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feat(surface-integral): add volume computation and improve domain checks in SurfaceAreaCalculator

feat-integrator
mckay 2 months ago
parent
07fe15f863
commit
9a5c7ad0f9
4 changed files with 133 additions and 95 deletions
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  1. 1
      primitive_process/interface/base/subface.hpp
  2. 12
      surface_integral/interface/SurfaceIntegrator.hpp
  3. 52
      surface_integral/interface/flat_index_group.hpp
  4. 163
      surface_integral/src/SurfaceIntegrator.cpp

1
primitive_process/interface/base/subface.hpp
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@ -67,6 +67,7 @@ EXTERN_C struct PE_API subface {
double v) const = 0;
virtual std::function<internal::equation_intermediate_t(internal::constraint_curve_intermediate &&)>
fetch_solver_evaluator() const = 0;
virtual bool is_implicit_equation_intermediate() const {return true;};
primitive_data_center_ptr_t data_center{};
internal::paired_model_matrix_ptr_t model_matrices{};

12
surface_integral/interface/SurfaceIntegrator.hpp
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@ -3,7 +3,7 @@
#include <base/subface.hpp>
#include <container/stl_alias.hpp>
#include "flat_index_group.hpp"
#include <container/wrapper/flat_index_group.hpp>
namespace internal
{
@ -37,6 +37,7 @@ public:
// 计算面积主函数
template <typename Func>
double calculate(Func&& func, int gauss_order = 3) const;
double compute_volume(int gauss_order = 4) const;
private:
const subface& m_surface; // 引用原始曲面
@ -49,14 +50,15 @@ private:
// 私有辅助函数
// 直线u=u_val与边界的交点
std::vector<double> find_vertical_intersections(double u_val);
std::vector<double> find_vertical_intersections(double u_val) const;
bool is_point_inside_domain(double u, double v);
bool is_u_near_singularity(double u, double tol = 1e-6);
bool is_point_inside_domain(double u, double v) const;
bool is_u_near_singularity(double u, double tol = 1e-6) const;
void sort_and_unique_with_tol(std::vector<double>& vec, double epsilon = 1e-8);
void sort_and_unique_with_tol(std::vector<double>& vec, double epsilon = 1e-8) const;
};
double newton_method(const std::function<equation_intermediate_t(double)>& F,
double v_initial,
double tolerance = 1e-8,

52
surface_integral/interface/flat_index_group.hpp
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@ -1,52 +0,0 @@
#pragma once
#include <container/stl_alias.hpp>
#include <iterator/counting_iterator.hpp>
struct flat_index_group {
stl_vector_mp<uint32_t> index_group{}; /// a list of indices in the group
stl_vector_mp<uint32_t> start_indices{}; /// a list of start indices for each group in the flat index group
inline size_t size() const { return start_indices.size() - 1; }
struct group_index_looper {
auto begin() const { return counting_iterator<uint32_t>{0}; }
auto end() const { return counting_iterator<uint32_t>{static_cast<uint32_t>(parent_group.size())}; }
const flat_index_group& parent_group{};
};
auto group_indices() const { return group_index_looper{*this}; }
struct group_looper {
auto begin() const
{
return std::next(parent_group.index_group.begin(), *(parent_group.start_indices.begin() + group_idx));
}
auto end() const
{
return std::next(parent_group.index_group.begin(), *(parent_group.start_indices.begin() + group_idx + 1));
}
const flat_index_group& parent_group{};
const uint32_t group_idx{};
};
auto group(uint32_t group_idx) const { return group_looper{*this, group_idx}; }
inline auto group_index_iter_begin() const { return counting_iterator<uint32_t>{0}; }
inline auto group_index_iter_end() const { return counting_iterator<uint32_t>{static_cast<uint32_t>(size())}; }
inline auto group_begin(uint32_t group_idx) const
{
return std::next(index_group.begin(), *(start_indices.begin() + group_idx));
}
inline auto group_end(uint32_t group_idx) const
{
return std::next(index_group.begin(), *(start_indices.begin() + group_idx + 1));
}
};

