Fix 4th/5th derivative coefficients in NaturalQuinticSpline::Evaluate

[CodeReclaimers]

Lines 219 and 225 use factor 60 (= 5*4*3, correct for the 3rd derivative) where 120 (= 5!, needed for the 4th and 5th derivatives) is required. The 4th and 5th derivatives are returned at half their correct values.

Fix: introduce r120 = 120 and use it in place of r60 on lines 219 and 225.

Test (CMakeLists.txt)

cmake_minimum_required(VERSION 3.14)
project(test_issue_6_1 LANGUAGES CXX)
set(CMAKE_CXX_STANDARD 17)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(GTE_ROOT "${CMAKE_CURRENT_SOURCE_DIR}/../../GTE")
add_executable(test_issue_6_1 test_issue_6_1.cpp)
target_include_directories(test_issue_6_1 PRIVATE "${GTE_ROOT}")

Test (test_issue_6_1.cpp)

#include <cmath>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <Mathematics/NaturalQuinticSpline.h>

static bool test_derivatives_vs_coefficients()
{
    using Real = double;
    using Vec = gte::Vector<1, Real>;

    std::vector<Real> times = { 0.0, 1.0, 2.0 };
    Vec v0, v1, v2;
    v0[0] = 0.0; v1[0] = 1.0; v2[0] = 0.0;
    std::vector<Vec> f0 = { v0, v1, v2 };
    Vec d0, d1, d2;
    d0[0] = 1.0; d1[0] = 0.0; d2[0] = -1.0;
    std::vector<Vec> f1 = { d0, d1, d2 };

    gte::NaturalQuinticSpline<1, Real> spline(true, f0, f1, times);
    auto const& c = spline.GetPolynomials()[0];
    Real c4 = c[4][0], c5 = c[5][0];

    // Analytically: p''''(u) = 24*c4 + 120*c5*u, p'''''(u) = 120*c5
    Real u = 0.7;
    Real d4_expected = 24.0 * c4 + 120.0 * c5 * u;
    Real d5_expected = 120.0 * c5;

    Vec jet[6];
    spline.Evaluate(0.7, 5, jet);
    return std::fabs(jet[4][0] - d4_expected) < 1e-10
        && std::fabs(jet[5][0] - d5_expected) < 1e-10;
}

int main()
{
    return test_derivatives_vs_coefficients() ? EXIT_SUCCESS : EXIT_FAILURE;
}