Given start point, angles in each rotational axis and a direction, calculate end point

Question

I have a start point in 3D coordinates, e.g. (0,0,0).

I have the direction I am pointing, represented by three angles - one for each angle of rotation (rotation in X, rotation in Y, rotation in Z) (for the sake of the example let's assume I'm one of those old logo turtles with a pen) and the distance I will travel in the direction I am pointing.

How would I go about calculating the end point coordinates?

I know for a 2D system it would be simple:

new_x = old_x + cos(angle) * distance
new_y = old_y + sin(angle) * distance

but I can't work out how to apply this to 3 dimensions

I suppose another way of thinking about this would be trying to find a point on the surface of a sphere, knowing the direction you're pointing and the sphere's radius.

Answer 1

First of all, for positioning a point in 3D you only need two angles (just like you only needed one in 2D)

Secondly, for various reasons (slow cos&sin, gimbal lock, ...) you might want to store the direction as a vector in the first place and avoid angles alltogether.

Anyway, Assuming direction is initially z aligned, then rotated around x axis followed by rotation around y axis.

x=x0 + distance * cos (angleZ) * sin (angleY)

Y=y0 + distance * sin (Anglez)

Z=z0 + distance * cos (angleZ) * cos (angleY)