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 $\theta$θ, the point will have new coordinates, which we’ll call $x'$x′, $y'$y′, and $z'$z′. The equations for the new coordinates use the cmath library functions sin and cos, as shown here:
After a $\theta$θ rotation around the x-axis:$x' = x$x′=x$y'=y\cos(\theta)-z\sin(\theta)$y′=ycos(θ)−zsin(θ)$z'=y\sin(\theta)+z\cos(\theta)$z′=ysin(θ)+zcos(θ)
After a $\theta$θ rotation around the y-axis:$x'=x\cos(\theta)+z\sin(\theta)$x′=xcos(θ)+zsin(θ)$y'=y$y′=y$z'=-x\sin(\theta)+z\cos(\theta)$z′=−xsin(θ)+zcos(θ)
After a $\theta$θ rotation around the z-axis:$x'=x\cos(\theta)-y\sin(\theta)$x′=xcos(θ)−ysin(θ)$y'=x\sin(\theta)+y\cos(\theta)$y′=xsin(θ)+ycos(θ)$z'=z$z′=z

My answer:

to be continued…

reference:

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