#include <gtest/gtest.h>
#include "SurfaceIntegrator.hpp"

using namespace internal;

// 一个简单的方程：f(v) = v^2 - 2, df = 2v，根为 sqrt(2)
TEST(SurfaceAreaCalculatorTest, NewtonMethodConverges)
{

    auto F = [](double v) -> equation_intermediate_t {
        implicit_equation_intermediate iei;
        iei.f = v * v - 2.0;
        iei.df = 2.0 * v;
        return equation_intermediate_t{iei};
    };

    double v_initial = 1.0;
    double tolerance = 1e-8;
    int max_iterations = 20;

    double root = newton_method(F, v_initial, tolerance, max_iterations);

    EXPECT_NEAR(root, std::sqrt(2.0), tolerance);
}