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NuoDaJia02
2025-10-24 11:12:14 +08:00
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gjk_interface/CMakeLists.txt Normal file
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cmake_minimum_required(VERSION 3.8)
project(gjk_interface)
if(CMAKE_COMPILER_IS_GNUCXX OR CMAKE_CXX_COMPILER_ID MATCHES "Clang")
add_compile_options(-Wall -Wextra -Wpedantic)
endif()
add_compile_options(-g)
find_package(ament_cmake REQUIRED)
find_package(eigen3_cmake_module REQUIRED)
find_package(Eigen3 REQUIRED) # 查找Eigen3库
add_library(${PROJECT_NAME} SHARED
src/gjk_interface.cpp
)
ament_target_dependencies(gjk_interface
Eigen3
)
target_include_directories(${PROJECT_NAME}
PUBLIC
$<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}/include>
$<INSTALL_INTERFACE:include>
)
install(TARGETS ${PROJECT_NAME}
EXPORT export_${PROJECT_NAME}
ARCHIVE DESTINATION lib
LIBRARY DESTINATION lib
RUNTIME DESTINATION bin
)
install(
DIRECTORY include/
DESTINATION include
)
ament_export_targets(export_${PROJECT_NAME} HAS_LIBRARY_TARGET)
ament_export_include_directories(include)
ament_package()

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#ifndef GJK_INTERFACE_HPP
#define GJK_INTERFACE_HPP
#include <vector>
#include <Eigen/Dense>
typedef enum {
COLLISION_RESULT_NO_COLLISION = 0,
COLLISION_RESULT_COLLISION = 1,
COLLISION_RESULT_ERROR = -1
} CollisionResultE;
struct OBB {
Eigen::Vector3d center; // 中心
Eigen::Vector3d axis[3]; // 3条正交的棱边方向轴（单位向量）
double halfExtent[3]; // 沿各轴的半长（从中心到面的距离）
};
namespace gjk_interface {
bool gjkCollisionJudge(const std::vector<Eigen::Vector3d>& polyA, const std::vector<Eigen::Vector3d>& polyB);
OBB createOBBFromVertices(const std::vector<Eigen::Vector3d>& vertices,
const float length, const float width, const float height);
bool checkOBBCollision(const OBB &obb1, const OBB &obb2);
} // namespace gjk_interface
#endif // GJK_INTERFACE_HPP

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<?xml version="1.0"?>
<?xml-model href="http://download.ros.org/schema/package_format3.xsd" schematypens="http://www.w3.org/2001/XMLSchema"?>
<package format="3">
<name>gjk_interface</name>
<version>0.0.0</version>
<description>gjk_interface</description>
<maintainer email="zj@todo.todo">zj</maintainer>
<license>Apache-2.0</license>
<buildtool_depend>ament_cmake</buildtool_depend>
<depend>Eigen3</depend>
<export>
<build_type>ament_cmake</build_type>
</export>
</package>

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gjk_interface/src/gjk_interface.cpp Normal file
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#include "math.h"
#include "gjk_interface.hpp"
#define POLY_SIMPLIFY_MAX_SIZE 4
using namespace Eigen;
namespace gjk_interface {
const Vector3d support(const std::vector<Vector3d>& poly, const Vector3d& dir)
{
float maxDot = -INFINITY;
Vector3d supportPoint;
for (const Vector3d& p : poly) {
float dot = p.dot(dir);
if (dot > maxDot) {
maxDot = dot;
supportPoint = p;
}
}
return supportPoint;
}
Vector3d supportMinkowski(const std::vector<Vector3d>& polyA, const std::vector<Vector3d>& polyB, Vector3d& dir)
{
Vector3d simplexPoint = support(polyA, dir);
const Vector3d oppositeDir = dir * -1;
simplexPoint = simplexPoint - support(polyB, oppositeDir);
return simplexPoint;
}
Vector3d checkLineSegment3D(const Vector3d& v0, const Vector3d& v1) {
Vector3d a = v1 - v0; // 线段方向向量
Vector3d b = -v1; // 从v1到原点的向量
float aDotA = a.dot(a);
Vector3d bParallel = a * (a.dot(b) / aDotA); // 平行投影
Vector3d bPerp = b - bParallel; // 垂直投影（新方向）
return bPerp;
}
Vector3d GetNormalToOri(const Vector3d& a, const Vector3d& b, const Vector3d& c) {
Vector3d ab = b - a;
Vector3d ac = c - a;
Vector3d ad = -a;
Vector3d n_initial = ab.cross(ac);
Vector3d n_outer = (n_initial.dot(ad) < 0) ? -n_initial : n_initial;
return n_outer;
}
Vector3d GetDir(const std::vector<Vector3d>& simplex) {
if (simplex.size() == 1) {
return -simplex[0];
} else if (simplex.size() == 2) {
return checkLineSegment3D(simplex[0], simplex[1]);
} else if (simplex.size() == 3) {
return GetNormalToOri(simplex[0], simplex[1], simplex[2]);
}
return Vector3d(0, 0, 0);
}
bool CheckTetrahedronHaveZero(const std::vector<Vector3d>& simplex) {
Vector3d A = simplex[0];
Vector3d B = simplex[1];
Vector3d C = simplex[2];
Vector3d D = simplex[3]; // 最新点（面ABC的对
// 构造线性方程组 Ax = b（求解alpha, beta, gamma）
Matrix3d mat;
mat.col(0) = A - D; // x1-x4, y1-y4, z1-z4
mat.col(1) = B - D; // x2-x4, y2-y4, z2-z4
mat.col(2) = C - D; // x3-x4, y3-y4, z3-z4
Vector3d b = -D; // -x4, -y4, -z4
// 求解方程组：mat * [alpha; beta; gamma] = b
if (mat.determinant() == 0) {
return true;
}
Vector3d x = mat.inverse() * b;
float alpha = x(0), beta = x(1), gamma = x(2);
float delta = 1 - alpha - beta - gamma;
// 判定4个权重是否均为正（允许1e-6误差）
const float eps = 1e-6;
return (alpha > eps) && (beta > eps) && (gamma > eps) && (delta > eps);
}
bool CheckTetrahedronHaveZero2(const std::vector<Vector3d>& simplex) {
Vector3d A = simplex[0];
Vector3d B = simplex[1];
Vector3d C = simplex[2];
Vector3d D = simplex[3]; // 最新点（面ABC的对
// 构造线性方程组 Ax = b（求解alpha, beta, gamma）
auto scalar_triple = [](const Vector3d& a, const Vector3d& b, const Vector3d& c) {
return a.dot(b.cross(c)); // Eigen封装了叉积和点积，底层运算与手动计算一致
};
double v0 = scalar_triple(B, C, D);
double v1 = scalar_triple(A, C, D);
double v2 = scalar_triple(A, B, D);
double v3 = scalar_triple(A, B, C);
// 判断所有符号是否一致（均正或均负）
bool all_positive = (v0 > 0) && (v1 > 0) && (v2 > 0) && (v3 > 0);
bool all_negative = (v0 < 0) && (v1 < 0) && (v2 < 0) && (v3 < 0);
return all_positive || all_negative;
}
bool gjkCollisionJudge(const std::vector<Vector3d>& polyA, const std::vector<Vector3d>& polyB)
{
// 初始搜索方向（从A中心指向B中心）
Vector3d centerA(0, 0, 0), centerB(0, 0, 0);
for (const auto& p : polyA) {
centerA = centerA + p;
}
for (const auto& p : polyB) {
centerB = centerB + p;
}
centerA = centerA / polyA.size();
centerB = centerB / polyA.size();
Vector3d dir = centerB - centerA;
// 初始化单纯形
std::vector<Vector3d> simplex;
Vector3d newPoint = supportMinkowski(polyA, polyB, dir);
simplex.push_back(newPoint);
int maxIndex = 3;
