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 top of the next column. 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 abit 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 c math library functions sin and cos, as shown here: After a a rotation around the x-axis: x’ = x y’ y cos(theta)-z sin(theta) z’ = y sin(theta) +z cos(theta)Show transcribed image text 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 top of the next column. 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 abit 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 c math library functions sin and cos, as shown here: After a a rotation around the x-axis: x’ = x y’ y cos(theta)-z sin(theta) z’ = y sin(theta) +z cos(theta)

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