Line3DCompare.h

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#include <cmath>
#include <vector>
#include <iostream>
 
struct Vector3D
{
    double x, y, z;
 
    // Constructors
    Vector3D() : x(0), y(0), z(0) {}
    Vector3D(double x, double y, double z) : x(x), y(y), z(z) {}
 
    // Operations
    Vector3D operator-(const Vector3D& v) const {
        return {x - v.x, y - v.y, z - v.z};
    }
    Vector3D cross(const Vector3D& v) const {
        return {y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x};
    }
    double dot(const Vector3D& v) const {
        return x * v.x + y * v.y + z * v.z;
    }
    double magnitude() const {
        return std::sqrt(x*x + y*y + z*z);
    }
};
 
 
bool areCoplanar(const Vector3D& d1, const Vector3D& d2, const Vector3D& v) {
    return std::abs(d1.cross(d2).dot(v)) < 1e-6;
}
 
 
bool areParallel(const Vector3D& d1, const Vector3D& d2) {
    Vector3D crossProduct = d1.cross(d2);
    return crossProduct.magnitude() < 1e-6;
}
 
 
bool areCoincident(const Vector3D& d1, const Vector3D& v) {
    return std::abs(d1.dot(v)) < 1e-6;
}
 
 
double shortestDistance(const Vector3D& d1, const Vector3D& d2, const Vector3D& v) {
    return std::abs(v.dot(d1.cross(d2))) / d1.cross(d2).magnitude();
}
 
 
void compareLines(const FitLine3D& line1, const FitLine3D& line2)
{
    Vector3D P1(line1.fitParameters[0], line1.fitParameters[1], line1.fitParameters[2]);
    Vector3D d1(line1.fitParameters[3], line1.fitParameters[4], line1.fitParameters[5]);
 
    Vector3D P2(line2.fitParameters[0], line2.fitParameters[1], line2.fitParameters[2]);
    Vector3D d2(line2.fitParameters[3], line2.fitParameters[4], line2.fitParameters[5]);
 
    Vector3D v = P2 - P1;
 
    // Check for coplanarity
    if (areCoplanar(d1, d2, v)) {
        std::cout << "The lines are coplanar." << std::endl;
    } else {
        std::cout << "The lines are not coplanar." << std::endl;
    }
 
    // Check for parallel, coincident, or skewed
    if (areParallel(d1, d2)) {
        if (areCoincident(d1, v)) {
            std::cout << "The lines are coincident." << std::endl;
        } else {
            std::cout << "The lines are parallel." << std::endl;
        }
    } else {
        std::cout << "The lines are skewed." << std::endl;
    }
 
    // Print the shortest distance between the lines
    double distance = shortestDistance(d1, d2, v);
    std::cout << "Shortest distance between the lines: " << distance << std::endl;
}