163
surface_integral/src/SurfaceIntegrator.cpp
View File

@ -3,6 +3,7 @@
#include <Eigen/Geometry> // For vector and cross product operations
#include <cmath> // For math functions like sqrt
#include <set>
#include <iostream>
namespace internal
{
@ -81,6 +82,7 @@ void SurfaceAreaCalculator::set_ubreaks(const stl_vector_mp<double>& u_breaks) {
template <typename Func>
double SurfaceAreaCalculator::calculate(Func&& func, int gauss_order) const
{
auto solver = m_surface.fetch_solver_evaluator();
// 在u方向进行高斯积分
auto u_integrand = [&](double u) {
// 对每个u，找到v方向的精确交点
@ -89,13 +91,22 @@ double SurfaceAreaCalculator::calculate(Func&& func, int gauss_order) const
// 在v方向进行高斯积分
auto v_integrand = [&](double v) {
// 判断点是否在有效域内
if (IsPointInsideself(u, v, self.outerEdges, self.innerEdges, self.Umin, self.Umax, self.Vmin, self.Vmax)) {
if (is_point_inside_domain(u, v)) {
try {
gp_Pnt p;
gp_Vec dU, dV;
surface->D1(u, v, p, dU, dV);
// 获取两个方向的 evaluator
auto eval_du = m_surface.fetch_curve_constraint_evaluator(parameter_v_t{}, v); // 固定 v，变 u → 得到 ∂/∂u
auto eval_dv = m_surface.fetch_curve_constraint_evaluator(parameter_u_t{}, u); // 固定 u，变 v → 得到 ∂/∂v
const double jacobian = dU.Crossed(dV).Magnitude();
auto res_u = eval_du(u); // f(u,v), grad_f = ∂r/∂u
auto res_v = eval_dv(v); // f(u,v), grad_f = ∂r/∂v
Eigen::Vector3d p = res_u.f.template head<3>(); // 点坐标 (x,y,z)
Eigen::Vector3d dU = res_u.grad_f.template head<3>(); // ∂r/∂u
Eigen::Vector3d dV = res_v.grad_f.template head<3>(); // ∂r/∂v
// ✅ 计算面积元：||dU × dV||
Eigen::Vector3d cross = dU.cross(dV);
double jacobian = cross.norm(); // 雅可比行列式（面积缩放因子）
return func(u, v, p, dU, dV) * jacobian;
} catch (...) {
return 0.0; // 跳过奇异点
@ -111,7 +122,7 @@ double SurfaceAreaCalculator::calculate(Func&& func, int gauss_order) const
// 检查区间中点是否有效
double mid_v = (a + b) / 2.0;
if (IsPointInsideself(u, mid_v, self.outerEdges, self.innerEdges, self.Umin, self.Umax, self.Vmin, self.Vmax)) {
if (is_point_inside_domain(u, mid_v)) {
v_integral += integrate_1D(a, b, v_integrand, gauss_order);
} else {
std::cout << "uv out of domain: (" << u << "," << mid_v << ")" << std::endl;
@ -140,8 +151,73 @@ double SurfaceAreaCalculator::calculate(Func&& func, int gauss_order) const
return integral;
}
// 在 SurfaceAreaCalculator 类中添加：
double SurfaceAreaCalculator::compute_volume(int gauss_order) const
{
double total_volume = 0.0;
// 外层：对 u 分段积分
auto u_integrand = [&](double u) {
std::vector<double> v_breaks = find_vertical_intersections(u);
double v_integral = 0.0;
// 内层：对 v 积分
auto v_integrand = [&](double v) -> double {
if (!is_point_inside_domain(u, v)) {
return 0.0;
}
try {
// 获取偏导数
auto eval_du = m_surface.fetch_curve_constraint_evaluator(parameter_v_t{}, v); // ∂/∂u
auto eval_dv = m_surface.fetch_curve_constraint_evaluator(parameter_u_t{}, u); // ∂/∂v
auto res_u = eval_du(u);
auto res_v = eval_dv(v);
Eigen::Vector3d p = res_u.f.template head<3>(); // r(u,v)
Eigen::Vector3d dU = res_u.grad_f.template head<3>(); // r_u
Eigen::Vector3d dV = res_v.grad_f.template head<3>(); // r_v
// 计算 r · (r_u × r_v)
Eigen::Vector3d cross = dU.cross(dV);
double mixed_product = p.dot(cross);
return mixed_product; // 注意：不是 norm，是点积
} catch (...) {
return 0.0;
}
};
for (size_t i = 0; i < v_breaks.size() - 1; ++i) {
double a = v_breaks[i];
double b = v_breaks[i + 1];
double mid_v = (a + b) / 2.0;
if (is_point_inside_domain(u, mid_v)) {
v_integral += integrate_1D(a, b, v_integrand, gauss_order);
}
}
return v_integral;
};
// 在 u 方向积分
for (size_t i = 0; i < m_u_breaks.size() - 1; ++i) {
double a = m_u_breaks[i];
double b = m_u_breaks[i + 1];
double mid_u = (a + b) / 2.0;
auto v_intersections = find_vertical_intersections(mid_u);
if (!v_intersections.empty()) {
total_volume += integrate_1D(a, b, u_integrand, gauss_order, is_u_near_singularity(mid_u));
}
}
// 乘以 1/3
return std::abs(total_volume) / 3.0;
}
// 直线u=u_val与边界的交点
std::vector<double> SurfaceAreaCalculator::find_vertical_intersections(double u_val)
std::vector<double> SurfaceAreaCalculator::find_vertical_intersections(double u_val) const
{
std::vector<double> intersections;
std::vector<int32_t> uPositionFlags;
@ -168,7 +244,7 @@ std::vector<double> SurfaceAreaCalculator::find_vertical_intersections(double u_
if (v1.x() != v2.x()) {
// "The line segment is vertical (u₁ == u₂), so there is no unique v value corresponding to the given u."
double v_initial = v1.y() + (v2.y() - v1.y()) * (u_val - v1.x()) / (v2.x() - v1.x());
auto curve_evaluator = m_surface.fetch_curve_constraint_evaluator(u_val);
auto curve_evaluator = m_surface.fetch_curve_constraint_evaluator(parameter_u_t{}, u_val);
auto solver_evaluator = m_surface.fetch_solver_evaluator();
auto target_function = [&](double v) -> equation_intermediate_t {
constraint_curve_intermediate temp_res = curve_evaluator(v);
@ -196,8 +272,9 @@ std::vector<double> SurfaceAreaCalculator::find_vertical_intersections(double u_
NOTE: when v_intersect - v < threshold, further checks are required to accurately determine if the intersection point lies
precisely on the boundary segment.
*/
bool is_point_inside_domain(double u, double v)
bool SurfaceAreaCalculator::is_point_inside_domain(double u, double v) const
{
bool is_implicit_equation_intermediate = m_surface.is_implicit_equation_intermediate();
uint32_t group_idx = 0, intersection_count = 0;
for (uint32_t element_idx = 0; element_idx < m_uv_plane.chains.index_group.size() - 1; element_idx++) {
if (element_idx > m_uv_plane.chains.start_indices[group_idx + 1]) group_idx++;
@ -206,18 +283,29 @@ bool is_point_inside_domain(double u, double v)
uint32_t vertex_idx2 = m_uv_plane.chains.index_group[element_idx + 1];
auto v1 = m_uv_plane.chain_vertices[vertex_idx1], v2 = m_uv_plane.chain_vertices[vertex_idx2];
if ((v1.x() <= u && v2.x() > u) || (v2.x() < u && v1.x() >= u)) {
double v_intersected = v1.y() + (v2.y() - v1.y()) * (u_val - v1.x()) / (v2.x() - v1.x());
if (v_interdected - v >= 1e-6) {
double v_initial = v1.y() + (v2.y() - v1.y()) * (u - v1.x()) / (v2.x() - v1.x());
if (v_initial - v >= 1e-6) {
intersection_count++;
} else if (std::abs(v_intersected - v) < 1e-6) {
auto curve_evaluator = m_surface.fetch_curve_constraint_evaluator(u);
auto solver_evaluator = m_surface.fetch_solver_evaluator();
auto target_function = [&](double v) -> equation_intermediate_t {
constraint_curve_intermediate temp_res = curve_evaluator(v);
return solver_evaluator(std::move(temp_res));
};
