The position of a point

Question:

Specify, design, and implement a class that can be used to keep track of the position of a point in three-dimensional space. For example, consider the point drawn at the picture below. The point shown there has three coordinates: x = 2.5, y = 0, and z = 2.0. Include member functions to set a point to a specified location, to shift a point a given amount along one of the axes, and to retrieve the coordinates of a point. Also provide member functions that will rotate the point by a specified angle around a specified axis.

To compute these rotations, you will need a bit of trigonometry. Suppose you have a point with coordinates x, y, and z. After rotating this point (counter-clockwise) by an angle $\theta$ , the point will have new coordinates, which we’ll call $x'$ , $y'$ , and $z'$ . The equations for the new coordinates use the cmath library functions sin and cos, as shown here:
After a $\theta$ rotation around the x-axis: $x' = x$ $y'=y\cos(\theta)-z\sin(\theta)$ $z'=y\sin(\theta)+z\cos(\theta)$
After a $\theta$ rotation around the y-axis: $x'=x\cos(\theta)+z\sin(\theta)$ $y'=y$ $z'=-x\sin(\theta)+z\cos(\theta)$
After a $\theta$ rotation around the z-axis: $x'=x\cos(\theta)-y\sin(\theta)$ $y'=x\sin(\theta)+y\cos(\theta)$ $z'=z$

My answer:

point.h

#pragma once
class point {
public:
	point() {
		x = y = z = 0;
	};
	point(double m, double n, double q) {
		set_position(m, n, q);
	};
	void set_position(double m, double n, double q);
	void move_x(double m);
	void move_y(double m);
	void move_z(double m);
	void rotate_x(double a);
	void rotate_y(double a);
	void rotate_z(double a);
	void print_point();
private:
	double x, y, z;
};

point.cpp

#include "pch.h"
#include "point.h"
#include <cmath>
#include <iostream>

void point::set_position(double m, double n, double q)
{
	x = m;
	y = n;
	z = q;
}

void point::move_x(double m)
{
	std::cout << "shift along x-axis by " << m << std::endl;
	x += m;
}

void point::move_y(double m)
{
	std::cout << "shift along y-axis by " << m << std::endl;
	y += m;
}

void point::move_z(double m)
{
	std::cout << "shift along z-axis by " << m << std::endl;
	z += m;
}

void point::rotate_x(double a)
{
	std::cout << "rotate around the x-axis by " << a << std::endl;
	double tmp_y;
	tmp_y = y * cos(a) - z * sin(a);
	z = y * sin(a) + z * cos(a);
	y = tmp_y;
}

void point::rotate_y(double a)
{
	std::cout << "rotate around the y-axis by " << a << std::endl;
	double tmp_x;
	tmp_x = x * cos(a) + z * sin(a);
	z = -x * sin(a) + z * cos(a);
	x = tmp_x;
}

void point::rotate_z(double a)
{
	std::cout << "rotate around the z-axis by " << a << std::endl;
	double tmp_x;
	tmp_x = x * cos(a) - y * sin(a);
	y = x * sin(a) + y * cos(a);
	x = tmp_x;
}

void point::print_point()
{
	std::cout << "(x, y, z) = (" << x << ", " << y << ", " << z << ")" << std::endl;
}

测试代码：

#include "point.h"
#include <iostream>

#define PI 3.14159265

int main()
{
	point a(2.5, 0, 2.0);
	a.move_x(1);
	a.move_y(1.5);
	a.move_z(-2.5);
	a.rotate_x(PI / 2);
	a.rotate_y(PI / 4);
	a.rotate_z(3 * PI / 4);
	a.print_point();
	a.set_position(5, 5, 5);
	a.print_point();
}

结果：

reference:

整理自《Data Structures and Other Objects Using C++ ( Fourth Edition )》Michael Main, Walter Savitch. p120