gistfile1.cpp

#include <iostream>
#include <cmath>

#define GET_VECTOR(x) { cout << "Insert vector [" << #x << "] "; cin >> x; }

class Vector {
public:

  double x;
	double y;
	double z;

	Vector(double ax = 0, double ay = 0, double az = 0):x(ax),y(ay),z(az) { };

	friend std::istream& operator >> (std::istream &is, Vector &a) {
		is >> a.x >> a.y >> a.z;
		return is;
	}

	friend std::ostream& operator << (std::ostream &os, const Vector &a) {
		os << "(" << a.x << ", " << a.y << ", " << a.z << ")";
		return os;
	}

	// Addition: return = this - B
	Vector operator - (const Vector &b) {
		return Vector(this->x - b.x, this->y - b.y, this->z - b.z);
	}

	// Addition: return = this + B
	Vector operator + (const Vector &b) {
		return Vector(this->x + b.x, this->y + b.y, this->z + b.z);
	}

	// Cross product: return = this X B
	Vector operator ^ (const Vector &b) {
		return Vector(this->y*b.z - this->z*b.y,
                      this->z*b.x - this->x*b.z,
                      this->x*b.y - this->y*b.x);
	}

	// Dot product: return = this * B
	double operator * (const Vector &b) {
		return (this->x*b.x + this->y*b.y + this->z*b.z);
	}

	// Scalar product: return = this * f
	Vector operator * (const double &f) {
		return Vector(f*this->x, f*this->y, f*this->z);
	}

	// Scalar product: return = f * this
	friend Vector operator * (const double &f, Vector a) {
		return Vector(f*a.x, f*a.y, f*a.z);
	}

	// Convert the vector to an unary vector.
	void normalize() {
		double rt = x*x + y*y + z*z;
		if (rt > 0) {
			rt = sqrt(rt);
			x /= rt; y /= rt; z /= rt;
		}
	}
};

using namespace std;

int main() {
	Vector p1, p2, p3, p, v;

	GET_VECTOR(p1);
	GET_VECTOR(p2);
	GET_VECTOR(p3);
	GET_VECTOR(p);
	GET_VECTOR(v);

	v.normalize();

	Vector p21 = p2 - p1;
	Vector p31 = p3 - p1;

	Vector normal = p21 ^ p31;	// normal plane: N = (P2 - P1) X (P3 - P1)
	normal.normalize();
	double v_n = v * normal;	// V * N

	if (abs(v_n) > 0) {		// check if solution exists: N * V != 0
		double t = ((p1 - p) * normal)/v_n;
		if (t < 0) {
			cout << "No shadow" << endl;
		}
		else {
			cout << "S: " << (p + t * v) << endl;
		}
	}
	else {
		cout << "Plane parallel to V or no plane" << endl;
	}
	return 0;
}