BSpline, HermiteSpline. Native support for any degree: linear, quadratic, cubic, quartic, and beyond.
CompositeCurve concatenates segments with automatic G1 alignment. TransformedCurve, RigidTransform, and PromotedCurve embed and position curves across dimensions.
CachedIntrinsicCurve checkpoints along arc length for fast re-evaluation and uniform sampling.
Path planning and motion primitives for robotics and vehicles
Track, road, and rail geometry design
Game and simulation tooling that needs smooth, controllable splines
CAD/CAM workflows that benefit from curvature-aware construction