pse example 4.3 - the long jump.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)
{
	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;

	throw "exception";
}

int _tmain(int argc, _TCHAR* argv[])
{	
	// A long-jumper leaves the ground at an angle of 20.0° above
	// the horizontal and at a speed of 11.0 m/s. (a) How far does
	// he jump in the horizontal direction? (Assume his motion is
	// equivalent to that of a particle.)

	// For the purposes of solving the problem, let's take 
	//   point A as the initial position
	//   point B as the peak position
	//   point C as the final position.

	// First we'll get the answer in a symbolic form.

	Obj objA; // An Obj representing the object at A

	objA.position = Point(0, 0);

	auto thA = Symbolic("thA"); // angle at point A
	auto vA = Symbolic("vA");   // velocity at point A

	objA.velocity = Point::FromAngle(thA, vA);
	objA.acceleration = Point(0, -g);
		
	objA.time = 0;

	Obj objB;

	// The horizontal velocity at B is the same as it is at A.
	// The vertical velocity at B is 0;

	objB.velocity = Point(objA.velocity.x, 0);
	objB.acceleration = Point(0, -g);

	auto timeB = CalcTime(objA, objB);
	auto timeC = timeB * 2;

	// Let's display the object at the three states, A, B, C:

	cout << "object at point A:" << endl;
	objA.Print();
	cout << endl ;

	cout << "object at point B:" << endl;
	objA.AtTime(timeB).Print();
	cout << endl;

	cout << "object at point C:" << endl;
	objA.AtTime(timeC).Print();
	cout << endl;
	
	// Now let's get the numerical answer.

	// Subsitute the numerical values to get a numerical timeB value:

	auto timeBNum = timeB[g==9.8, thA==Radians(20), vA==11][Pi==3.14159];

	cout << "numerical time at B is ";
	cout << timeBNum << endl << endl;

	// Let's reassign some symbols to their numerical values:

	Pi = 3.14159;
	thA = Radians(20);
	vA = 11;
	g = 9.8;

	// Re-run the calculation to get the numerical values.

	objA.velocity = Point::FromAngle(thA, vA);
	objA.acceleration = Point(0, -g);

	cout << "object at point A (numerical): " << endl;
	objA.AtTime(0).Print();
	cout << endl;

	cout << "object at point B (numerical): " << endl;
	objA.AtTime(timeBNum).Print();
	cout << endl;

	cout << "object at point C (numerical): " << endl;
	objA.AtTime(timeBNum*2).Print();
	cout << endl;

	cout << "How far does he dump in the horizontal direction?" << endl;
	cout << objA.AtTime(timeBNum*2).position.x << endl << endl;

	cout << "What is the maximum height reached?" << endl;
	cout << objA.AtTime(timeBNum).position.y << endl;

	system("pause");
	return 0;
}