while (true) {
dir = GetDir(simplex);
if (dir.dot(dir) < 1e-6) {
return true;
}
newPoint = supportMinkowski(polyA, polyB, dir);
if (newPoint.dot(newPoint) < 1e-6) {
return true;
}
if (newPoint.dot(dir) < -(1e-6)) {
return false;
}
simplex.push_back(newPoint);
if (simplex.size() == POLY_SIMPLIFY_MAX_SIZE) {
bool haveZero = CheckTetrahedronHaveZero2(simplex);
if (haveZero) {
return true;
} else {
float maxLength = 0;
for (size_t i = 0; i < POLY_SIMPLIFY_MAX_SIZE; i++) {
Vector3d simplexPoint = simplex[i];
float newLength = simplexPoint.dot(simplexPoint);
if (maxLength < newLength) {
maxLength = newLength;
maxIndex = i;
}
}
simplex.erase(simplex.begin() + maxIndex);
}
}
}
return false;
}
// 从8个顶点提取OBB参数
OBB createOBBFromVertices(const std::vector<Eigen::Vector3d>& vertices,
const float length, const float width, const float height) {
if (vertices.size() != 8) {
throw std::invalid_argument("OBB创建失败:必须输入8个顶点");
}
OBB obb;
obb.center = (vertices[1] + vertices[2] + vertices[4] - vertices[0]) * (1.0 / 2.0);
// 正交化（格拉姆-施密特过程），确保3条轴正交
obb.axis[0] = (vertices[1] - vertices[0]).normalized();
obb.axis[1] = (vertices[2] - vertices[0]).normalized();
obb.axis[2] = (vertices[4] - vertices[0]).normalized();
obb.halfExtent[0] = length * (1.0 / 2.0);
obb.halfExtent[1] = width * (1.0 / 2.0);
obb.halfExtent[2] = height * (1.0 / 2.0);
return obb;
}
// 计算OBB在指定轴上的投影范围（min, max）
std::pair<double, double> projectOBB(const OBB& obb, const Vector3d& axis) {
// OBB中心在轴上的投影
double centerProj = obb.center.dot(axis);
// OBB沿轴的总投影长度（半长在轴上的投影之和）
double totalExtent = 0.0;
for (int i = 0; i < 3; ++i) {
totalExtent += obb.halfExtent[i] * fabs(obb.axis[i].dot(axis));
}
return { centerProj - totalExtent, centerProj + totalExtent };
}
// 判断两个投影范围是否重叠
bool areProjectionsOverlapping(double aMin, double aMax, double bMin, double bMax) {
return !(aMax < bMin - 1e-6 || bMax < aMin - 1e-6); // 1e-6为浮点误差容限
}
// OBB碰撞检测主函数（输入：两个长方体的8个顶点，共16个）
bool checkOBBCollision(const OBB &obb1, const OBB &obb2) {
// 2. 定义所有需要检查的分离轴（共15条）
std::vector<Vector3d> separationAxes;
// 2.3 两个OBB轴的两两叉积（3×3=9条）
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Vector3d crossAxis = obb1.axis[i].cross(obb2.axis[j]);
if (crossAxis.dot(crossAxis) > 1e-6) { // 排除零向量（轴平行时叉积为零
Vector3d crossAxisNormalized = crossAxis.normalized();
auto [aMin, aMax] = projectOBB(obb1, crossAxisNormalized);
auto [bMin, bMax] = projectOBB(obb2, crossAxisNormalized);
if (!areProjectionsOverlapping(aMin, aMax, bMin, bMax)) {
// 找到分离轴，判定为不碰撞
return false;
}
}
}
}
// 2.1 第一个OBB的3条轴
for (int i = 0; i < 3; ++i) {
auto [aMin, aMax] = projectOBB(obb1, obb1.axis[i]);
auto [bMin, bMax] = projectOBB(obb2, obb1.axis[i]);
if (!areProjectionsOverlapping(aMin, aMax, bMin, bMax)) {
// 找到分离轴，判定为不碰撞
return false;
}
}
// 2.2 第二个OBB的3条轴
for (int i = 0; i < 3; ++i) {
auto [aMin, aMax] = projectOBB(obb1, obb2.axis[i]);
auto [bMin, bMax] = projectOBB(obb2, obb2.axis[i]);
if (!areProjectionsOverlapping(aMin, aMax, bMin, bMax)) {
// 找到分离轴，判定为不碰撞
return false;
}
}
// 所有轴均重叠，判定为碰撞
return true;
}
}