bsplines Rust Library

Rust library for vectorized, N-dimensional B-spline curves and their derivatives based on nalgebra.

🚧 This Library is Under Construction 🚧

• Use iterators and simplify loops
• Use thiserror
• Refactor visibility and folder structure
• Refactor method selection and settings structs
• Add benchmarks and improve performance

lib.rs:

bsplines is a library for vectorized, N-dimensional B-spline curves and their derivatives based on [nalgebra].

Features

• Create N-dimensional (N = 1, 2, 3,...) curves of arbitrary polynomial degree p.
• Efficient curve evaluation for all available derivatives k = 0, 1,... , p.
• Built with nalgebra to store point data in contiguous arrays
• Multiple methods for
  • curve generation
  • curve parametrization
  • knot generation
  • [curve manipulation][manipulation]
    • knot insertion
    • reversing
    • splitting
    • merging

What are B-Splines?

B-splines are parametric functions composed of piecewise, polynomial basis functions of degree p > 0. These piecewise polynomials are joined so that the parametric function is p-1 times continuously differentiable. The overall functions are parametrized over finite domains with a so-called knot vector with the co-domain being an N-dimensional vector space, that is defined by control points. They can describe [curves][curve], but also surfaces. These characteristics lead to many desirable properties. The piecewise definition makes B-spline functions versatile allowing to interpolate or approximate complex-shaped and high-dimensional data, while maintaining a low polynomial degree. Because of the polynomial nature, all possible derivatives are accessible.

![A 2D B-Spline curve.][img-curve]

Still, evaluations or spatial manipulations can be executed fast because only local polynomial segments must be considered and the associated numerical procedures are stable. Lastly, polynomials represent a memory-efficient way of storing spatial information as few polynomial coefficients suffice to describe complex shapes.

Literature: