getting the x,y, and z angle of two points?

Question

Alright, so I got two vectors that each contain a x y and z. We'll call them a and b.

atan2(double y, double x)
Converts rectangular coordinates (x, y) to polar (r, theta).

I create a new point in the middle of the two points.

Vector3 middle = new Vector3(//order x,y,z
        (max.getX() - min.getX())/2,
        (max.getY() - min.getY())/2,
        (max.getZ() - min.getZ())/2
        );

To get the y angle I use the formula Math.toDegrees(Math.atan2(middle.getX(), middle.getZ()))

Answer 1

if you have two points, we can state the following let $P_1(x_1,y_1,z_1)$ and $P_2(x_2,y_2,z_2)$ be your two points and $\alpha, \beta, \gamma$, the angles to the X,Y,Z axes respectively; if we want to find the direction (or the angles two the X,Y,Z axes) of the segment formed by the two points $\overline{P_1 P_2}$ these are obtained from these formulas: $$\cos{\alpha}=\frac{\Delta x}{d},\cos{\beta}=\frac{\Delta y}{d},\cos{\gamma}=\frac{\Delta z}{d}$$

where d is the distance between the two points which is given by the following formula: $$d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}$$

Once you've found the values of each cosine, you can use their inverse trigonometric function to find each angle, we would have this: $$\alpha = \arccos{\frac{\Delta x}{d}}, \beta = \arccos{\frac{\Delta y}{d}}, \gamma = \arccos{\frac{\Delta z}{d}}$$

Alternatively, if you are looking for th angles that each point forms with the three axes, let $O(0,0,0)$ be the origin and use it to find the direction of the two segments $\overline{O P_1}$ and $\overline{O P_2}$ as explained above.

I hope that this is what your looking for.

Regards Tristian.