double v_solution = newton_method(target_function, v_initial);
if (std::abs(v_solution - v) > 0) { intersection_count++; }
} else if (std::abs(v_initial - v) < 1e-6) {
// Only use Newton's method for implicit surfaces (scalar equation)
// Newton requires f(v) and df/dv as scalars — only implicit provides this.
// Skip parametric surfaces (vector residual) — treat initial guess as final
if (is_implicit_equation_intermediate) {
auto curve_evaluator = m_surface.fetch_curve_constraint_evaluator(parameter_u_t{}, u);
auto solver_evaluator = m_surface.fetch_solver_evaluator();
auto target_function = [&](double v) -> equation_intermediate_t {
constraint_curve_intermediate temp_res = curve_evaluator(v);
auto full_res = solver_evaluator(std::move(temp_res));
// ensure solver_eval returns implicit_equation_intermediate)
return std::get<internal::implicit_equation_intermediate>(full_res);
};
double v_solution = newton_method(target_function, v_initial);
if (std::abs(v_solution - v) > 0) { intersection_count++; }
}
else{
continue;
}
}
}
/*
@ -228,7 +316,7 @@ bool is_point_inside_domain(double u, double v)
return intersection_count % 2 == 1; // in domain
}
bool is_u_near_singularity(double u, double tol = 1e-6)
bool SurfaceAreaCalculator::is_u_near_singularity(double u, double tol) const
{
for (auto idx : m_uv_plane.singularity_vertices) {
double singular_u = m_uv_plane.chain_vertices[idx].x();
@ -242,7 +330,7 @@ bool is_u_near_singularity(double u, double tol = 1e-6)
return false;
}
void SurfaceAreaCalculator::sort_and_unique_with_tol(std::vector<double>& vec, double epsilon)
void SurfaceAreaCalculator::sort_and_unique_with_tol(std::vector<double>& vec, double epsilon) const
{
if (vec.empty()) return;
@ -259,35 +347,34 @@ void SurfaceAreaCalculator::sort_and_unique_with_tol(std::vector<double>& vec, d
vec.resize(write_index + 1);
}
// 牛顿法求解器
double newton_method(const std::function<equation_intermediate_t(double)>& F,
double v_initial,
double tolerance,
int max_iterations)
// Only accepts functions that return implicit_equation_intermediate
double newton_method(
const std::function<internal::implicit_equation_intermediate(double)>& F,
double v_initial,
double tolerance = 1e-6,
int max_iterations = 20)
{
double v = v_initial;
for (int i = 0; i < max_iterations; ++i) {
equation_intermediate_t res = F(v);
double f = res.f;
double df = res.df;
auto res = F(v); // Known type: implicit_equation_intermediate
double f_val = res.f;
double df_val = res.df;
if (std::abs(f) < tolerance) {
std::cout << "✅ Converged in " << i + 1 << " iterations. v = " << v << std::endl;
if (std::abs(f_val) < tolerance) {
std::cout << "Converged at v = " << v << std::endl;
return v;
}
if (std::abs(df) < 1e-10) {
std::cerr << "⚠️ Derivative near zero. No convergence." << std::endl;
if (std::abs(df_val) < 1e-10) {
std::cerr << "Derivative near zero." << std::endl;
return v;
}
v -= f / df;
std::cout << "Iteration " << i + 1 << ": v = " << v << ", f = " << f << std::endl;
v = v - f_val / df_val;
}
std::cerr << "❌ Did not converge within " << max_iterations << " iterations." << std::endl;
std::cerr << "Newton failed to converge." << std::endl;
return v;
}

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