I need to translate a point (P1) in 3D a certain amount, call it stepSize, along a vector described by a heading composed of three angles (basically pitch, roll and yaw).  I know that in homogeneous coordinates the following translation matrix would be used and I can multiply my existing point by Tv to get the new point.  However, I need something slightly different.  I have P1 and want the new point, P2 to be separated by stepSize so I need to recover Vx, Vy and Vz as given in the matrix above (from Wikipedia).  Any general suggestions about how to go about that?  I will do this in R once I know what to do.EDIT:  Here is some additional information.  I am trying to do 3D Turtle Graphics which are very much analogous to aircraft position and headings.  Specifically, I am writing code to implement the 3D L-systems described here.  This figure from the book gives the coordinate system used in that field (rather non-standard if you ask me).So I have my 'turtle' at the origin of this system, I have a given standard stepSize, and I have saved the most recent headings, which are the angles around each of the axes H, L and U.  I want to move the turtle forward by stepSize.  In the graphics system I am using, I have the current Cartesian coordinates of the turtle, and I need to compute the offset in the x, y and z directions to be added to the current position to get the new position (then repeat ...).  A small (?) complication is that the graphics drawing system I am using has the (+)ive x/L axis going to the right, not left as in the book figure.  H in the figure corresponds to the (+)-ive y-axis, and U to the (+)-ive z axis.  Ugh.
Translate a 3D point along a heading
linear algebra;matrices;computational geometry