pse example 4.4 - a bullseye every time.cpp

#include "stdafx.h"

#include "..\..\include\symbolicc++.h"

Symbolic Pi = "Pi";

Symbolic g = "g";

Symbolic Radians(Symbolic n) { return n * Pi / 180; }

Symbolic Degrees(Symbolic n) { return 180 * n / Pi; }

class Point
{
public:
	
	Symbolic x;
	Symbolic y;
	
	Point() { x = "NOTSET" ; y = "NOTSET"; }

	Point(Symbolic x_val, Symbolic y_val)
	{
		x = x_val;
		y = y_val;
	}

	void Print()
	{
		cout << "Point(" << x << ", " << y << ")";
	}

	static Point FromAngle(Symbolic angle, Symbolic mag)
	{ return Point(cos(angle) * mag, sin(angle) * mag); }

	Point operator+(Point p) { return Point(x + p.x, y + p.y); }

	Point operator*(Symbolic sym) { return Point(x * sym, y * sym); }

	Point operator/(Symbolic sym) { return Point(x / sym, y / sym); }
};

void Unset(Symbolic &sym) { sym = "NOTSET"; }

bool IsSet(Symbolic sym) 
{ 
	if (sym == "NOTSET")
		return false;
	else
		return true;
}

bool HasVal(Symbolic sym) 
{ 
	if (sym == "NOTSET")
		return false;
	else
		return true;
}

class Obj
{
public:
	Point position, velocity, acceleration;

	Symbolic time;

	void Print()
	{
		// cout << "Obj:" << endl;
		cout << "time:           " << time << endl;
		cout << "position.x:     " << position.x << endl;
		cout << "position.y:     " << position.y << endl;
		cout << "velocity.x:     " << velocity.x << endl;
		cout << "velocity.y:     " << velocity.y << endl;
		cout << "acceleration.x: " << acceleration.x << endl;
		cout << "acceleration.y: " << acceleration.y << endl;
	}

	Obj AtTime(Symbolic t)
	{
		Obj obj;

		obj.time = t;

		auto dt = t - time;

		obj.acceleration = acceleration;
		obj.velocity = velocity + acceleration * dt;
		obj.position = position + velocity * dt + acceleration * dt * dt / 2;

		return obj;
	}
};

Symbolic CalcTime(Obj& a, Obj& b, int flag=0)
{
	if (HasVal(b.velocity.x) &&
		HasVal(a.velocity.x) &&
		HasVal(a.acceleration.x) &&
		a.acceleration.x != 0.0 &&
		a.acceleration.x != 0)
		return (b.velocity.x - a.velocity.x) / a.acceleration.x;

	if (HasVal(b.velocity.y) &&
		HasVal(a.velocity.y) &&
		HasVal(a.acceleration.y) &&
		a.acceleration.y != 0.0 &&
		a.acceleration.y != 0)
		return (b.velocity.y - a.velocity.y) / a.acceleration.y;

	if (HasVal(a.position.x) &&
		HasVal(b.position.x) &&
		HasVal(a.velocity.x) &&
		a.velocity.x != 0 &&
		a.velocity.x != 0.0)
		return (b.position.x - a.position.x) / a.velocity.x;

	if (HasVal(b.position.x) &&
		HasVal(a.position.x) &&
		HasVal(a.velocity.x) &&
		HasVal(a.acceleration.x) &&
		a.acceleration.x != 0 &&
		a.acceleration.x != 0.0)
	{
		
		if (flag == 0)
			return
				(-a.velocity.x + sqrt(pow(a.velocity.x, Symbolic(2)) - 2 * a.acceleration.x * (a.position.x - b.position.x)))
				/
				a.acceleration.x;
		else
			return
				(-a.velocity.x - sqrt(pow(a.velocity.x, Symbolic(2)) - 2 * a.acceleration.x * (a.position.x - b.position.x)))
				/
				a.acceleration.x;
	}

	throw "exception";
}

auto _g = Point(0, -g);

int _tmain(int argc, _TCHAR* argv[])
{	
	// In a popular lecture demonstration, a projectile is fired at a
	// target in such a way that the projectile leaves the gun at the
	// same time the target is dropped from rest.
	// Show that if the gun is initially aimed at the stationary
	// target, the projectile hits the target.

	Obj obj1A; // object 1 at A

	obj1A.position = Point(0,0);

	auto th = Symbolic("th");
	auto v1A = Symbolic("v1A"); // The velocity of object 1 at A

	obj1A.velocity = Point::FromAngle(th, v1A);

	obj1A.acceleration = _g;

	obj1A.time = 0;


	Obj obj1C; // object 1 at C

	obj1C.position = Point();

	auto w = Symbolic("w");

	obj1C.position.x = w;

	obj1C.velocity = Point();

	obj1C.velocity.x = obj1A.velocity.x;

	obj1C.acceleration = _g;

	auto timeAC = CalcTime(obj1A, obj1C);

	cout << "time from A to C:" << endl;
	cout << timeAC << endl << endl;

	cout << "Height of object 1 at C:" << endl;
	cout << obj1A.AtTime(timeAC).position.y << endl << endl;


	Obj obj2B; // Object 2 at B

	auto h = Symbolic("h");

	obj2B.position = Point(w, h);
	obj2B.velocity = Point(0, 0);
	obj2B.acceleration = _g;

	auto obj2D = obj2B.AtTime(timeAC);

	cout << "Height of object 2 at D:" << endl;
	cout << obj2D.position.y << endl << endl;

	// The answer is in terms of 'h'.
	// Let's write it in terms of 'w'.

	// tan(th) = h / w
	//
	// h = w tan(th)

	cout << "Height of object 2 at D (in terms of h):" << endl;
	cout << obj2D.position.y[h == w * tan(th)] << endl << endl;

	if (obj1A.AtTime(timeAC).position.y == obj2D.position.y[h == w * tan(th)])
		cout << "object 1 and object 2 are at the same height" << endl;

	system("pause");
	return 0;
}