geom::CubicSplineObject Concept Reference

Concept for a cubic spline. More...

#include <geomc/shape/CubicSpline.h>

Concept definition

template<typename S, typename T, index_t N>
concept geom::CubicSplineObject =  requires (S s, const VecType<T,N> control_pts[4]) {
    S(control_pts);
    S(control_pts[0], control_pts[1], control_pts[2], control_pts[3]);
    { S::basis()         } -> std::convertible_to<const SimpleMatrix<T,4,4>&>;
    { S::inverse_basis() } -> std::convertible_to<const SimpleMatrix<T,4,4>&>;
    { s.control_points() } -> std::convertible_to<const VecType<T,N>*>;
    { s.bounds()         } -> std::same_as<Rect<T,N>>;
    { s.velocity(T(0))   } -> std::same_as<VecType<T,N>>;
    { s(T(0))            } -> std::same_as<VecType<T,N>>;
}

Detailed Description

Concept for a cubic spline.

A cubic spline is a curve defined by four control points, and a basis matrix. The control points have different meanings for each type of spline, but all cubic splines are interconvertible.

The basis matrix converts control points to cubic polynomial coefficients. The resultant vector has the coefficients in order of increasing power.