refactor newton method and introduce test with googleTest

surface_integral/interface/SurfaceIntegrator.hpp

@@ -52,11 +52,13 @@ private:
     std::vector<double> find_vertical_intersections(double u_val);
 
     bool   is_point_inside_domain(double u, double v);
-    double newton_method(const std::function<equation_intermediate_t(double)>& F,
+
-                         double                                                v_initial,
-                         double                                                tolerance      = 1e-8,
-                         int                                                   max_iterations = 100);
     void   sort_and_unique_with_tol(std::vector<double>& vec, double epsilon = 1e-8);
 };
 
+double newton_method(const std::function<equation_intermediate_t(double)>& F,
+                        double                                                v_initial,
+                        double                                                tolerance      = 1e-8,
+                        int                                                   max_iterations = 100);
+
 } // namespace internal

surface_integral/src/SurfaceIntegrator.cpp

@@ -232,8 +232,26 @@ bool is_point_inside_domain(double u, double v)
     return intersection_count % 2 == 1; // in domain
 }
 
+
+void SurfaceAreaCalculator::sort_and_unique_with_tol(std::vector<double>& vec, double epsilon)
+{
+    if (vec.empty()) return;
+
+    std::sort(vec.begin(), vec.end());
+
+    size_t write_index = 0;
+    for (size_t read_index = 1; read_index < vec.size(); ++read_index) {
+        if (std::fabs(vec[read_index] - vec[write_index]) > epsilon) {
+            ++write_index;
+            vec[write_index] = vec[read_index];
+        }
+    }
+
+    vec.resize(write_index + 1);
+}
+
 // 牛顿法求解器
-double SurfaceAreaCalculator::newton_method(const std::function<equation_intermediate_t(double)>& F,
+double newton_method(const std::function<equation_intermediate_t(double)>& F,
                                             double                                                v_initial,
                                             double                                                tolerance,
                                             int                                                   max_iterations)
@@ -264,22 +282,5 @@ double SurfaceAreaCalculator::newton_method(const std::function<equation_interme
     return v;
 }
 
-void SurfaceAreaCalculator::sort_and_unique_with_tol(std::vector<double>& vec, double epsilon)
-{
-    if (vec.empty()) return;
-
-    std::sort(vec.begin(), vec.end());
-
-    size_t write_index = 0;
-    for (size_t read_index = 1; read_index < vec.size(); ++read_index) {
-        if (std::fabs(vec[read_index] - vec[write_index]) > epsilon) {
-            ++write_index;
-            vec[write_index] = vec[read_index];
-        }
-    }
-
-    vec.resize(write_index + 1);
-}
-
 
 } // namespace internal

surface_integral/test/SurfaceIntegrator_test.cpp

@@ -0,0 +1,24 @@
+#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);
+}

surface_integral/xmake.lua

@@ -4,4 +4,10 @@ internal_library("surface_integral", "SI", os.scriptdir())
     add_rules("config.indirect_predicates.flags")
     add_deps("primitive_process", "shared_module")
 
-
+-- add Google Test target
+target("newton_method_test")
+    set_kind("binary")
+    add_deps("surface_integral") -- depend on the internal library surface_integral
+    add_files("test/SurfaceIntegrator_test.cpp")   
+    add_packages("gtest")
+target_end()