#include #include using namespace std; /*NOTE : To understand all what heppen you should have some knowledge about calculus in 3D spaces */ /* Hello every one .This code is about a 3D space system we will generate a namespace named space which containe these elements : - Coordinates3D: struct - Point : class - Vector : class - Line : class - Plan : class - Sphere : class */ /* Coordinates3D */ namespace space { template struct Coordinates { Coordinates(T cx = 0, T cy = 0, T cz = 0) { x = cx; y = cy; z = cz; } T x; T y; T z; }; } /* Point */ namespace space { template class Point { public: Point() : m_coor(0, 0, 0) { } Point(Coordinates const &coor) : m_coor(coor) { } // get accessor Coordinates getCoordinates() { return m_coor; } // set accessor void setCoordinates(Coordinates coor) { m_coor = coor; } private: Coordinates m_coor; }; } /* Vector */ namespace space { template class Vector { // spacial multiplication friend T operator*(const Vector &v1, const Vector &v2) { T x = v1.m_coor.x * v2.m_coor.x; T y = v1.m_coor.y * v2.m_coor.y; T z = v1.m_coor.z * v2.m_coor.z; return x + y + z; } // vectorial multiplication friend Vector operator^(const Vector &v1, const Vector &v2) { Vector v; v.m_coor.x = (v1.m_coor.y * v2.m_coor.z) - (v1.m_coor.z * v2.m_coor.y); v.m_coor.y = -(v1.m_coor.x * v2.m_coor.z) + (v1.m_coor.z * v2.m_coor.x); v.m_coor.z = (v1.m_coor.x * v2.m_coor.y) - (v1.m_coor.y * v2.m_coor.x); v.updateTall(); return v; } public: Vector() : m_coor(0, 0, 0), m_tall(0) { } Vector(Coordinates const &coor) : m_coor(coor) { updateTall(); } Vector(Point p1, Point p2) { m_coor.x = p2.getCoordinates().x; m_coor.x -= p1.getCoordinates().x; m_coor.y = p2.getCoordinates().y; m_coor.y -= p1.getCoordinates().y; m_coor.z = p2.getCoordinates().z; m_coor.z -= p1.getCoordinates().z; updateTall(); } // get accessor Coordinates getCoordinates() { return m_coor; } T getTall() { return m_tall; } // set accessor void setCoordinates(Coordinates coor) { m_coor = coor; } private: Coordinates m_coor; T m_tall; // calculate the tall void updateTall() { T x = pow(m_coor.x, 2); T y = pow(m_coor.y, 2); T z = pow(m_coor.z, 2); m_tall = x + y + z; m_tall = sqrt(m_tall); } }; } /*Line*/ namespace space { template class Line { public: Line(Point p, Vector v) : m_vect(v), m_point(p) { } // methods bool contain(Point p) { // t1calculus T t1; if (m_vect.getCoordinates().x == 0) { t1 = 0; } else { t1 = p.getCoordinates().x - m_point.getCoordinates().x; t1 /= m_vect.getCoordinates().x; } // t2 calculus T t2; if (m_vect.getCoordinates().y == 0) { t2 = 0; } else { t2 = p.getCoordinates().y - m_point.getCoordinates().y; t2 /= m_vect.getCoordinates().y; } // t3 calculus T t3; if (m_vect.getCoordinates().z == 0) { t3 = 0; } else { t3 = p.getCoordinates().z - m_point.getCoordinates().z; t3 /= m_vect.getCoordinates().z; } return (t1 == t2) && (t2 == t3); } T distance(Point p) { Vector v(m_point, p); v = v ^ m_vect; return v.getTall() / m_vect.getTall(); } // get accessors Vector getVector() { return m_vect; } Point getPoint() { return m_point; } // set accessors void setVector(Vector const &v) { m_vect = v; } void setPoint(Point const &p) { m_point = p; } private: Vector m_vect; Point m_point; }; } /* Plan */ namespace space { template class Plan { public: Plan(Point p, Vector v) : m_vect(v), m_point(p) { initializePrivateData(); } // methods void showEquation() { if (a != 0) { cout << a << "x"; } if (b != 0) { cout << "+ "; cout << b << "y "; } if (c != 0) { cout << "+ "; cout << c << "z "; } if (d != 0) { cout << "+ "; cout << d; } cout << " = 0" << endl; } bool contain(Point p) { T x = a * p.getCoordinates().x; T y = b * p.getCoordinates().y; T z = c * p.getCoordinates().z; T result = x + y + z + d; return result == 0; } T distance (Point p) { T x = a * p.getCoordinates().x; T y = b * p.getCoordinates().y; T z = c * p.getCoordinates().z; T dis = x + y + z + d; dis = abs (dis); dis /= m_vect.getTall (); return dis; } // get accessors Vector getVector() { return m_vect; } Point getPoint() { return m_point; } // set accessors void setVector(Vector const &v) { m_vect = v; initializePrivateData (); } void setPoint(Point const &p) { m_point = p; initializePrivateData (); } private: Vector m_vect; Point m_point; T a; T b; T c; T d; void initializePrivateData() { a = m_vect.getCoordinates().x; b = m_vect.getCoordinates().y; c = m_vect.getCoordinates().z; T ax = a * m_point.getCoordinates().x; T bx = b * m_point.getCoordinates().y; T cx = c * m_point.getCoordinates().z; d = ax + bx + cx; d *= -1; } }; } /* Sphere */ namespace space { template class Sphere { public : Sphere (Point center, T rayon) : m_center (center), m_rayon (rayon) {} // methods bool contain (Point p) { return distance () == m_rayon; } T distance (Point p) { Vector v (m_center, p); return v.getTall (); } // get accessors Point getCenter () { return m_center; } T getRayon () { return m_rayon; } // set accessors void setCenter (Point center) { m_center = center; } void setRayon (T rayon) { m_rayon = rayon; } private : Point m_center; T m_rayon; }; } // for tests int main() { space::Coordinates c1(0, 1, 3); space::Coordinates c2(3, 2, -2); space::Point p1(c1); space::Point p2(c2); space::Vector v1(p1, p2); space::Vector v2(c1); cout << v2 * v1 << endl; space::Vector v3; v3 = v2 ^ v1; cout << v2 * v3 << endl; cout << v2.getTall() << endl; cout << v3.getTall() << endl; space::Line l(p1, v2); if (l.contain(p1)) { cout << "yes" << endl; } cout << l.distance(p2) << endl; space::Plan plan(p1, v1); plan.showEquation(); if (plan.contain(p1)) { cout << "yes" << endl; } cout << plan.distance (p2) << endl; space::Sphere s (p2, 4); cout << s.distance (p1) << endl; return 0; }

Space calc