B-spline utility for C++17

BSpline.h

/***************************************************************************
BSpline.h - Utilities for BSpline operations

This is a C++ adaptation of Tagussan's JavaScript BSpline library. Typically
BSpline basis functions are implemented recursively by De Boor's algorithm,
but in this case we're using pre-calculated uniform knot BSpline bases for
speed. Unlike Tagussan's library, this only supports 2D coordinate systems.

---

The MIT License (MIT)

Copyright (c) 2014-2024 KP, Tagussan

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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The above copyright notice and this permission notice shall be included in all
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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SOFTWARE.
***************************************************************************/
#pragma once

#include <vector>
#include <utility>

namespace bspline {
  
struct XYf { float x, y; };

template <unsigned int Degree>
class BSpline
{
public:
    BSpline(std::vector<XYf> points):
        points(std::move(points))
    {
    }

    constexpr float Basis(float x)
    {
        static_assert(Degree >= 2 && Degree <= 5, "Degree must be within range 2-5");

        if constexpr (Degree == 2)
        {
            if (-0.5 <= x && x < 0.5)
                return 0.75 - x * x;
            else if (0.5 <= x && x <= 1.5)
                return 1.125 + (-1.5 + x / 2.0) * x;
            else if (-1.5 <= x && x < -0.5)
                return 1.125 + (1.5 + x / 2.0) * x;
            else
                return 0;
        }
        else if constexpr (Degree == 3)
        {
            if (-1 <= x && x < 0)
                return 2.0 / 3.0 + (-1.0 - x / 2.0) * x * x;
            else if (1 <= x && x <= 2)
                return 4.0 / 3.0 + x * (-2.0 + (1.0 - x / 6.0) * x);
            else if (-2 <= x && x < -1)
                return 4.0 / 3.0 + x * (2.0 + (1.0 + x / 6.0) * x);
            else if (0 <= x && x < 1)
                return 2.0 / 3.0 + (-1.0 + x / 2.0) * x * x;
            else
                return 0;
        }
        else if constexpr (Degree == 4)
        {
            if (-1.5 <= x && x < -0.5)
                return 55.0 / 96.0 + x * (-(5.0 / 24.0) + x * (-(5.0 / 4.0) + (-(5.0 / 6.0) - x / 6.0) * x));
            else if (0.5 <= x && x < 1.5)
                return 55.0 / 96.0 + x * (5.0 / 24.0 + x * (-(5.0 / 4.0) + (5.0 / 6.0 - x / 6.0) * x));
            else if (1.5 <= x && x <= 2.5)
                return 625.0 / 384.0 + x * (-(125.0 / 48.0) + x * (25.0 / 16.0 + (-(5.0 / 12.0) + x / 24.0) * x));
            else if (-2.5 <= x && x <= -1.5)
                return 625.0 / 384.0 + x * (125.0 / 48.0 + x * (25.0 / 16.0 + (5.0 / 12.0 + x / 24.0) * x));
            else if (-1.5 <= x && x < 1.5)
                return 115.0 / 192.0 + x * x * (-(5.0 / 8.0) + x * x / 4.0);
            else
                return 0;
        }
        else if constexpr (Degree == 5)
        {
            if (-2 <= x && x < -1)
                return 17.0 / 40.0 + x * (-(5.0 / 8.0) + x * (-(7.0 / 4.0) + x * (-(5.0 / 4.0) + (-(3.0 / 8.0) - x / 24.0) * x)));
            else if (0 <= x && x < 1)
                return 11.0 / 20.0 + x * x * (-(1.0 / 2.0) + (1.0 / 4.0 - x / 12.0) * x * x);
            else if (2 <= x && x <= 3)
                return 81.0 / 40.0 + x * (-(27.0 / 8.0) + x * (9.0 / 4.0 + x * (-(3.0 / 4.0) + (1.0 / 8.0 - x / 120.0) * x)));
            else if (-3 <= x && x < -2)
                return 81.0 / 40.0 + x * (27.0 / 8.0 + x * (9.0 / 4.0 + x * (3.0 / 4.0 + (1.0 / 8.0 + x / 120.0) * x)));
            else if (1 <= x && x < 2)
                return 17.0 / 40.0 + x * (5.0 / 8.0 + x * (-(7.0 / 4.0) + x * (5.0 / 4.0 + (-(3.0 / 8.0) + x / 24.0) * x)));
            else if (-1 <= x && x < 0)
                return 11.0 / 20.0 + x * x * (-(1.0 / 2.0) + (1.0 / 4.0 + x / 12.0) * x * x);
            else
                return 0;
        }
    }

    XYf SeqAt(float n)
    {
        float margin = Degree + 1.0;
        if (n < margin)
            return points.front();
        else if (points.size() + margin <= n)
            return points.back();
        else
            return points[n - margin];
    }

    XYf CalcAt(float t)
    {
        t *= (Degree + 1) * 2 + points.size();

        float ti = floor(t);
        XYf result = {0, 0};
        for (float i = ti - Degree; i <= ti + Degree; i++)
        {
            result.x += SeqAt(i).x * Basis(t - i);
            result.y += SeqAt(i).y * Basis(t - i);
        }

        return result;
    }

public:
    std::vector<XYf> points;
};

} // namespace bspline